diff --git "a/-9E1T4oBgHgl3EQfCwJj/content/tmp_files/load_file.txt" "b/-9E1T4oBgHgl3EQfCwJj/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/-9E1T4oBgHgl3EQfCwJj/content/tmp_files/load_file.txt" @@ -0,0 +1,616 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf,len=615 +page_content='Crucial role of Fe in determining the hard magnetic properties of Nd2Fe14B Juba Bouaziz∗ Department of Physics, University of Warwick, Coventry CV4 7AL, UK and Peter Gr¨unberg Institut and Institute for Advanced Simulation, Forschungszentrum J¨ulich & JARA, D-52425 J¨ulich, Germany Christopher E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Patrick Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK Julie B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Staunton† Department of Physics, University of Warwick, Coventry CV4 7AL, UK (Dated: January 10, 2023) Nd2Fe14B’s unsurpassed, hard magnetic properties for a wide range of temperatures result from a combination of a large volume magnetization from Fe and a strong single-ion anisotropy from Nd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Here, using finite temperature first-principles calculations, we focus on the other crucial roles played by the Fe atoms in maintaining the magnetic order on the Nd sublattices, and hence the large magnetic anisotropy, and directly generating significant uniaxial anisotropy at high temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We identify effective spins for atomistic modelling from the material’s interacting electrons and quantify pairwise and higher order, non-pairwise magnetic interactions among them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We find the Nd spins couple most strongly to spins on sites belonging to two specific Fe sublattices, 8j1, 8j2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Moreover the Fe 8j1 sublattice also provides the electronic origin of the unusual, nonmonotonic temperature dependence of the anisotropy of Y2Fe14B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Our work provides atomic-level resolution of the properties of this fascinating magnetic material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The elemental lanthanides show remarkable magnetic properties deriving from their partially-filled shells of atomic-like 4f electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' However, direct exploitation of these properties is hindered by low magnetic order- ing temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' No elemental lanthanide retains its magnetism at room temperature, with the highest Curie temperature Tc being 292 K for Gd [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Combining the lanthanides with other elements can strengthen the magnetic interactions and allow ordering to persist to higher temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The most successful example of this paradigm is the rare-earth/transition-metal (RE- TM) family of permanent magnets [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Specifically, Nd- Fe-B demonstrates exceptional magnetic strength over a wide range of temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Having revolutionized com- puter hard disk technology in the last century, Nd-Fe-B is again under intense investigation owing to its use in elec- tric vehicle motors and renewable energy turbines [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The RE-TM magnetic interactions are most simply de- scribed in terms of the exchange field Bexch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' In this picture, the TM-3d electrons produce an effective mag- netic field which couples to the spin magnetic moments of the RE ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' A minimal model to describe the RE ions and the high magnetic anisotropy they generate combines this exchange field with the interaction with an external field Bext and the crystal field ˆVCF, which describes the (predominantly) electrostatic interaction of the 4f charge cloud with its environment [4–7]: HRE = 2µB ˆS · Bexch + µB (ˆL + 2ˆS) · Bext + ˆVCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' (1) ˆS and ˆL are the total spin and orbital angular mo- mentum operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Values of the exchange field can be extracted by fitting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1 to experimental data ob- tained in inelastic neutron scattering (INS) or magneti- zation measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Experimental estimates of Bexch are far stronger than fields achievable in the laboratory (µBBexch/kB >∼ 300 K [8], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Bexch >∼ 450 T) as required to maintain magnetic order above room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Going beyond a phenomenological understanding of RE ordering requires an atomistic picture of the mag- netic interactions among effective spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Nd2Fe14B has a tetragonal crystal structure with 68 atoms per unit cell ([8] [9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The RE atoms occupy two crystallographically distinct sites (RE4f and RE4g), which (together with Fe4c and B4g atoms) form planes encapsulating the remain- ing 5 Fe sublattices (4e, 8j1, 8j2, 16k1, 16k2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' For the Nd sites the spins come from the localized f-electrons but for the TM sites the local effective spins, or local moments, emerge from the material’s itinerant electron fluid [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Spin-polarized regions at atomic sites form from co-operative behavior of the valence electrons and at finite temperatures their orientations fluctuate on rel- atively long time scales compared to the remaining elec- tronic degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' These local magnetic moments are the pertinent, effective spins for the TM aspect of the atomistic modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' A conceptually simple model assumes interactions only between pairs of spins (ij) according to the classical Heisenberg model, −Jij ˆSi · ˆ Sj where ˆSi represents an effective spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Previous works [12, 13] calculate such Jij parameters from first principles within density-functional theory (DFT) [12, 13], and use them directly in atomistic spin dynamics simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' With the TM magnetocrys- talline anisotropy (MCA) modelled as a sum of single arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='02868v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='mtrl-sci] 7 Jan 2023 2 c) (c) (b) Nd spin Nd+Fe spin Nd orb Fe orb Exp (a) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' (a) Nd2Fe14B’s magnetization versus (T/Tc) from DLM-DFT calculations compared to experiment [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' (b) Sub-lattice resolved magnetic order parameters and (c) Weiss fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The dots indicate the full DLM-DFT results, dashed lines from a pair-wise interaction model and continuous lines from a fit of the DLM-DFT results to the model discussed in the text Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' ion-like terms, assumed to be substantial, and RE crystal field coefficients taken from experiment, the simulations can reproduce the magnetization behavior of Nd2Fe14B, including the spin reorientation transition at low tem- perature, and represent the current state-of-the-art in modelling these magnets [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Although such a pair-wise Heisenberg model is computationally straightforward to implement, it is nonetheless a clear presumption for a magnetic metal like Nd-Fe-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Despite the huge technical importance of the material, the role of “beyond Heisen- berg” itinerant electron spin features has yet to be elu- cidated for Nd-Fe-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Moreover the MCA from the spin- orbit coupling of the itinerant d-electrons is also not guar- anteed to be single-ion like [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' In this letter we quantify the significance of both these aspects and propose ways to improve atomistic spin modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The disordered local moment (DLM) picture imple- mented within DFT provides an appropriate ab initio framework [10, 15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The approach combines statisti- cal mechanics of the effective spins (local moments, {ei}) and DFT, to describe the complementary evolution of electronic and magnetic structure as a material’s tem- perature is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Strongly correlated 4f-electron effects are treated with a parameter free, self interaction correc- tion (SIC) approach [17, 18] which incorporates Hund’s rules naturally [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' As such DLM-DFT can describe temperature-dependent magnetic properties of perma- nent magnets as shown recently for the RECo5 fam- ily [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The crucial RE contribution to the anisotropy is accounted by crystal field theory, calculating the CF coef- ficients within DFT using a robust numerical method [16] so that the modelling is independent of any prior fit of phenomenological parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Here we investigate the nature of magnetic order in Nd2Fe14B, sublattice-resolved, and describe the mag- netic interactions among the effective spins associated with both RE and TM sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We show that the interac- tions among the TM spins are influenced by the global magnetic order and its impact and link with the spin- polarised electrons of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' This is in essence a multi-spin coupling effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We find significant diversity in the behavior of the Fe local moments depending on their location in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' While most TM spins are ferromagnetically-coupled, some interact antiferromag- netically with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' This leads to some frustration and a peculiar strong suppression of magnetic order on the 8j1 sites which are located roughly midway between the Nd-containing layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We also find that the Nd spins couple most strongly to spins on sites belonging to this Fe sublattice along with those on another (8j2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Further- more we discover a link between this 8j1 sublattice and the unusual non-monotonic temperature dependence of the non-RE MCA of the isostructural material Y2Fe14B, resolving a longstanding a puzzle [11, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Finally our calculation of the anisotropy field of Nd2Fe14B across a range of temperatures agrees well with experiment and confirms the vital role played by the Fe spins for the functionality of this champion magnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Apart from the local moments themselves, the cen- tral quantities in DLM-DFT theory are Weiss fields {hi} which, analogously to the exchange field of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='1, drive the ordering of the local moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' However, unlike Bexch, the Weiss fields are not phenomenological, but instead are rigorously defined by thermal averages over the local moment orientational configurations {ei} of the magnetic energy Ω{ei} [10, 15], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' hi = � 3 4π ⟨Ω⟩ei;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='T dei .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' (2) where ⟨X⟩ei denotes the average of X with the restric- tion that the orientation of the moment on site i is fixed as ei and the order parameters of the local moments, {mi} are the averages {⟨ei⟩} [10, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' ⟨Ω⟩�ei;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='T is calcu- lated from DFT [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Crucially no prior prescription is assumed for the form of the magnetic interactions inher- ent in the first-principles Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' For a pairwise Heisenberg model, the magnetic energy Ω{ei} = −1/2 � ij Jijei · ej with Weiss fields linear in the {mi}, hi = � j Jijmj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3 16k1 16k2 8j1 8j2 f g 4e 4c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The relative strengths of interactions between sites in the unit cell (boron sites not included), Jij, (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3) highlight- ing the RE-TM ones (sites 48–51 and 52–55 correspond to 4f and 4g respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Numerical