diff --git "a/EtE4T4oBgHgl3EQffQ30/content/tmp_files/load_file.txt" "b/EtE4T4oBgHgl3EQffQ30/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/EtE4T4oBgHgl3EQffQ30/content/tmp_files/load_file.txt" @@ -0,0 +1,1651 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf,len=1650 +page_content='Type II multiferroic order in two-dimensional transition metal halides from first principles spin-spiral calculations Joachim Sødequist and Thomas Olsen∗ Computational Atomic-Scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, 2800 Kgs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lyngby, Denmark (Dated: January 13, 2023) We present a computational search for spin spiral ground states in two-dimensional transition metal halides that are experimentally known as van der Waals bonded bulk materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Such spin spirals break the rotational symmetry of the lattice and lead to polar ground states where the axis of polarization is strongly coupled to the magnetic order (type II multiferroics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We apply the generalized Bloch theorem in conjunction with non- collinear density functional theory calculations to find the spiralling vector that minimizes the energy and then include spin-orbit coupling to calculate the preferred orientation of the spin plane with respect to the spiral vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find a wide variety of magnetic orders ranging from ferromagnetic, stripy anti-ferromagnetic, 120◦ non-collinear structures and incommensurate spin spirals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The latter two introduce polar axes and are found in the majority of materials considered here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spontaneous polarization is calculated for the incommensurate spin spirals by performing full supercell relaxation including spinorbit coupling and the induced polarization is shown to be strongly dependent on the orientation of the spiral planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also test the effect of Hubbard corrections on the results and find that for most materials LDA+U results agree qualitatively with LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' An exception is the Mn halides, which are found to exhibit incommensurate spin spiral ground states if Hubbard corrections are included whereas bare LDA yields a 120◦ non-collinear ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' INTRODUCTION The recent discovery of ferromagnetic order in two- dimensional (2D) CrI3 [1] has initiated a vast interest in 2D magnetism [2–4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Several other materials have subsequently been demonstrated to preserve magnetic order in the mono- layer limit when exfoliated from magnetic van der Waals bonded compounds and the family of 2D magnets is steadily growing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A crucial requirement for magnetic order to persist in the 2D limit is the presence of magnetic anisotropy that breaks the spin rotational symmetry that would otherwise ren- der magnetic order at finite temperatures impossible by the Mermin-Wagner theorem [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is exemplified by the cases of 2D CrBr3 [6, 7] and CrCl3 [8, 9], which are isostructural to CrI3 and while the former remains ferromagnetic in the atomic limit due to easy-axis anisotropy (like CrI3) the lat- ter has a weak easy plane that forbids proper long range or- der.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Other materials with persisting ferromagnetic order in the 2D limit include the metallic compounds Fe3/4/5GeTe2 [10–12] and the anisotropic insulator CrSBr [13], which has an easy-axis aligned with the atomic plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Finally, FePS3 [14] and MnPS3 [15] constitute examples of in-plane anti- ferromagnets that preserve magnetic order in the monolayer limit due to easy-axis anisotropy, whereas the magnetic order is lost in monolayers of the isostructural easy-plane compound NiPS3 [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The 2D materials mentioned above all consti- tute examples of rather simple collinear magnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' However, the ground state of three-dimensional magnetic materials of- ten exhibit complicated non-collinear order that gives rise to a range of interesting properties [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Such materials, are so far largely lacking from the field of 2D magnetism and the discov- ery of new non-collinear 2D magnets would greatly enhance ∗ tolsen@fysik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='dtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='dk the possibilities of constructing versatile magnetic materials using 2D magnets as building blocks [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The ground state of the classical isotropic Heisenberg model can be shown to be a planar spin spiral characterised by a propagation vector Q [19] and such spin configurations thus comprise a broad class of states that generalise the concept of ferromagnetism and anti-ferromagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In fact, spin spiral order is rather common in layered van der Waals bonded ma- terials [20] and it is thus natural to investigate the ground state order of the corresponding monolayers for spin spiral order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Moreover, for non-bipartite magnetic lattices the concept of anti-ferromagnetism is not unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is exemplified by the abundant example of the triangular lattice where one may con- sider the cases of anti-aligned ferromagnetic stripes or 120◦ non-collinear order, which can be represented as spin spirals of Q = (1/2,0) and Q = (1/3,1/3) respectively [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The concept of spin spirals thus constitute a general framework for specifying the magnetic order, which may or may not be com- mensurate with the crystal lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Finite spin spiral vectors typically break symmetries inher- ent to the crystal lattice and may thus induce physical prop- erties that are predicted to be absent if one only considers the crystal symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In particular, the spin spiral may yield a polar axis that lead to ferroelectric order [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Such materials are referred to as type II multiferroics and examples include MnWO4 [24], CoCr2O4 [25], LiCu2O2 [26] and LiCuVO4 [27] as well as the triangular magnets CuFeO2 [28], CuCrO2 [28], AgCrO2 [29] and MnI2 [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition to these ma- terials, 2D NiI2 has recently been shown to host a spin spiral ground state that induces a spontaneous polarization [31] and 2D NiI2 thus comprises the first example of a 2D type II mul- tiferroic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The prediction of new materials with certain desired prop- erties can be vastly accelerated by first principles simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In general, the search for materials with spin spiral ground states is complicated by the fact that the magnetic order re- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='05107v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='mtrl-sci] 12 Jan 2023 2 quires large super cells in the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' However, if one neglects spinorbit coupling, spin spirals of arbitrary wavevec- tors can be represented in the chemical unit cell by utilising the generalized Bloch theorem that encodes the spiral in the boundary conditions [32, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This method has been applied in conjunction with density functional theory (DFT) to a wide range of materials and typically produces results that are in good agreement with experiments [34–38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the present work we use DFT simulations in the frame- work of the generalized Bloch theorem to investigate the mag- netic ground state of monolayers derived from layered van der Waals magnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We then calculate the preferred orientation of the spiral plane by adding a single component of the spinorbit coupling in the normal direction of various trial spiral planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This yields a complete classification of the magnetic ground state for these materials under the assumption that higher or- der spin interactions can be neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' On the other hand, the effect of higher order spin interactions can be quantified by deviations between spin spiral energies in the primitive unit cell and a minimal super cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The results for all compounds are discussed and compared with existing knowledge from ex- periments on the parent bulk materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Finally, we analyse the spontaneous polarization in all cases where an incommensu- rate ordering vector is predicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' II we summarise the theory used to obtain spin spiral ground states based on the generalized Bloch theorem and briefly outline the implemen- tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' III we present the results and summarise the magnetic ground states of all the investigated materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' IV provides a conclusion and outlook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' THEORY A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Generalized Bloch’s Theorem The Heisenberg model plays a prominent role in the the- ory of magnetism and typically gives an accurate account of the fundamental magnetic excitations as well as the thermo- dynamic properties of a given material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the isotropic case it can be written as H = −1 2 ∑ i j Ji jSi ·Sj, (1) where Si is the spin operator for site i and Ji j is the exchange coupling between sites i and j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In a classical treatment, the spin operators are replaced by vectors of fixed magnitude and it can be shown that the classical energy is minimised by a planar spin spiral [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Such a spin configuration is charac- terised by a wave vector Q, which is determined by the set of exchange parameters Ji j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spin at site i is rotated by an an- gle Q · Ri with respect to the origin and the wave vector may or may not be commensurate with the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In a first principles framework it is thus natural to search for planar spin spiral ground states that give rise to periodically modulated magnetisation densities satisfying mq(r+Ri) = Uq,Rimq(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (2) Here Ri is a lattice vector (of the chemical unit cell) and Uq,Ri is a rotation matrix that rotates the magnetisation by an an- gle q · Ri around the normal of the spiral plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the ab- sence of spinorbit coupling we are free to perform a global rotation of the magnetisation density and we will fix the spi- ral plane to the xy-plane from hereon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the framework of DFT, the magnetisation density (2) gives rise to an exchange- correlation magnetic field satisfying the same symmetry un- der translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' If spinorbit coupling is neglected the Kohn- Sham Hamiltonian thus commutes with the combined action of translation (by a lattice vector) and a rotation of spinors by the angle q·Ri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This implies that the Kohn-Sham eigenstates can be written as ψq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k(r) = eik·rU† q(r) � u↑ q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k(r) u↓ q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k(r) � (3) where u↑ q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k(r) and u↓ q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k(r) are periodic in the chemical unit cell and the spin rotation matrix is given by Uq(r) = � eiq·r/2 0 0 e−iq·r/2 � (4) This is known as the generalized Bloch Theorem (GBT) and the Kohn-Sham equations can then be written as HKS q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='kuq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k = εq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='kuq,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k (5) where the generalized Bloch Hamiltonian: HKS q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='k = e−ik·rUq(r)HKSU† q(r)eik·r (6) is periodic in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Here k is the crystal momentum, q is the spiral wave vector and HKS is the Kohn-Sham Hamil- tonian, which couples to the spin degrees of freedom through the exchange-correlation magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the present work, we will not consider constraints be- sides the boundary conditions defined by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For a given q we can thus obtain a unique total energy Eq and the mag- netic ordering vector is determined as the point where Eq has a minimum (denoted by Q) when evaluated over the entire Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' However, if the chemical unit cell contains more than one magnetic atom there may be different local ex- trema corresponding to different intracell alignments of mag- netic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In order ensure that the correct ground state is obtained it is thus pertinent to perform a comparison be- tween calculations that are initialised with different relative magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' As a simple example of this, one may consider a honeycomb lattice of magnetic atoms where the ferromagnetic and anti-ferromagnetic configurations both cor- respond to q = 0, but are distinguished by different intracell orderings of the local magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We will discuss this in the context of CrI3 in section III C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also note that the true magnetic ground state is not nec- essarily representable by the ansatz (2) and one is therefore not guaranteed to find the ground state by searching for spin spirals based on the minimal unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In figure 1 we show four examples of possible magnetic ground states of the tri- angular lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Three of these correspond to spin spirals of 3 Q = (1/3, 1/3) Q = (1/2, 0) Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14) Q = (0, 1/2) (a) Γ M/S K X Y (b) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (a) Examples of magnetic structures in the triangular lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The Q = (1/3,1/3) (corresponding to the high symmetry point K) is the classical ground state in the isotropic Heisenberg model with nearest neighbour antiferromagnetic exchange and is degenerate with Q = (−1/3,−1/3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The stripy antiferromagnetic Q = (1/2,0) (corresponding to the high symmetry point M) is only found for CoI2 in the present study and is degenerate with Q = (0,1/2) and Q = (1/2,1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The incommensurate spiral with Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14) corresponds to the prediction of NiI2 in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The rectangular cell with Q = (0,1/2) is a bicollinear antiferromagnet that corresponds to superpositions of (0, ±1/4) states in the primitive cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (b) Brillouin zone of the hexagonal (blue) and rectangular (orange) unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The high symmetry band paths used to sample the spiral ordering vectors are shown in black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' the minimal unit cell while the fourth - a bicollinear antifer- romagnet - requires a larger unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The bicollinear state may arise as a consequence of higher order exchange interac- tions, which tend to stabilize linear combinations of degener- ate single-q states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spinorbit coupling In the presence of spinorbit coupling, the spin spiral plane will have a preferred orientation and the magnetic ground state is thus characterised by a normal vector ˆn0 of the spiral plane as well as the spiral vector Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spinorbit coupling is, however, incompatible with application of the GBT and has to be ap- proximated in a post processing step when working with the spin spiral representation in the chemical unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It can be shown that first order perturbation theory only involves contri- butions from the spinorbit components orthogonal to the plane [39] ⟨ψq,ˆn|L·S|ψq,ˆn⟩ = ⟨ψq,ˆn|(L· ˆn)(S· ˆn)|ψq,ˆn⟩, (7) and this term is thus expected to yield the most important con- tribution to the spinorbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Since (L · ˆn)(S · ˆn) com- mutes with a spin rotation around the axis ˆn, the spin spi- ral wavefunctions remain eigenstates when such a term is in- cluded in HKS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This approach was proposed by Sandratskii [40] and we will refer to it as the projected spinorbit coupling (PSO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For the spin spiral calculations in the present work we include spinorbit coupling non-selfconsistently by performing a full diagonalization of the HKS q,k including the PSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The mag- netic ground state is then found by evaluating the total energy at all normal vectors ˆn, which will yield ˆn0 as the normal vec- tor that minimizes the energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Computational Details The GBT has been implemented in the electronic structure software package GPAW [41], which is based on the projector augmented wave method (PAW) and plane waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The im- plementation uses a fully non-collinear treatment within the local spin density approximation where both the interstitial and atom-centered PAW regions are handled non-collinearly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spinorbit coupling is included non-selfconsistently [42] as de- scribed in Section II B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The implementation is described in de- tail in Appendix V A and benchmarked for fcc Fe in Appendix V B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find good agreement with previous results from the literature and we also assert that results from spin spiral cal- culations within the GBT agree exactly with supercell calcu- lations without spinorbit in the case of bilayer CoPt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Finally, we compare the results of the PSO approximations with full inclusion of spinorbit coupling for both supercells and GBT spin spirals of the CoPt bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find exact agreement be- tween the PSO in the supercell and GBT spin spiral and the approximation only deviates slightly compared to full spinor- bit coupling for the supercell calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' All calculations have been carried out with a plane wave cutoff of 800 eV, a k-point density of 14 ˚A and a Fermi smear- ing of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The structures and initial magnetic moments are taken from the Computational Materials Database (C2DB) [43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='In order to find the value of Q, which describes the ground state magnetic order, we calculate Eq along a represen- tative path connecting high symmetry points in the Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' While the true value of Q could be situated away from such high symmetry lines we deem this approach sufficient for the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' RESULTS A comprehensive review on the magnetic properties of lay- ered transition metal halides was provided in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Here we present spin spiral calculations and extract the magnetic properties of the corresponding monolayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition to the magnetic moments, the properties are mainly characterised by a spiral ordering vector Q and the normal vector to the spin spiral plane ˆn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The materials either have AB2 or AB3 stoi- chiometries and we will discuss these cases separately below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 4 Q Emin [meV] (θ,ϕ) Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' IP order BW [meV] PSO BW [meV] mΓ [µB] ∆εQ [eV] TiBr2 (1/3, 1/3) 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='12 (90,90) 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 TiI2 (1/3, 1/3) 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='33 (90,90) 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 NiCl2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06) -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='81 (90,31) FM ∥ 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='81 NiBr2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='11, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='11) -8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='62 (44,0) FM ∥, HM 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='62 NiI2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14) -28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='48 (64,0) HM 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='28 VCl2 (1/3, 1/3) 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='07 (90,0) 120◦ 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='96 VBr2 (1/3, 1/3) 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='21 (90,18) 120◦ 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 VI2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14) -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='43 (6,0) stripe 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='96 MnCl2 (1/3, 1/3) 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='48 (90,15) stripe or HM 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='92 MnBr2 (1/3, 1/3) 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='13 (90,15) stripe ∥ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='76 MnI2 (1/3, 1/3) 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='32 (0,0) HM 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='41 FeCl2 (0, 0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 (0, 0)∗ FM ⊥ 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5∗ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 FeBr2 (0, 0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 (0, 0)∗ FM ⊥ 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8∗ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 FeI2 (0, 0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 (0, 0)∗ stripe ⊥ 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9∗ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 CoCl2 (0, 0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 (90,90)∗ FM ∥ 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2∗ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 CoBr2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='03) -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='04 (0,0) FM ∥ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 CoI2 (1/2, 0) 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='95 (90,90) HM 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Summary of magnetic properties of the AB2 compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The ground state ordering vector is denoted by Q and Emin is the ground state energy relative to the ferromagnetic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The normal vector of the spiral plane is defined by the angles θ and ϕ (see text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also display the experimental in-plane order of the parent layered compound (Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' IP order).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition we state the spin spiral band width BW, the magnetic moment per unit cell in the ferromagnetic state mΓ and the band gap at the ordering vector ∆εQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For the case of NiI2, mΓ deviates from an integer value because the ferromagnetic state is metallic in LDA (whereas the spin spiral ground state has a gap).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The cases of FeX2, CoCl2 and CoBr2 are half metals, which enforces integer magnetic moment despite the metallic ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The asterisks indicate ferromagnets where full spinorbit coupling was included and the angles then refer to the direction of the spins rather that the spiral plane normal vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We have performed LDA and LDA+U calculations for all materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In most cases, the Hubbard corrections does not make any qualitative difference although the spiral ordering vector does change slightly and we will not discuss these cal- culations further here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The Mn halides comprise an exception to this where LDA+U calculations differ significantly from those of bare LDA and the LDA+U calculations will be dis- cussed separately for these materials below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For the AB2 materials, we find 12 that exhibit a spiral or- der that breaks the crystal symmetry and yields a ferroelec- tric ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For six of these compounds we have calcu- lated the spontaneous polarization by performing full relax- ation (including self-consistent spinorbit coupling) in super- cells hosting the spiral order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Magnetic ground state of AB2 materials The AB2 materials all have space group P¯3m1 correspond- ing to monolayers of the CdI2 (or CdCl2) prototype.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The mag- netic lattice is triangular and a few representative possibilities for the magnetic order is illustrated in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The magnetic properties of all the considered compounds are summarized in table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition to the ordering vector Q we provide the angles θ and φ, which are the polar and azimuthal an- gles of ˆn0 with respect to the out-of-plane direction and the ordering vector respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It will be convenient to consider three limiting cases of the orientation of spin spiral planes: the proper screw (θ = 90,ϕ = 0), the out-of-plane cycloid (θ = 90,ϕ = 90) and the in-plane cycloid (θ = 0,ϕ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also provide the ground state energy relative to the fer- romagnetic configuration (Q = (0,0)), the band gap, the spin spiral band width, which reflects the strength of the magnetic interactions and the PSO band width, which is the energy dif- ference between the easy and hard orientations of the spiral plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The magnetic moments are calculated as the total mo- ment in the unit cell using the ferromagnetic configurations without spinorbit interaction and thus yields an integer num- ber of Bohr magnetons for insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The magnitude of the local magnetic moments (obtained by integrating the magne- tization density over the PAW spheres) in the ground state are generally found to be very close to the moments in the ferro- magnetic configuration, unless explicitly mentioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spin spiral energy dispersions are provided for all AB2 materials in the supporting information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The different classes of materials are described in detail below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' NiX2 The nickel halides all have ground states with incommen- surate spiral vectors between Γ and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Experimentally, both NiI2 and NiBr2 in bulk form have been determined to have in- commensurate spiral vectors [45–47] in qualitative agreement with the LDA results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The case of NiCl2, however, have been found to have ferromagnetic intra-layer order whereas we find a rather small spiral vector of Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In bulk NiI2 the experimental ordering vector Qexp = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1384,0,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='457) has an in-plane component in the ΓM- direction with a magnitude of roughly 1/7 of a recipro- cal lattice vector, while for the monolayer we find Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14,0), which is in the ΓK-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Evaluating the spin spiral energy in the entire Brillouin zone, however, re- veals a nearly degenerate ring encircling the Γ-point with a 5 Γ M K Γ −20 0 20 40 E(q) [meV] (a) K G M 28 18 8 0 10 20 30 40 Energy [meV] (b) IP Screw OoP IP −44 −42 −40 Esoc(θ, ϕ) [meV] θ ϕ θ (c) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spin spiral energy of NiI2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Left: the spin spiral energy as a function of q without spinorbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Center: Spin spiral energy in evaluated in entire Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Right: spiral energy as a function of spiral plane orientation evaluated at the minimum Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spiral plane orientation is parameterized in terms of the polar angle θ and azimuthal angle ϕ (measured from Q) of the spiral plane normal vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' radius of roughly 1/5 of a reciprocal lattice vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The point qM = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='21,0) thus comprises a very shallow saddle point with an energy that exceeds the minimum by merely 2 meV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is illustrated in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also show a scan of the spin spiral energy (within the PSO approximation) as a func- tion of orientation of the spin spiral plane on a path that con- nects the limiting cases of in-plane cycloid, out-of-plane cy- cloid and proper screw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' An unconstrained spin spiral calcu- lation using the rectangular unit cell of figure 1 does not re- veal any new minima in the energy, which implies that the ground state is well represented by a single-q spiral and that higher order exchange interactions are neglectable in NiI2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The normal vector of the spiral makes an angle of 64◦ with the out-of-plane direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This orientation is in good agree- ment with the experimental assignment of a proper screw (along Qexp = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1384,0,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='457)), which corresponds to a tilt of 55◦±10◦ with respect to the c-axis [47], but disagrees with the model proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [31] where the spiral was found to be a proper screw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' At low temperatures NiBr2 has been reported to exhibit Qexp = (x,x,3/2) where x changes continuously from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='027 at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 K to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='09 at 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 K and then undergoes first order transi- tion at 24 K to intra-layer ferromagnetic order [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The struc- ture predicted here is close to the one observed in bulk at 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The