Calculating temperature-dependent properties of Nd2Fe14B permanent magnets by atomistic spin model simulations

Authors: Qihua Gong, Min Yi, Richard F. L. Evans, Bai-Xiang Xu, and Oliver Gutfleisch

Temperature-dependent magnetic properties of Nd2Fe14B permanent magnets, i.e., saturation magnetization M_s(T), effective magnetic anisotropy constants K_eff_i(T) (i=1,2,3), domain-wall width δ_w (T), and exchange stiffness constant A_e(T), are calculated by using ab initio informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd2Fe14B by using the eisenberg exchange of Fe−Fe and Fe−Nd atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions, which is approximately expanded into an energy formula featured by second-, fourth-, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, M_s(T), δ_w(T), and K_eff_i(T), agree well with the experimental results. A_e(T) is estimated through a general continuum description of the domain-wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. A_e is found to ecrease more slowly than K_eff_1 with increasing temperature and approximately scale with normalized magnetization as A_e(T)∼m^1.2. Specifically, the possible domain-wall configurations at temperatures below the spin-reorientation temperature and the associated δ_w and A_e are identified. This work provokes a scale bridge between ab initio calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.

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