# Fileset [Supplemental_Material_Nishino.pdf](https://mdr.nims.go.jp/filesets/64b07e89-fa35-4def-a29f-9a7a36f8e9da/download) ## Creator [Masamichi Nishino](https://orcid.org/0000-0002-2060-2303), [Rachida Lamouri](https://orcid.org/0000-0003-1820-5277), Hisazumi Akai ## Rights [In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Atomistic model analysis of the spin reorientation transition in ( Nd 1 − x Dy x ) 2 Fe 14 B systems](https://mdr.nims.go.jp/datasets/6c5773ff-b6c7-4ff2-8ad5-1073ab4e63c2) ## Fulltext Supplemental Material for “Atomistic model analysis of the spin reorientationtransition in (Nd1−xDyx)2Fe14B systems”Masamichi Nishino1,∗, Rachida Lamouri1, and Hisazumi Akai21Research Center for Materials Nanoarchitectonics, National Institute for Materials Sci-ence, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan2Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan1 Magnetic parameters of the atomistic model1.1 Magnetic moments in Nd2Fe14B and Dy2Fe14BFigure S1 depicts the magnitudes of the magnetic moments s = |s| of the constituentatoms in Nd2Fe14B and Dy2Fe14B, estimated by first-principles calculations using AkaiKKR(MACHIKANEYAMA code) [1]. We find that the differences in magnetic moments be-tween the corresponding atomic species in Nd2Fe14B and Dy2Fe14B are minimal. It shouldbe noted that for Fe and B atoms, Si = si, while for Nd and Dy atoms, Si = si +J i, asexplained in the main text.mFigure 1: Magnetic moments of the constituent atoms in Nd2Fe14B and Dy2Fe14B. Rdenotes Nd and Dy in Nd2Fe14B and Dy2Fe14B, respectively.1.2 Exchange interactions in Nd2Fe14B and Dy2Fe14BFigures S2(a) and S2(b) show the distribution of the exchange interactions (2Jijsisj) asa function of the interatomic distance (R), estimated using AkaiKKR for Nd2Fe14B andDy2Fe14B, respectively. We observe that both systems exhibit similar distributions ofexchange interactions, and the values are nearly identical. The exchange interactionsbetween Nd atoms (Nd–Nd), between Dy atoms (Dy–Dy), and between B and Fe atoms(B–Fe) contribute only marginally.*Corresponding author: nishino.masamichi@nims.go.jp1Figure S3 presents a comparison of the distributions of the exchange interactions(2Jijsisj) as a function of the interatomic distance (R) for Fe–Fe and R–Fe bonds inNd2Fe14B and Dy2Fe14B.(a) (b)R (Å) R (Å)2J ijs is j (K)2J ijs is j (K)Figure 2: Distribution of the exchange interactions (2Jijsisj) as a function of the inter-atomic distance (R) for (a) Nd2Fe14B and (b) Dy2Fe14B.2J ijs is j (K)R (Å)Figure 3: Comparison of the distributions of the exchange interactions (2Jijsisj) as afunction of the interatomic distance (R) for Fe–Fe and R–Fe bonds in Nd2Fe14B andDy2Fe14B.21.3 Parameters of the crystal electric field energies for Nd andDy atomsThe values of Amn for Nd atoms in Nd2Fe14B and for Dy atoms in Dy2Fe14B are listed inTable 1 and the corresponding values of ⟨rn⟩ are shown in Table 2.Table 1: Amn in units of Ka−n0 [2].A02 A04 A06Nd 295 −12.3 −1.84Dy 302 −12.7 −0.973Table 2: Values of ⟨r2⟩, ⟨r4⟩, and ⟨r6⟩ in units of an0 , where a0 is the Bohr radius [3].⟨r2⟩ ⟨r4⟩ ⟨r6⟩Nd 1.001 2.401 12.396Dy 0.726 1.322 5.1021.4 Anisotropy energies of Fe atomsThe anisotropy energies Ds2 of Fe atoms in R2Fe14B, along with their site occupancies,are presented in Table 3.Table 3: Anisotropy energies Ds2 (K) of Fe atoms [4].Fe(c) Fe(e) Fe(j1) Fe(j2) Fe(k1) Fe(k2)D(s)2 (K) −24.8 −0.348 12.4 6.73 6.38 4.41Site occupancies 4 4 8 8 16 163References[1] http://kkr.issp.u-tokyo.ac.jp/jp/[2] M. Yamada, H. Kato, H. Yamamoto, and Y. Nakagawa, Phys. Rev. B 38, 620 (1988).[3] A. J. Freeman and R. E. Watson, Phys. Rev. 127, 2058 (1962).[4] Y. Miura, H. Tsuchiura, and T. Yoshioka, J. Appl. Phys. 115, 17A765 (2014).4