discrepancy could be due to the magnetoelastic defor- mation [49] that has been associated with the modulation of the spiral vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This effect could in principle be captured by relaxing the structure in supercell calculations, but the small wavelength spirals require prohibitively large supercells and are not easily captured by first principles methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It is also highly likely that LDA is simply not accurate enough to de- scribe the intricate exchange interactions that define the true ground state in this material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bulk NiCl2 is known to be an inter-layer antiferromag- net with ferromagnetically ordered layers [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find the ground state to be a long wavelength incommensurate spin spiral with Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06), which is in rather close prox- imity to ferromagnetic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The ground state energy is less than 1 meV lower than the ferromagnetic state, but we cannot say at present whether this is due to inaccuracies of LDA or if the true ground state indeed exhibits spiral magnetic order in the monolayer limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' VX2 The three vanadium halides are insulators and whereas VCl2 and VBr2 are found to form Q = (1/3,1/3) spiral struc- tures, VI2 has an incommensurate ground state with Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The magnetic ground state of VCl2 and VBr2 is in good agreement with experiments on bulk materials where both have been found to exhibit out-of-plane 120◦ order [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This structure is expected to arise from strong nearest neigh- bour anti-ferromagnetic interactions between the V atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The case of VI2 has a significantly smaller spiral band width, signalling weaker exchange interactions compared to VCl2 and VBr2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A collinear energy mapping based on the Perdew- Burke-Ernzerhof (PBE) exchange-correlation functional [44] yields a weakly ferromagnetic nearest neighbour interaction for VI2 and strong anti-ferromagnetic interactions for VCl2 and VBr2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is in agreement with the present result, which indicate that the magnetic order of VI2 is not dominated by nearest neighbour interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Experimentally [52], the bulk VI2 magnetic order has been found to undergo a phase transition at 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 K from a 120◦ state to a bicollinear state with Q = (1/2,0), where the spins are perpendicular to Q and tilted by 29◦ from the z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Such a bicollinear state implies that the true ground state is a double- q state stabilized by higher order spin interactions and cannot be represented as a spin spiral in the primitive unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' To check whether LDA predicts the experimental ground state we have therefore performed spiral calculations in the rectangular cell shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The result is shown in figure 3 along with the spiral calculation in the primitive cell and we do not find any new minima in the super cell calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We have initalized angles in the super cell caluculation such that they corresponds to bicollinear order and the angles are observed to relax to the single-q spin spiral of the primitive cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It is likely that LDA is insufficient to capture the subtle higher order exchange interactions in this material, but it is possible that the monolayer simply has a magnetic order that differs 6 Γ K M Γ X S Y Γ S −4 −2 0 2 4 E(q) [meV/uc] FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spin spiral energies of VI2 obtained from the primitive cell (black) and the rectangular super cell (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The dashed lines repeat the primitive cell results on the corresponding super cell path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' from the individual layers in the bulk material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the PSO approximation we find that VCl2 and VBr2 pre- fer out-of-plane spiral planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The energy is rather insensitive to ϕ forming a nearly degenerate subspace of ground states with a slight preference of the proper screw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The ground state of VI2 is found to be close to the in-plane cycloid with a nor- mal vector to the spiral plane forming a 6◦ angle with Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spinorbit corrections in VI2 are also found to be the smallest compared to other iodine based transition metal halides stud- ied here and the ground state energy only deviates by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 meV per unit cell from the out-of-plane cycloid, which constitutes the orientation of the spin plane with highest energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' MnX2 The manganese halides are all found to form 120◦ ground states, which is in agreement with previous theoretical studies [53] using PBE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In contrast to the other insulators studied in the present work, however, we find that the results are qualita- tively sensitive to the inclusion of Hubbard corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This was also found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [54], where the sign of the nearest neighbour exchange coupling was shown to change sign when a Hubbard U parameter was included in the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' With U = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 eV we find that all three compounds has spiral ground states with incommensurate spiral vector Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='11,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='11,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Moreover, spin spiral band width in the LDA+U calculations decrease by more than an order of magnitude compared to the bare LDA calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The experimental magnetic structure of the manganese halides are rather complicated, exhibiting several magnetic phase transitions in a range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 K below the initial order- ing temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In particular MnI2 (MnBr2) has been found to have three (two) complex non-collinear phases [55], and MnCl2 has two complex phases that are possibly collinear [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The experimental ground state of bulk MnCl2 not unam- biguously known, but under the assumption of collinearity a possible ground state contains 15 Mn atoms in an extended stripy pattern [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Due to the weak and subtle nature of mag- netic interactions in the manganese compounds, however, it is not unlikely that the ground state in the monolayers can dif- fer from that of bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is corroborated by an experimental study of MnCl2 intercalated by graphite where a helimagnetic ground state with Qexp = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='153,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='153) was found [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is rather close to our predicted ordering vector obtained from LDA+U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Experimentally, bulk MnBr2 is found to exhibit a stripy bicollinear uudd order at low temperatures [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The order cannot be represented by a spiral in the minimal cell, but re- quires calculations in rectangular unit cells with spiral order Q = (0,1/2) similar to VI2 discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We have calcu- lated the high symmetry band path required to show this order and do not find any new minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It is likely that the situation resembles MnCl2 where a single-q spiral has been observed for decoupled monolayers in agreement with our calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' FeX2 We find all the iron halides to have ferromagnetic ground states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For FeCl2 and FeBr2 this is in agreement with the experimentally determined magnetic order for the bulk com- pounds [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In contrast, FeI2 has been reported to exhibit a bicollinear antiferromagnetic ground state [60] similar to the case of MnBr2 discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It is again possible that the ground state of the monolayer (calculated here) could differ from the magnetic ground state of the bulk compound as has been found for MnCl2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' LDA predict the three compounds to be half metals, mean- ing that the majority spin bands are fully occupied and only the minority bands have states at the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This en- forces an integer number of Bohr magnetons (four) per unit cell at any q-vector in the spin spiral calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Thus longi- tudinal fluctuations are expected to be strongly suppressed in iron halides and it is likely that these materials can be accu- rately modelled by Heisenberg Hamiltonians despite the itin- erant nature of the electronic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The projected spin orbit coupling is not applicable to collinear structures and we therefore include full spin orbit coupling, which is compatible with the Q = (0,0) ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find that all the iron compounds have an out-of- plane easy axis, which is in agreement with experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The bandwidth provided in table I then simply corresponds to the magnetic anisotropy energy which is smallest for FeCl2 and increases for the heavier Br and I compounds as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' CoX2 We predict CoCl2 to have an in-plane ferromagnetic ground state in agreement with the experimentally determined mag- netic order of the bulk compound [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' CoBr2 is found to have a long wavelength spin spiral with Q = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='03,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='03).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spi- ral energy in the vicinity of the Γ-point is, however, extremely flat with almost vanishing curvature and the ground state en- ergy is merely 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='04 meV lower than the ferromagnetic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We regard this as being in agreement with the experimental re- port of intra-layer ferromagnetic order in the bulk compound [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 7 The case of CoI2 deviates substantially from the other two halides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' CoCl2 and CoBr2 are half-metals with m = 3 µB per unit cell, whereas CoI2 is an ordinary metal with m ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 µB per unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find the magnetic ground state of CoI2 to be stripy anti-ferromagnetic with Q = (1/2,0), whereas ex- periments on the bulk compound have reported helimagnetic in-plane order with Qexp = (1/6,1/8,1/2) in the rectangular cell [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note, however, that the calculated local mag- netic moments vary strongly with q (up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 µB) in the spin spiral calculations, which signals strong longitudinal fluctu- ations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This could imply that the material comprises a rather challenging case for DFT and LDA may be insufficient to treat this material properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spontaneous polarization of AB2 materials The materials in table I that exhibit spin spiral ground states are expected to introduce a polar axis due to spinorbit cou- pling and thus allow for spontaneous electric polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The stripy antiferromagnet with Q = (1/2,0) preserves a site- centered inversion center and remains non-polar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition, the case of Q = (1/3,1/3) with in-plane orientation of the spi- ral plane breaks inversion symmetry, but retains the three-fold rotational symmetry (up to translation of a lattice vector) and therefore cannot acquire components of in-plane polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' To investigate the effect of symmetry breaking we have constructed 7×1 supercells of VI2 and the Ni halides and per- formed a full relaxation of the q = (1/7,0) spin spiral com- mensurate with the supercell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is not exactly the spin spi- rals found as the ground state from LDA, but we will use these to get a rough estimate of the spontaneous polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that this is very close to the in-plane component of Qexp for bulk NiI2, which is found to be nearly degenerate with the predicted ground state (see figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The other materi- als exhibit similar near-degeneracies, but the calculated polar- ization could be sensitive to which spiral ordering vector is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We have chosen to focus on the incommensurate spi- rals, but note that all the Q = (1/3,1/3) materials of table II are expected to introduce a spontaneous polarization as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Besides the incommensurate spirals we thus only include the cases of MnBr2 and MnI2 where the Q = (1/3,1/3) spirals may be represented in √ 3 × √ 3 supercells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The former case represents an example of a proper screw while the latter is an in-plane cycloid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The experimental order in the Mn halides materials is complicated, and our LDA+U calculations yield an ordering vector that differs from that of LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' However, here we mostly consider these examples for comparison and to check the symmetry constraints on the polarization in the Q = (1/3,1/3) spirals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In order to calculate the spontaneous polarization we relax the atomic positions in the super cells both with and without spinorbit coupling (included self-consistently) and calculate the 2D polarization from the Berry phase formula [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The results are summarized in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We can separate the effect of relaxation from the pure electronic contribution by calcu- lating the polarization (including spin-orbit) of the structures that were relaxed without spinorbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' These numbers are stated in brackets in table II as well as the total polarization (including relaxation) and the angles that define the orienta- tion of the spiral plane with respect to Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The self-consistent calculations yield the optimal orientations of the spiral planes without the PSO approximations and it is reassuring that the orientation roughly coincides with the results of the GBT and the PSO approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The magnitude of polarization largely scales with the atomic number of ligands (as expected from the strength of spinorbit coupling) and the iodide compounds thus produce the largest polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The in-plane cycloid in MnI2 only give rise to out-of-plane polarization as expected from sym- metry and the Q = (1/3,1/3) proper screw in MnBr2 has po- larization that is strictly aligned with Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The latter results is expected for any proper screw in the ΓK-direction because Q then coincides with a two-fold rotational axis and the ground state remains invariant under the combined action of this ro- tation and time-reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Since the polarization is not affected by time-reversal it must be aligned with the two- fold axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The polarization vectors of the remaining materials (except for NiCl2) are roughly aligned with the intersection between the spiral plane and the atomic plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It is interesting to note that the calculated magnitudes of to- tal polarization are 5-10 times larger than the prediction from the pure electronic contribution where the atoms were not re- laxed with spinorbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also tried to calculate the polarization by using the Born effective charge tensors (with- out spin-orbit) and the atomic deviations from the centrosym- metric positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' However, this approximation severely un- derestimates the polarization and even produces the wrong sign of the polarization in the case of NiBr2 and NiI2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' To obtain reliable values for the polarization it is thus crucial to include the relaxation effects and take the electronic contribu- tion properly into account (going beyond the Born effective charge approximation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [31] a value of 141 fC/m was predicted in 2D NiI2 from the gKNB model [62] and this is comparable to the values found in table II without relaxation effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' When relaxation is included we find a magnitude of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 pC/m for NiI2, which is an order of magnitude larger com- pared to the previous prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The results are, however, not directly comparable since Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [31] considered a spiral along the ΓK direction whereas the present result is for a spiral along ΓM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [31] finds the polarization to be aligned with Q in agreement with the symmetry considerations above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Finally, the values for the spontaneous polarization in table II may be compared with those of ordinary 2D ferroelectrics, which are typically on the order of a few hundred pC/m for in-plane ferroelectrics and a few pC/m for out-of-plane ferro- electrics [63] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In all of these type II multiferroics, the orientation of the induced polarization depends on the direction of the ordering vector, which may thus be switched by application of an ex- ternal electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We have checked explicitly that the sign of polarization is changed if we relax a right-handed instead of a left-handed spiral (corresponding to a reversed ordering vector).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The small values of spontaneous polarization in these materials implies that rather modest electric fields are required for switching the ordering vector and thus comprise an in- 8 (θ,ϕ) P∥ P⊥ Pz VI2 (11, 0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 (-31) 290 (96) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='05 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='11) NiCl2 (90, -30) -37 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4) 76 (15) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5(-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1) NiBr2 (69, -10) 12 (-6) 340 (32) 26 (37) NiI2 (70, 0) 8 (-48) 1890 (400) -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='18 (12) MnBr2 (90, 0) 430 (38) 0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='02) 0 (0) MnI2 (0, 0) 0 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 (-7) 260 (-105) TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Orientation of spin planes, and 2D polarization (in fC/m) of selected transition metal halides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' P∥ denotes the polarization along Q, while P⊥ denotes the polarization in the atomic plane orthogonal to Q and Pz is the polarization orthogonal to the atomic plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The numbers in brackets are the polarization values obtained prior to re- laxation of atomic positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We have used 7×1 supercells for the V and Ni halides and √ 3× √ 3 supercells for the Mn halides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' All calcu- lations are set up with left-handed spirals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The numbers in brackets state the spontaneous polarization without relaxation effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' teresting alternative to standard multiferroics such as BiFeO3 and YMnO3, where the coercive electric fields are orders of magnitude larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Magnetic ground state of AB3 materials The AB3 materials all have space group P¯3m1 correspond- ing to monolayers of the BI3 (or AlCl3) prototype.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The mag- netic lattice is the honeycomb motif, thus hosting two mag- netic ions in the primitive cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Several materials of this pro- totype have been characterized experimentally, but here we only present results for the Cr compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is due to the fact that experimental data of in-plane order is missing for all but CrX3, FeCl3 and RuCl3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Moreover, all magnetic com- pounds were found to have a simple ferromagnetic ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' RuCl3 is a well known insulator with stripy antiferro- magnetic in-plane order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' However, bare LDA finds a metallic state and both Hubbard corrections and self-consistent spinor- bit coupling are required to obtain the correct insulating state [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The latter is incompatible with the GBT approach and we have not pursued this further here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bulk FeCl3 is known to be an insulating helimagnet with Q = ( 4 15, 1 15, 3 2) [65], while we find the monolayer to be a metallic ferromagnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For CrI3 we compare the spin spiral dispersion to the spiral energy determined by a third nearest neighbour energy map- ping procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The prototype thus serves as a testing ground for applying unconstrained GBT to materials with multiple magnetic atoms in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We analyse the intracell an- gle between the Cr atoms of CrI3 and provide an expression for generating good initial magnetic moments for GBT calcu- lations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We finally discuss the observed deviations from the classical Heisenberg model and to what extend the flat spiral spectrum can be used to obtain the magnon excitation spec- trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' CrX3 The chromium trihalides are of considerable interest due to the versatile properties that arise across the three different halides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Monolayer CrI3 was the first 2D monolayer that were demonstrated to host ferromagnetic order below 45 K [1] and has spurred intensive scrutiny in the physics of 2D magnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The magnetic order is governed by strong magnetic easy-axis anisotropy, which is accurately reproduced by first principles simulations [66, 67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In contrast, monolayers of CrCl3 exhibit ferromagnetic interactions as well, but no proper long range order due easy-plane anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Instead, these monolayers exhibit Kosterlitz-Thouless physics, which give rise to quasi long range order below 13 K [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The GBT is not really necessary to find the ground state of the monolayer chromium halides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' They are all ferromagnetic and insulating and only involve short range exchange interac- tions that are readily obtained from collinear energy mapping methods [66–68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nevertheless, the gap between the acoustic and optical magnons in bulk CrI3 has been proposed to arise from either (second neighbor) Dzyalosinskii-Moriya interac- tions [69] or Kitaev interactions [70, 71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The former could in principle be extracted directly from planar spin-spiral calcu- lations [40], while the latter requires conical spin spirals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The origin of this gap is, however, still subject to debate [72] and here we will mainly focus on the magnetic interactions that do not rely on spinorbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the following we will focus on CrI3 as a representative member of the family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The honeycomb lattice contains two magnetic atoms per unit cell and the magnetic moments at the two sites will in general differ by an angle ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Since we do not impose any con- straints except for the boundary conditions specified by q, the angle will be relaxed to its optimal value when the Kohn-Sham equations are solved self-consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The convergence of ξ, may be a tedious process since the total energy has a rather weak dependence on ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For a given q the classical energy of the model (1) is minimized by the angle ξ 0 given by tanξ 0 = −ImJ12(q) ReJ12(q), (8) where J12(q) = ∑ i J12 0i e−iq·Ri (9) is the Fourier transform of the inter-sublattice exchange cou- pling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' If one assumes nearest neighbour interactions only, ξ 0 becomes independent of exchange parameters and the result- ing expression thus comprises a suitable initial guess for the inter-sublattice angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that the classical spiral en- ergy is independent of ξ (in the absence of spinorbit coupling) when J12(q) = 0 and the angle may be discontinuous at such q-points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This occurs for example in the magnetic honeycomb lattice at the K-point (q = (1/3,1/3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In general, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (8) has two solutions that differ by π and only one of these minimzes the energy while the other maximizes it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The maximum en- ergy constitutes an ”optical” spin spiral branch, which is if interest if one wishes to extract the exchange coupling con- stants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spiral energies of CrI3 (with optimized intracell angles) are shown in figure 4, where we show both the ferromagnetic (ξ = 0) and the antiferromagnetic (ξ = π) results on the ΓK 9 Γ M K Γ 0 10 20 30 E(q) [meV] Mapping FM AFM Γ M K Γ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='92 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='94 m [µB] Γ M K Γ 0 90 180 ξ [o] FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (Left: spin spiral energies of CrI3 compared to third nearest neighbour energy mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Right: angles beteen the two magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spin spirals are initialised with angles determined by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (8) which are shown in black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The moments are collinear on the ΓK path and so the AFM solution is also quasi-stable in DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Center: the magnitude of local magnetic moments along the spiral path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also show the spiral energy obtained from the model (1) with exchange parameters calculated from a collinear en- ergy mapping using four differnet spin configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We get J1 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='47 meV, J2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='682 meV and J3 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='247 meV for the first, second and nearest neighbour interactions respectively, which is in good agreement with previous LDA calculations [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The model spiral energy is seen to agree very well with that obtained from the GBT, which largely validates such a three-parameter model (when spinorbit is neglected).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We do, however, find a small deviation in the regions between high- symmetry points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This is likely due to higher order exchange interaction, which will deviate in the two approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For example, a biquadratic exchange term [38], will cancel out in any collinear mapping, but will influence the energies ob- tained from the GBT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Biquadratic exchange parameters could thus be extracted from the deviation between the two calcula- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In figure 4 we also show the calculated values of ξ and the magnitude of the local magnetic moment at the Cr sites along the path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The self-consistent intracell angles are found to match very well with the initial guess, except for a slight deviation on the Brillouin zone boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This corroborates the fact that exchange couplings beyond second neighbours are insignificant (the second nearest neighbor coupling is an intra-sublattice interaction and does not influence the angle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It is also rather instructive to analyze the variation in the magnitude of local magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In general, the map- ping of electronic structure problems to Heisenberg types of models like (1) rests on an adiabatic assumption where it is assumed that the magnitude of the moments are fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' How- ever, the present variation in the magnitude of moments does not imply a breakdown of the adiabatic assumption, but re- flects that DFT should be mapped to a quantum mechanical Heisenberg model rather than a classical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In particu- lar, the ratio of spin expectation values between the ferromag- netic ground state and the (anti-ferromagnetic) state of highest energy is approximately ⟨Si⟩AFM/⟨Si⟩FM = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='83 in the quan- tized model [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' While this ratio is somewhat smaller than the difference between ferromagnetic and anti-ferromagnetic moments found here, the result does imply that the magni- tude of moments should depend on q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' And the fact that the q = 0 anti-ferromagnetic moments are smaller than the ferro- magnetic ones in a self-consistent treatments reflects that DFT captures part of the quantum fluctuations inherent to the model (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that the spin spiral energy Eq calculated from the isotropic Heisenberg model using the optimal angle given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (8) is related to the dynamical excitations (magnon ener- gies) by ω± q = E± q /S and the spiral energies thus comprise a simple method to get the magnetic excitation spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' How- ever, even if a model like (1) fully describes a magnetic mate- rial (no anisotropy or higher order terms) there will be a sys- tematic error in the extracted exchange parameters (and re- sulting magnon spectrum) if the parameters are extracted by mapping to the classical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The reason is, that the clas- sical energies correspond to expectation values of spin con- figurations with fixed magnitude of the spin, which is not ac- commodated in a self-consistent approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This error is di- rectly reflected by the variation of the magnitude of moments in figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The true exchange parameters can only be ob- tained either by mapping to eigenstates of the model [74] or by considering infinitesimal rotations of the spin, which may be handled non-selfconsistently using the magnetic force the- orem [37, 75–78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nevertheless, the deviations between ex- change parameters obtained from classical and quantum me- chanical energy mapping typically deviates by less than 5 % [74] and for insulators it is a good approximation to extract the magnon energies from planar spiral calculations although the mapping is only strictly valid in the limit of small q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' CONCLUSION AND OUTLOOK In conclusion, we have demonstrated the abundance of spi- ral magnetic order in 2D transition metal dichalcogenides from first principles calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The calculations imply that type II multiferroic order is rather common in these materials and we have calculated the spontaneous polarization in a se- lected subset of these using fully relaxed structures in super cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' While the super cell calculations does not correspond to the exact spirals found from the GBT, the calculations show that relaxation effects plays a crucial role for the induced po- larization and should be taken into account in any quantitative analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The spontaneous polarization in type II multifer- roics is in general rather small compared to what is found in ordinary 2D ferroelectrics and could imply that the chirality 10 of spirals are switchable by small electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' It would be highly interesting to calculate the coercive field for switch- ing in these materials, but due to the importance of relaxation effects and spin-orbit coupling this is a non-trivial computa- tion that cannot simply be obtained from the Born effective charges and force constant matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The GBT comprises a powerful framework for extract- ing the magnetic properties of materials from first princi- ples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition to the single-q states considered here, one may use super cells to extract the importance of higher order exchange interactions and unravel the possibility of having multi-q ground states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In addition, for non-centrosymmetric materials, the PSO approach may be readily applied to ob- tain the Dzyaloshinskii-Moriya interactions, which may lead to Skyrmion lattice ground states or stabilize other multi-q states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Implementation In the PAW formalism we expand the spiral spinors using the standard PAW transformation [79] ψq,k(r) = ˆ T ˜ψq,k(r) = ˜ψq,k(r)+∑ a ∑ i (φ a i (r)− ˜φ a i (r)) � dr[ ˜pa i (r)]∗ ˜ψq,k(r), (10) where ˜ψq,k(r) is a smooth (spinor) pseudo-wavefunction that coincides with ψq,k(r) outside the augmentation spheres and devi- ates from ψq,k(r) by the second term inside the augmentation spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The all-electron wavefunction ψq,k(r) is thus expanded in terms of (spinor) atomic orbitals φ a i inside the PAW spheres and the expansion coefficients are given by the overlap between the pseudowavefunction and atom-centered spinor projector functions ˜pa i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (3) we may write this as ψq,k(r) = eik·rU† q(r) ˜uq,k(r)+∑ a ∑ i (φ a i (r)− ˜φ a i (r)) � dr[ ˜pa i (r)]∗eik·rU† q(r) ˜uq,k(r) = eik·rU† q(r) ˜uq,k(r)+∑ a ∑ i (φ a i (r)− ˜φ a i (r)) � dr[e−ik·rUq(r) ˜pa i (r)]∗ ˜uq,k(r) = eik·rU† q(r) ˜uq,k(r)+∑ a ∑ i (φ a i (r)− ˜φ a i (r)) � dr[ ˜pa i,q,k(r)]∗ ˜uq,k(r) ≡ Tq,k ˜uq,k(r), (11) where Uq(r) was given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (4) and we defined ˜pa i,q,k(r) = e−ik·rUq(r) ˜pa i (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (12) The PAW transformed Kohn-Sham equations then read ˜Hq,k ˜uq,k(r) = εq,kSq,k ˜uq,k(r), (13) with ˜Hq,k = T † q,kHTq,k, Sq,k = T † q,kTq,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (14) Calculations in the framework of the GBT thus requires two modifications compared to the approach for solving the ordinary Kohn-Sham equations in the PAW formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 1) The k-dependence of the standard Bloch Hamiltonian is replaced by k → k ∓ q/2 for spin-up and spin down components respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 2) Different spin dependent projector functions has to be applied when calculating the projector overlaps with the spin-up and spin-down components of the psudowavefunctions (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (12)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Benchmark The LDA implementation of the GBT have been tested by checking that our results agree with similar calculations from the literature and by verifying internal consistency by compar- ing with super cell calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The case of fcc Fe has been found to have a spin spiral ground state [81] and the calcu- lation of the ordering vector Q has been become a standard benchmark for spin spiral implementations [82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In previous simulations the ordering vector was found to be rather sensi- tive to the lattice constant and in figure 6 we show the spin spi- ral energies along the ΓXW path using the experimental lattice constant as well as the lattice constant which has been found to reproduce the experimental ordering vector [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The cal- culated value of Q is in good agreement with previous reports in both cases [83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also confirm a similar low energy bar- 11 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 qx 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 E − E0 [eV] Spiral Supercell FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Comparison between GBT spin spiral calculations and su- percell calculations without spinorbit coupling in monolayer CoPt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 100 120 140 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='58 ˚A (exp) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='50 ˚A Γ X W −20 −10 0 E(q) [meV] FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spin spiral energies of fcc Fe for the experimental lattice constant (red) and a strained latice constant, which is known to re- produce the experimental spin spiral order in (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The dashed vertical lines indicate the minima found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' rier between the two local minima, as is expected from LDA [84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In order to check internal consistency we have investigated the case of monolayer CoPt [40] where we compare spin spi- ral energies calculated using the GBT with energies calculated from super cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We thus construct a 16x1 super cell of the CoPt monolayer and consider spirals with qc = ( n 16) in units of reciprocal lattice vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' This allows us to extract 16 different spiral energies in the supercell using standard non-collinear DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In order to compare the two methods we have used a k-point grid of 16×16×1 for the GBT and 1×16×1 for the supercell and a plane wave cutoff of 700 eV for both calcu- lations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 5 we compare the results without spinorbit coupling and find excellent agreement between supercell and GBT calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that when spinorbit coupling is neglected one has Eq = E−q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Since spinorbit coupling is incompatible with the GBT one has to resort to approximate schemes to include it in the cal- culations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In the present work we have used the PSO method proposed by Sandratskii [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 7 we compare spin spi- ral calculations with supercell calculations where the spinorbit coupling has been included either fully or by the PSO method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The PSO method is fully compatible with the GBT and we −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='25 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 qx 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='20 E − E0 [eV] Spiral Proj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' SOC Spiral Full SOC SC Full SOC SC Projected SOC FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Comparison between GBT spin spiral calculations and super- cell calculations with projected and full spinorbit coupling in mono- layer CoPt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' find excellent agreement between the spin spiral energies cal- culated with the GBT and with supercells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The PSO approach is, however an approximation and the correct result can only be obtained from the supercell using the full spinorbit cou- pling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We see that the PSO calculations are in good agreement with those obtained from full spinorbit coupling but overesti- mates the energies at the Brillouin zone boundary by a few percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' In contrast, if one tries to include the full spinor- bit operator in the GBT calculations (by diagonalizing HKS including spinorbit coupling on a basis of GBT eigenstates without spinorbit coupling) the energies are severely under- estimated with respect to the exact result (from the supercell calculation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that the spiral energies including spinor- bit coupling shows a slight asymmetry between points at q and −q, which can be related to the Dzyaloshinskii-Moriya inter- actions in the system [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 12 [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Huang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Clark, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Navarro-Moratalla, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Klein, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cheng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Seyler, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhong, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Schmidgall, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' McGuire, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cobden, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xiao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jarillo-Herrero, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xu, Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature 546, 270 (2017), arXiv:1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='05892.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gibertini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Koperski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Morpurgo, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Novoselov, Magnetic 2D materials and heterostructures, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nanotechnol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 14, 408 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gong and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, Two-dimensional magnetic crystals and emergent heterostructure devices, Science (80-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 363, eaav4450 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [4] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jiang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xing, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Guo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Liu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhao, Recent progress on 2D magnets: Fundamental mechanism, structural design and modification, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 8, 031305 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [5] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mermin and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wagner, Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 17, 1133 (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [6] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Shang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jiang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rasmita, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gao, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yu, Direct Photoluminescence Probing of Ferromagnetism in Monolayer Two-Dimensional CrBr 3, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 19, 3138 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [7] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sun, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Song, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Anderson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Brunner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F¨orster, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Shalomayeva, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taniguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Watanabe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gr¨afe, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' St¨ohr, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wrachtrup, Magnetic domains and domain wall pinning in atomically thin CrBr3 revealed by nanoscale imag- ing, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 12, 1989 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [8] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Song, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wilson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Clark, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taniguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Watanabe, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xiao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' McGuire, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cobden, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xu, Atomically Thin CrCl 3 : An In-Plane Layered Antiferromagnetic Insulator, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 19, 3993 (2019), arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='00261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bedoya-Pinto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Pandeya, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gargiani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Valvi- dares, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sessi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taylor, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Radu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Parkin, Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer, Science (80-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 374, 616 (2021), arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='07605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [10] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Fei, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Huang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Malinowski, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Song, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sanchez, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xiao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' May, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cob- den, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xu, Two-dimensional itinerant ferro- magnetism in atomically thin Fe3GeTe2, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 17, 778 (2018), arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='02559.