values in meV are given in [9] along with specific site coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Red/blue color indicates FM/AF interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Consequently beyond-pairwise terms are clearly identi- fied in DLM-DFT theory from the non-linear dependence of the Weiss fields on the {mi} [21–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The {mi} order parameters, describing an equilibrium state at a temper- ature T, are given by the self-consistent solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='2 and mi = (−1/βhi + coth βhi), the Langevin function, (β = 1/kBT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Figure 1(a) shows the magnetization as a function of T compared to experiment and resolved into the RE and TM spin and orbital components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The magnetization is directed along θ = 45◦ in the (xz)-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Full cal- culational details are given in the Supplemental Mate- rial [9] and references [16, 26–28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The contribution from a particular site i is found by multiplying its local mo- ment magnitude, µi, by the order parameter mi(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The Fe and Nd spin moments interact antiferromagnetically (AF) and order in an anti-parallel alignment in a fer- rimagnetic state, but the large orbital moment of Nd, pointing opposite to its spin, leads to overall ferromag- netic (FM) order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The Fe orbital moments are small (∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='05µB/atom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The calculated Tc is 1058 K, which, although an overestimate of 473 K in comparison to the experiment [11], is reasonable for a first-principles theory which uses a mean field approximation for the statistical mechanics of the effective spins [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' On each of the six Fe and two Nd sublattices ([8, 9] the magnetic order varies from complete, {mi = 1}, at T = 0K to zero above Tc, {mi = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Figure 1(b) shows how the temperature dependence of magnetic or- der varies across the sublattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The Nd sublattices dis- order more quickly than all the Fe sublattices except the 8j1 one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Complementary information in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1(c) shows that Weiss fields, {hi}, promote strong ordering when large and have considerable sublattice variation, notably the factor ∼4 difference between the 8j1 and 8j2 sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Analysis of {hi}, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='2, reveals the presence and importance of interactions that fall outside those of a Heisenberg-like model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' For such a pairwise model the Jij interactions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 2), directly obtained from the Weiss fields for small values of the {mi}, are used to construct the model’s Weiss fields and {mi} at all T (dashed lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' There are large discrepancies from the full ab initio DLM-DFT data away from Tc, leading us to propose a more realistic representation of the interac- tions which is straightforward to incorporate into atom- istic spin modelling of the magnet’s properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' It leads to a magnetic energy per unit cell ¯Ω = −1 2 � ij Jijmi · mj − 1 4 � i BI(mi · M)2, (3) where i, j run over the sites in the unit cell, I denotes one of the 8 sub-lattices to which the site i belongs and M is the total magnetization per unit cell, M = � i µimi where the order parameters on the RE sites are anti- parallel to the TM sites for the ferrimagnetic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The second, higher order term captures the effect of the over- all spin-polarization of the electronic structure on the effective interactions between the local moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Com- puting Weiss fields from this expression fits the DLM- DFT calculations very well as shown by the full curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1(c) and ¯Ω closely approximates ⟨Ω⟩T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Table I lists the BI parameters that measure the sublattice-dependent size of these higher order, multi-spin terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' System 4c 4e 8j1 8j2 16k1 16k2 Rf Rg Nd2Fe14B -15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='42 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='31 -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='06 -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='38 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='82 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='44 -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='53 -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='41 Y2Fe14B 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='68 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='91 -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='27 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='25 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Effective, multi-spin interaction constants (in µeV), BI, for Nd2Fe14B and Y2Fe14B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 2 shows the relative strengths of the Jij interac- tions between pairs of sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' They are represented on a 64 × 64 grid (56 Fe sites and 8 RE sites and arranged according to sublattice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Numerical values are given as Supplemental Material [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Assuming a range less than roughly 5˚A, they can be directly used in atomistic spin simulations together with the terms from Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The figure illustrates the vital importance on the RE mag- netic ordering of the hexagonal nets of Fe atoms [8, 9] from the k1, k2 and notably sites on the j1 and j2 sublat- tices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Indeed the largest contributions to the Weiss fields at the RE sites originate from the j1 and j2 sublattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The