Dynamical aspects of magnetization reversal in the neodymium permanent magnet by a stochastic Landau-Lifshitz-Gilbert simulation at finite temperature: Real-time dynamics and quantitative estimation of coercive force

Abstract

The Nd magnet, ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$, is an important material because of its high coercivity applied in modern technologies. However, the microscopic mechanism of the coercivity has not been well understood. We study the magnetization reversal of a single grain of the magnet at a finite temperature by a real-time stochastic Landau-Lifshitz-Gilbert simulation of an atomistic model, which enables us to analyze dynamical properties reflecting the atomic-scale magnetic structure. There exist difficulties to estimate long relaxation times of the reversal quantitatively, i.e., the limitation of simulation time and also dependence on the damping factor $\ensuremath{\alpha}$. Here we develop a statistical method to estimate precisely long relaxation times in the stochastic region, by which one can identify an initial transient process and a long-time regular relaxation process. The relaxation time is found to largely depend on $\ensuremath{\alpha}$ especially in the stochastic region. However, it is found that a sharp increase of the relaxation time with lowering an external magnetic field causes a close location of the threshold fields for different values of $\ensuremath{\alpha}$. By making use of this fact, we quantitatively estimate the coercive field at which the relaxation time is 1 s.