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Seo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' An, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hwang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Eom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Seo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sta- nia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Muntwiler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taniguchi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Min, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yeom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Choi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Shim, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, Nearly room temperature ferromagnetism in a magnetic metal-rich van der Waals metal, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 6, eaay8912 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [12] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Su, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Fu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zou, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Guo, Magnetic critical behavior of the van der Waals Fe5GeTe2 crystal with near room temperature ferromag- netism, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 10, 15345 (2020), arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='06825.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Dismukes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Telford, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wiscons, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nuckolls, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Dean, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Roy, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhu, Magnetic Order and Symmetry in the 2D Semiconductor CrSBr, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 21, 3511 (2021), arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='10715.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ryoo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Park, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cheong, Ising-Type Magnetic Order- ing in Atomically Thin FePS 3, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 16, 7433 (2016), arXiv:1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='04169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Long, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Henck, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gibertini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Dumcenco, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taniguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Watanabe, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Giannini, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Morpurgo, Persistence of Magnetism in Atomically Thin MnPS 3 Crystals, Nano Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 20, 2452 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [16] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Park, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jeon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Park, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cheong, Suppression of magnetic ordering in XXZ-type antiferromagnetic monolayer NiPS3, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 10, 345 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [17] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Qin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Feng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='- R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Leng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chen, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Liu, Noncollinear spintronics and electric-field control: a review, Rare Met.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 39, 95 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sierra, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Fabian, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kawakami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Roche, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Valenzuela, Van der Waals heterostructures for spintronics and opto-spintronics, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nanotechnol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 16, 856 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [19] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kaplan, Classical Spin-Configuration Stability in the Pres- ence of Competing Exchange Forces, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 116, 888 (1959).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' McGuire, Crystal and magnetic structures in layered, transition metal dihalides and trihalides, Crystals 7, 121 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chernyshev and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhitomirsky, Spin waves in a tri- angular lattice antiferromagnet: Decays, spectrum renormal- ization, and singularities, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B 79, 144416 (2009), arXiv:0901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [22] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Maksimov, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' White, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chernyshev, Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' X 9, 021017 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [23] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kimura, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Goto, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Shintani, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ishizaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Arima, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokura, Magnetic control of ferroelectric polarization, Na- ture 426, 55 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [24] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taniguchi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Abe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Takenobu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Iwasa, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Arima, Ferroelectric polarization flop in a frustrated magnet mnwo4 in- duced by a magnetic field, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 97, 097203 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yamasaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Miyasaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kaneko, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' He, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Arima, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokura, Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 96, 207204 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [26] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Park, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Choi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cheong, Ferroelec- tricity in an s = 1/2 chain cuprate, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 98, 057601 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [27] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Naito, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sato, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yasui, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kobayashi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kobayashi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sato, Ferroelectric transition induced by the incommensu- rate magnetic ordering in licuvo4, Journal of the Physical Soci- ety of Japan 76, 023708 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [28] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kimura, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lashley, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ramirez, Inversion- symmetry breaking in the noncollinear magnetic phase of the triangular-lattice antiferromagnet CuFeo2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B 73, 220401 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Seki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Onose, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokura, Spin-driven ferroelectricity in triangular lattice antiferromagnets acro2 (a = Cu, ag, li, or na), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 101, 067204 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [30] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kurumaji, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Seki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ishiwata, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Murakawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokunaga, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kaneko, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokura, Magnetic-field induced competi- tion of two multiferroic orders in a triangular-lattice helimagnet mni2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 106, 167206 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [31] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Song, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Occhialini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ergec¸en, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ilyas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Amoroso, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Barone, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kapeghian, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taniguchi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Botana, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Picozzi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gedik, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Comin, Evidence for a single-layer van der Waals multiferroic, Nature 602, 601 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [32] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sandratskii and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Guletskii, Symmetrised method for 13 the calculation of the band structure of noncollinear magnets, Journal of Physics F: Metal Physics 16, L43 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [33] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sandratskii, Symmetry analysis of electronic states for crystals with spiral magnetic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' General properties, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Matter 3, 8565 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [34] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bylander and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kleinman, Full potential ab initio calcu- lations of spiral spin density waves in fcc Fe, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B 58, 9207 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [35] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kurz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bihlmayer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hirai, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Blugel, Three- dimensional spin structure on a two-dimensional lattice: Mn/Cu(111), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 86, 1106 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [36] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sandratskii, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Singer, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S¸as¸ioˇglu, Heisen- berg Hamiltonian description of multiple-sublattice itinerant- electron systems: General considerations and applications to NiMnSb and MnAs, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B - Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Matter Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 76, 1 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [37] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zimmermann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bihlmayer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B¨ottcher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bouhassoune, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lounis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sinova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Heinze, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bl¨ugel, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Dup´e, Com- parison of first-principles methods to extract magnetic param- eters in ultrathin films: Co/Pt(111), Physical Review B 99, 214426 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gutzeit, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kubetzka, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Haldar, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Pralow, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Goerzen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wiesendanger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Heinze, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' von Bergmann, Nano-scale collinear multi-Q states driven by higher-order interactions, Na- ture Communications 13, 5764 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Heide, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bihlmayer, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bl¨ugel, Describing Dzyaloshin- skii–Moriya spirals from first principles, Physica B: Condensed Matter 404, 2678 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [40] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sandratskii, Insight into the dzyaloshinskii-moriya interac- tion through first-principles study of chiral magnetic structures, Physical Review B 96, 024450 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [41] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Enkovaara, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rostgaard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mortensen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Dułak, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ferrighi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gavnholt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Glinsvad, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Haikola, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hansen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kristoffersen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kuisma, a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Larsen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lehtovaara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ljungberg, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lopez-Acevedo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Moses, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ojanen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Petzold, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Romero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Stausholm-Møller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Strange, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tritsaris, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Vanin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Walter, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ham- mer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H¨akkinen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Madsen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nieminen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nørskov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Puska, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rantala, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Schiøtz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Thyge- sen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jacobsen, and Others, Electronic structure calcula- tions with GPAW: a