TM-TM interactions are particularly varied rang- ing from FM (red) for the majority to AF (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The j1 sites have AF interactions with e, c and RE sites and strong FM ones with j2 sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' This frustration drives this sublattice’s aversion to magnetic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The diver- sity of the interactions stems from the profound effect 60 40 30 40 20 Site 10 20 0 10 20 40 60 Site i4 that atom coordination and spacing of Fe atoms in a metallic material has on its magnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The archetype for this quintessentially itinerant electron effect is fcc Fe where squeezing the lattice turns ferromagnetic order anti-ferromagnetic and then destroys it [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The diverse nature of the magnetic order on the six Fe sub-lattices also has an impact on the intrinsic MCA generated by the system’s itinerant valence electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' As found for other TM metal magnets [15, 26], a simple fit in terms of a single ion model is unsatisfactory and, as found for other itinerant electron magnets, two-ion type terms should be included in the model [15, 31, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Further- more, on general grounds, modelling the MCA as a sum of single ion anisotropy terms must be done extremely carefully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The various Fe sites have different crystallo- graphic point symmetries, and their unique symmetry axes do not necessarily point along the c direction [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' There are important implications for atomistic spin dy- namics simulations [14, 31, 34] where it is not correct to assign a single ion anisotropy to each Fe atom with the same angular dependence and same symmetry axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Rather a simpler and more rigorous alternative would be to compute an anisotropy energy based on the vector sum of all moments in the same sublattice so that a single symmetry axis is recovered [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' While significantly smaller than from the f-electrons of the Nd atoms, the primarily TM component of the MCA grows in importance with rising T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' As the RE MCA drops swiftly along with the magnetic order [35, 36], the TM contribution can actually increase as shown ex- plicitly in measurements on Y2Fe14B [11, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Such non-monotonic temperature variation is puzzling, and has been attributed to a magnetostructural effect from an anisotropic expansion of the crystal lattice, compet- ing single-ion-like contributions [20] or competing single and two-ion MCA using atomistic spin dynamics simula- tions [31, 32] Since fully relativistic effects such as spin- orbit coupling are included in our DLM-DFT theory we investigate the MCA temperature dependence directly and show our results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3 for Y2Fe14B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Using the highly accurate, full potential (FP) KKR code [37, 38], we first calculate the MCA at T = 0K to be ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='9 meV/formula unit (FU) which agrees well with experimental values [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The same rapid loss of magnetic order with increasing temperature which we find for the Fe 8j1 sites in Nd2Fe14B (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1(b)) is also evident in Y2Fe14B [9] and this points to a significant role for this sublattice in the anomalous MCA T-dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We therefore carry out further FP MCA calculations where now the Fe 8j1 sites are constrained to be magnetically disordered (m8j1 = 0) via an equal weighting of local moments on each of these sites along the ±x and ±z directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The effect on the computed MCA is striking it increases greatly to ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='7 meV/FU - and we infer that the much faster decrease of 8j1 magnetic order with temperature relative to that on the other Fe sublattices is the key driver for the MCA T-dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' To test this proposition, we calibrate DLM-DFT MCA values against our T = 0K FP MCA calculations, given the current implementation with an atomic sphere ap- proximation (ASA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Although the ASA values are smaller than the FP ones, the same large increase of the value when the Fe 8j1 sites are magnetically disordered is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3 we show the DLM-DFT temperature de- pendent MCA both using the ASA (red curve) and also scaled by the ratio between the FP and our ASA T = 0K values (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The increase with temperature is evident, peaking at T/Tc = 50% in line with experiment [11] con- firming our proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Since the calculations are for a fixed lattice structure, we can exclude thermal expansion as a cause of the non-monotonic behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' We also show the effect on the MCA of forcing the Fe8j1 sublattice to remain magnetically disordered at all T, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' m8j1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The resulting unscaled MCA, shown in black in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3, is dramatically altered - the peak has gone and the MCA decays linearly with temperature and the T = 0K value is enhanced significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Clearly, establishment of mag- netic order on the Fe8j1 sublattice correlates with a sub- stantial drop in the (uniaxial) MCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 T/TC 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 K1 (meV/FU) Exp Th Th-8j1 Th-scl FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The T-dependence of the leading anisotropy constant, K1, of Y2Fe14B from DLM-DFT theory (red curve) and ex- periment (blue) [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The green curve shows the theory values, scaled to account for the difference between FP [37] and ASA ([9]) at T = 0K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The