Atomistic theory of thermally activated magnetization processes in Nd₂Fe₁₄B permanent magnet

To study the temperature dependence of magnetic properties of permanent magnets, methods of treating the thermal fluctuation causing the thermal 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 Nd₂Fe₁₄B magnet and the methods of studying them. We first propose an atomistic Hamiltonian and show various thermodynamic properties, for example, 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, 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. The upper limit of coercivity at room temperature was found to be about 3 T at room temperature. The coercivity of a polycrystalline magnet, that is, an ensemble of interactinve 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.为研究永磁体磁性能的温度依赖性，必须建立处理引发热激活现象的热涨落的方法。若要定量研究有限温度下的物性，我们需要获取原子级能量信息以计算正则系综分布。在本篇综述中，我们汇报了近期针对Nd₂Fe₁₄B磁体热物性及其研究方法的相关工作。我们首先提出了原子级哈密顿量，并展示了多种热力学性质，例如展现出自旋重取向转变的磁化强度温度依赖性、磁各向异性能、畴壁轮廓、交换刚度常数各向异性以及铁磁共振谱。此外，还介绍了大晶粒中的偶极-偶极相互作用（DDI）效应。除上述平衡态性质外，我们还借助随机朗道-栗弗席兹-吉尔伯特方程，以及通过蒙特卡洛模拟得到的自由能景观分析，研究了单晶粒矫顽力的温度依赖性。研究发现，室温下矫顽力的上限约为3 T。多晶磁体（即相互作用晶粒的集合体）的矫顽力预计会因晶界相的影响进一步降低，这一问题也得到了我们的研究。表面成核是畴壁脱钉过程中的关键因素。最后，我们研究了晶粒间的偶极-偶极相互作用效应，并从一阶反转曲线的视角讨论了晶粒的物性分布。