real-space implementation of the projector augmented-wave method, Journal of Physics: Condensed Mat- ter 22, 253202 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [42] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, Designing in-plane heterostructures of quantum spin Hall insulators from first principles: 1T’-MoS2 with adsor- bates, Physical Review B 94, 235106 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [43] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Haastrup, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Strange, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Pandey, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Deilmann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Schmidt, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hinsche, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gjerding, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Torelli, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Larsen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Riis-Jensen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gath, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jacobsen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mortensen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Thygesen, The Computational 2D Materials Database: High-throughput modeling and discov- ery of atomically thin crystals, 2D Materials 5, 042002 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gjerding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taghizadeh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rasmussen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ali, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bertoldo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Deilmann, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Knøsgaard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kruse, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Larsen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Manti, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Pedersen, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Petralanda, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Skovhus, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Svendsen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mortensen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Thygesen, Recent progress of the computational 2D materials database (C2DB), 2D Materials 8, 044002 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Adam, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Billerey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Terrier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mainard, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Regnault, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rossat-Mignod, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M´eriel, Neutron diffraction study of the commensurate and incommensurate magnetic structures of nibr2, Solid State Communications 35, 1 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [46] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Day and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ziebeck, Incommensurate spin structure in the low-temperature magnetic phase of nibr2, Journal of Physics C: Solid State Physics 13, L523 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kuindersma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sanchez, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Haas, Magnetic and struc- tural investigations on nii2 and coi2, Physica B+C 111, 231 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [48] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Adam, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Billerey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Terrier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mainard, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Regnault, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rossat-Mignod, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Meriel, Neutron diffraction study of the commensurate and incommensurate magnetic structures of nibr2, Solid State Communications 35, 1 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [49] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokunaga, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Okuyama, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kurumaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Arima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nakao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Murakami, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Taguchi, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tokura, Multiferroicity in nibr 2 with long-wavelength cycloidal spin structure on a triangular lattice, Physical Review B 84, 060406 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [50] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Pollard, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' McCann, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ward, Electronic and magnetic properties of 57fe in nicl2, nibr2, nii2 and coi2 from moss- bauer spectroscopy, Journal of Physics C: Solid State Physics 15, 6807 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [51] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kadowaki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ubukoshi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hirakawa, Neutron scatter- ing study of the triangular-lattice antiferromagnet vbr2, Journal of the Physical Society of Japan 54, 363 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [52] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kuindersma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Haas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sanchez, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Al, Magnetic struc- tures and properties of vi2, Solid State Communications 30, 403 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [53] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, High throughput study on mag- netic ground states with hubbard u corrections in transition metal dihalide monolayers, Nanoscale Advances 2, 495 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [54] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Torelli, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Thygesen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, High throughput com- putational screening for 2d ferromagnetic materials: the criti- cal role of anisotropy and local correlations, 2D Materials 6, 045018 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [55] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sato, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kadowaki, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Iio, Successive phase transitions in the hexagonal-layered heisenberg antiferromagnets mnx2 (x = br, i), Physica B: Condensed Matter 213-214, 224 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [56] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' MK Wilkinson, JW Cable and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Koehler, Neutron diffraction investigations of the two antiferromagnetic struc- tures of mncl2, Oak Ridge National Laboratory Report ORNL- 2430, 65 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [57] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wiesler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Suzuki, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Suzuki, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rosov, Determi- nation of anomalous superexchange in mnc l 2 and its graphite intercalation compound, Physical review letters 75, 942 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [58] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wollan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Koehler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wilkinson, Neutron diffraction study of the magnetic properties of mn br 2, Physical Review 110, 638 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wilkinson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cable, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wollan, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Koehler, Neutron diffraction investigations of the magnetic ordering in fe br 2, co br 2, fe cl 2, and co cl 2, Physical Review 113, 497 (1959).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [60] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gelard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Fert, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Meriel, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Allain, Magnetic structure of fei2 by neutron diffraction experiments, Solid State Commu- nications 14, 187 (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [61] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mekata, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kuriyama, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ajiro, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mitsuda, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yoshizawa, First-order magnetic transition in coi2, Journal of Magnetism and Magnetic Materials 104-107, 859 (1992), proceedings of the International Conference on Magnetism, Part II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [62] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xiang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Whangbo, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gong, General Theory for the Ferroelectric Polarization In- duced by Spin-Spiral Order, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 107, 157202 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [63] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kruse, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Petralanda, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gjerding, M, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Jacobsen, K, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Thygesen, K, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, Two-dimensional fer- roelectrics from high throughput computational screening, arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='13911 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [64] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Catuneanu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kee, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=', Kitaev magnetism in honeycomb rucl 3 with intermediate spin-orbit coupling, Physical Review B 91, 241110 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 14 [65] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Cable, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wilkinson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Wollan, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Koehler, Neutron- diffraction study of antiferromagnetic fe cl 3, Physical Review 127, 714 (1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [66] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lado and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Fern´andez-Rossier, On the origin of mag- netic anisotropy in two dimensional CrI 3, 2D Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 4, 035002 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [67] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Torelli and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, Calculating critical temperatures for ferromagnetic order in two-dimensional materials, 2D Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 6, 015028 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [68] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, Theory and simulations of critical temperatures in CrI 3 and other 2D materials: easy-axis magnetic order and easy- plane Kosterlitz–Thouless transitions, MRS Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 9, 1142 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [69] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chung, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Stone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kolesnikov, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Huang, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Dai, Topological Spin Excita- tions in Honeycomb Ferromagnet CrI3, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' X 8, 041028 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [70] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Feng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Xiang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bellaiche, Interplay be- tween Kitaev interaction and single ion anisotropy in ferromag- netic CrI3 and CrGeTe3 monolayers, npj Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 4, 57 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [71] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lee, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Utermohlen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Weber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hwang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' van Tol, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Goldberger, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Trivedi, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hammel, Fundamen- tal Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI3, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 124, 017201 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [72] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Do, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Paddison, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sala, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Williams, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kaneko, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kuwahara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' May, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Yan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' McGuire, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Stone, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lumsden, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Christianson, Gaps in topological magnon spectra: Intrinsic versus extrinsic effects, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B 106, L060408 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [73] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, Unified Treatment of Magnons and Excitons in Mono- layer CrI3 from Many-Body Perturbation Theory, Physical Re- view Letters 127, 166402 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [74] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Torelli and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, First principles Heisenberg models of 2D magnetic materials: the importance of quantum corrections to the exchange coupling, Journal of Physics: Condensed Mat- ter 32, 335802 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [75] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Liechtenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Katsnelson, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Antropov, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Gubanov, Local spin density functional approach to the theory of ex- change interactions in ferromagnetic metals and alloys, Journal of Magnetism and Magnetic Materials 67, 65 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [76] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bruno, Exchange Interaction Parameters and Adiabatic Spin- Wave Spectra of Ferromagnets: A “ Renormalized Magnetic Force Theorem”, Physical Review Letters 90, 087205 (2003), 0407739.