black curve shows K1 (unscaled) if the Fe 8j1 sublattice is constrained to be disordered magnetically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Our ultimate goal is to describe Nd2Fe14B’s large mag- netic anisotropy and its temperature variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' So to the TM MCA we add the dominant RE components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' These are calculated [6, 39] from the solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1 where the crystal field coefficients [9] are determined from first prin- ciples [16], and exchange field, Bexch provided directly by the DLM-DFT Weiss field for each Nd site (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1) di- vided by the computed Nd spin moment of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='66 µB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Our calculated exchange fields of 699 and 725 T for the RE f and g sites respectively are somewhat larger than those used in fits of experimental magnetization 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='0 T/Tc 0 5 10 µ0HA(T) Computed Computed-scl Exp (Hirosawa 1986) Exp (Grossinger 1986) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Evolution of the anisotropy field, HA, versus T/Tc from theory compared to experimental measurements (from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' [42], black curve, [11], blue curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The agreement is good above Tc/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The red and green curves use the non-RE MCA taken from the red and green curves of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' data (450–520 T [40]), but as pointed out in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' [8], the large number of parameters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 1 introduce sig- nificant uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' In principle, INS data would pro- vide a direct measure of the exchange fields but are not available for Nd-Fe-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Our proposed values are, however, supported by the good agreement between INS experi- ments [41] and our DLM-DFT calculations for the re- lated Gd2Fe14B magnet (324 T vs 307/319 T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The Gd exchange fields are substantially smaller than those cal- culated for Nd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The relative difference (∼2) mirrors that of the spin moments (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='46 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='66 µB) and reflects the similar Weiss fields we calculate for the two materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Using the method of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' [39] we calculate effective anisotropy constants K1(T), K2(T) and anisotropy field, µ0HA = 2K1/M ab initio which is shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The red/green curves show µ0HA which includes the non- RE contribution to the MCA of the red/green plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' 4 also shows the experimental measurements from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' [11, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Below T/Tc ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='5 there is some dis- crepancy between the two sets of experimental data, but above there is consistency between both the experiments and our calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The calculations show the clear importance of the Fe-dominated MCA to the anisotropy field at high temperatures - the red curve is over 1 T less than the green one over a range of temperatures despite the contributions from the non-RE MCAs differing by less than 30 µeV per Fe atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Nd2Fe14B’s spin reorientation transition (SRT) at 135K [8, 14, 43] is not described by our calculations owing to an underestimate of the high order crystal field coeffi- cients [14, 44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' This shortcoming exemplifies a more general challenge for theory modelling of low T strongly correlated f-electron effects to construct a robust way to significantly enhance the value of these coefficients [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Around room temperature and above, however, the ef- fects on the MCA from these high order terms are small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' This is also the temperature regime where the tenets of our DLM-DFT theory are valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Nd2Fe14B and the RE-TM permanent magnet family to which it belongs have a compelling set of attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Their technological value is enormous and growing and their magnetic properties, at a fundamental level, come from a rich and subtle combination of RE, localized, and TM, itinerant electron, effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' To enhance magnetic functionality and extract pointers for the development of even better materials, multiple interrelated aspects have to be accounted for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' Our ab initio DLM-DFT modelling has shown the importance of describing accurately the rich and complex itinerant electron magnetism associ- ated with the Fe sites and valence electrons generally for the production of the robust exchange field acting on the RE atoms, the higher order effective spin interactions and the nature of the non-f electron MCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The modifi- cations proposed here should be incorporated into future atomistic, effective spin and micromagnetic modelling to correctly describe these phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' The work was supported by EPSRC (UK) Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' EP/M028941/1 (J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=') and Royal Society Re- search Grant RGS\\R1\\201151 (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content=' ∗ j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='bouaziz@fz-juelich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='de † j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='staunton@warwick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQfCwJj/content/2301.02868v1.pdf'} +page_content='ac.' 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