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.