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [77] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Halilov, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Eschrig, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Perlov, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Oppeneer, Adi- abatic spin dynamics from spin-density-functional theory: Ap- plication to Fe, Co, and Ni, Physical Review B 58, 293 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [78] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Durhuus, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Skovhus, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Olsen, Plane wave imple- mentation of the magnetic force theorem for magnetic exchange constants: Application to bulk fe, co and ni, Journal of Physics: Condensed Matter (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [79] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bl¨ochl, Projector augmented-wave method, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' B 50, 17953 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [80] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Marsman and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Hafner, Broken symmetries in the crys- talline and magnetic structures of γ-iron, Physical Review B 66, 224409 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [81] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Tsunoda, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kunitomi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nicklow, Magnetic struc- ture of γ-fe precipitates in a cu matrix, Journal of Physics F: Metal Physics 17, 2447 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [82] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kurz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' F¨orster, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Nordstr¨om, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bihlmayer, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Bl¨ugel, Ab initio treatment of noncollinear magnets with the full- potential linearized augmented plane wave method, Physical Review B 69, 024415 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [83] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Garc´ıa-Su´arez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Newman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lambert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Pruneda, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Ferrer, First principles simulations of the magnetic and struc- tural properties of iron, The European Physical Journal B- Condensed Matter and Complex Systems 40, 371 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' [84] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Kn¨opfle, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Sandratskii, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' K¨ubler, Spin spiral ground state of γ-iron, Physical Review B 62, 5564 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 15 SUPPLEMENTARY INFORMATION - TYPE II MULTIFERROIC ORDER IN TWO-DIMENSIONAL TRANSITION METAL HALIDES FROM FIRST PRINCIPLES SPIN-SPIRAL CALCULATIONS Joachim Sødequist1 and Thomas Olsen1,∗ 1CAMD, Department of Physics, Technical University of Denmark, 2820 Kgs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Lyngby Denmark I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' SPIN SPIRAL DISPERSIONS The entire spin spiral dispersion carry more information than just the energy minima was reported we reported in the main text, these are shown here for in figures 2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' One can find not only the stability with respect to the ferromagnetic configuration, but also compare to any other configuration in the energy landscape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Additionally, we can observe whether the remain magnetic moments are unchanged during self-consistent field cycle, and we find this is generally true except for CoI2 and perhaps the titanium compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We note that the local magnetic moments found here are the integrated inside the PAW spheres of the respective atoms, thus these local moments does not integrate to the total moments reported in the main text since interstitial magnetization density is neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We also provide the projected spin orbit energies in figure 3 for the lowest energy state, naturally the shape will depend very much on the specific spiral, in some cases such as the q = K we find quite similar energies in the out-of-plane orientations, whereas incommensurate spirals tend to have more well defined minima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The in-plane orientations reported here are related by a 90◦ phase shift, but the dashed line highlight that they are indeed degenerate as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' SPIN SPIRAL CONVERGENCE An example of convergence of a intracell angle in a rectangular supercell of the hexagonal VI2 system is represented in 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We find that for all calculations which reach the convergence criteria on particularly the density, all converge the angle within some narrow region of the true angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' We observe that the number of iterations required increase dramatically, when the initial guess is further away from the true angle, hence highlighting the importance of choosing initial conditions according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' (8) in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Convergence of the intracell angle ξ in spin spiral ground state calculation of VI2 at the spiral vector q = (1/4,0,0) at varying different initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The calculations shown in red, did not reach the convergence criteria on the density within the time-wall of the calculation, while the blue were considered converged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' The black horizontal line is the expected angle for a smooth spin spiral as it if it was an equivalent spin spiral in the primitive unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Vl2convergence,g=(1/4,0,0),rect 175 150 125 5-angle 100 75 50 25 0 0 200 400 600 800 1000 SCF-count16 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spin spiral energies for AB2 magnets and the local magnetic moments of the magnetic atoms and ligands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' For ferromagnetic refer to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' TiBr2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 inf 0 [] Energy 10 Ti magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 [meV] I norm magnetic moment 20 Br magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Spin spiral energy [ 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 60 S 70 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 ocal 80 Lo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]Til2 Wave length ^ [A] inf 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 inf 0 n magnetic moment [lμsl] Energy 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 Ti magmom M 10 [me] I magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 Spin spiral energy 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 30 ocal norm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 Lo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]VCI2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 inf 0 一 门 Energy 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 10 V magmom [meV] moment Cl magmom 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 20 Spin spiral energy 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 5 30 40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]VBr2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 inf 0 门 : moment [lμl] Energy 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 V magmom [meV] Br magmom 10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Spin spiral energy 15 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 25 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]V12 Wave length 入 [A] inf 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 inf ６ Energy 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 V magmom [meV] 4 I magmom 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 I energy 2 Local norm magnetic 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 Spin spiral 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]MnCI2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 inf 0 Energy Mn magmom Local norm magnetic moment [ Spin spiral energy [meV] Cl magmom 10 2 15 20 K M q vector [A-1]MnBr2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 inf 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 [|μB|] Energy 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 Mn magmom [meV] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Br magmom 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 I energy Spin spiral 2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0 K M q vector [A-1]Mn12 Wave length ^ [A] inf 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 inf 0 Energy Mn magmom Spin spiral energy [meV] I magmom 10 15 20 K M q vector [A-1]CoBr2 Wave length 入 [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 inf Energy Co magmom [meV] 20 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Br magmom Spin spiral energy 15 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 Local norm magnetic i 10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0 K M q vector [A-1]Col2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 inf Energy 20 Co magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 Spin spiral energy [meV] I magmom 10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]NiCI2 Wave length 入 [A] inf 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 inf 50 Energy 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 Ni magmom Spin spiral energy [meV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 40 Cl magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 Local norm magnetic 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]NiBr2 Wave length 入 [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 inf 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 Energy n magnetic moment [lμbl 40 Ni magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 [meV] Br magmom 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 30 Spin spiral energy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 Local norm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]Nil2 Wave length ^ [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 inf 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 40 Energy magnetic moment [lμ] Ni magmom [meV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 30 I magmom 20 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 T energy 10 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 Spin spiral 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 norm 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 20 ocal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 30 - K M q vector [A-1]17 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Projected spin orbit energies of the ground state found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 2 TiBr2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 - [meV] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 E 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 - IP Screw OoP IP theta, phiTil2 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 [meV] 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 IP Screw OoP IP theta, phiVCI2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='69 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='70 [meV] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='71 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='72 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='73 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='74 IP Screw OoP IP theta, phiVBr2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='28 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='29 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='30 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='31 [meV] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='32 Jos: 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='33 E 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='34 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='35 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='36 IP Screw OoP IP theta, phiVI2 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 E 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='7 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='9 IP Screw OoP IP theta, phiMnCI2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='780 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='785 [meV] 790 Jos: E 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='795 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='800 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='805 IP Screw OoP IP theta, phiMnBr2 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='17 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='18 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='19 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='20 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='21 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='22 IP Screw OoP IP theta, phiMn12 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 [meV] 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 IP Screw OoP IP theta, phiCoBr2 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='38 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='40 [meV] 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='42 soc E 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='44 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='46 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='48 IP Screw OoP IP theta, phiCol2 40 41 [meV] 42 soc E 43 44 - 45 - IP Screw OoP IP theta, phiNiCI2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='050 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='055 [meV] 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='060 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='065 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='070 IP Screw OoP IP theta, phiNiBr2 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='65 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='70 [meV] 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='75 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='80 E 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='85 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='90 IP Screw OoP IP theta, phiNil2 40 41 - [meV] 42 43 44 : IP Screw OoP IP theta, phi18 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content=' Spin spiral energies for ferromagnetic AB2 magnets and the local magnetic moments on the atoms FeCI2 Wave length 入 [A] inf 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 inf 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 Energy : moment [lμb] 120 Fe magmom [meV] 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Cl magmom 100 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 Spin spiral energy 80 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Local norm magnetic 60 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0 M K q vector [A-1]FeBr2 Wave length 入 [A] inf 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='4 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 inf 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 Energy moment [lμBl] 80 Fe magmom 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Spin spiral energy [meV] Br magmom 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 60 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Local norm magnetic 40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0> 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 M K q vector [A-1]Fe12 Wave length 入 [A] inf 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='8 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 inf 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 40 Energy [8l] 35 Fe magmom 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 Spin spiral energy [meV] Local norm magnetic moment [ I magmom 30 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 15 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 0 M K q vector [A-1]CoCI2 Wave length 入 [A] inf 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='1 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='3 inf 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 50 Energy Local norm magnetic moment [lμbl Co magmom Spin spiral energy [meV] Cl magmom 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 30 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='5 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'} +page_content='0 K M q vector [A-1]' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EtE4T4oBgHgl3EQffQ30/content/2301.05107v1.pdf'}