Atomistic theory of thermally activated magnetization processes in Nd₂Fe₁₄B permanent magnet

Abstract

For the practical use of magnets, particularly at high temperatures, the temperature dependence of magnetic properties is an important ingredient. To study the temperature dependence, methods of treating the thermal fluctuation causing the so-called activation phenomena must be established. To study finite-temperature properties quantitatively, we need atomistic energy information to calculate the canonical distribution. In the present review, we report our recent studies on the thermal properties of the Nd 2 Fe 14 B magnet and the methods of studying them. We first propose an atomistic Hamiltonian and show various thermodynamic properties, e.g., the temperature dependences of the magnetization showing a spin reorientation transition, the magnetic anisotropy energy, the domain wall profiles, the anisotropy of the exchange stiffness constant, and the spectrum of ferromagnetic resonance. The effects of the dipole-dipole interaction (DDI) in large grains are also presented. In addition to these equilibrium properties, we also study coercivity, which is the most important issue for magnets. The temperature dependence of the coercivity of a single grain was studied using the stochastic Landau-Lifshitz-Gilbert equation and also by the analysis of the free energy landscape, which was obtained by Monte Carlo simulation. It was found that the upper limit of coercivity at room temperature is about 3T, which is significantly lower than the so-called theoretical coercivity given by a simple coherent rotation model. The coercivity of a polycrystalline magnet, i.e., an ensemble of grains, is expected to be reduced further by the effects of the grain boundary phase, which is also studied. Surface nucleation is a key ingredient in the domain wall depinning process. Finally, we study the effect of DDI among grains and also discuss the distribution of properties of grains from the viewpoint of first order reversal curve.

Macroscopic phenomenon of exchange coupling and microscopic effect on magnetization reversal in sintered Nd–Fe–B magnets

“…The smaller value of the thermal fluctuation field H f in Nd 13.5 Fe 79.76 M 0.94 B 5.8 indicates that the activation volume is larger and the exchange coupling effect is stronger [33] because the exchange coupling effect can reduce the fluctuation field. It also implies that the magnetization reversal undergoes the nucleation of the reversed domain wall at the grain boundary [34] since the activation size is several nanometers and a little larger than the theoretical value of domain wall size according to the obtained value of fluctuation field H f . The intergranular exchange coupling would suppress the reversed domain nucleation in the neighboring grains [35].…”

Quantitative estimation of coercive field in a ferromagnetic grain using field sweep simulation

“…The details of the model are given in our previous papers [26][27][28]39], in which the magnetic interactions were mainly obtained from first-principles computation methods. We showed the spin-reorientation transition temperature, T r = 150 K, which is close to the experimentally estimated temperature [7][8][9]49], and the critical temperature, T c ∼ 870 K, which is a little overestimated from the experimental values T c ∼ 600 K [4,7], due to an overestimation of the exchange interactions.…”

“…At finite temperatures, the Stoner-Wohlfarth mechanism, i.e., coherent rotation, does not hold in the magnetization reversal process, but the nucleation process is important because it is the trigger of magnetization reversal [23][24][25]. Nucleation occurs in a small region, i.e., nm scale, and to understand the microscopic process of nucleation, recently developed atomistic models [19,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] are quite useful.…”

“…Using the atomistic models, finite-temperature properties of the Nd magnet have recently been investigated. Quantitative analyses on the temperature dependence of magnetization accompanying a spin-reorientation transition [26][27][28]36,39], domain wall profiles [27,30,37,38], surface effects to magnetization reversal [30,40], nucleation features [19,32,33], ferromagnetic resonance [31], dysprosium substitution effect [41], etc., have been intensively performed.…”

原子論的スピンモデルによる永久磁石の磁気特性の研究 ―熱揺らぎおよび温度効果の取り扱いと将来展望―

“…下の原子論的ハミルトニアンを採用する [13][14][15]24) ．この系は 3 (Monte Carlo) 法がしばしば用いられる．モンテカルロ法で ギーの場合と同様に 11,35) ．h eff i は次 のように修正される． 原子論的スピンモデルによる永久磁石の磁気特性の研究 -熱揺らぎおよび温度効果の取り扱いと将来展望-…”