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 $\alpha$. 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 $\alpha$ 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 $\alpha$. By making use of this fact, we quantitatively estimate the coercive field at which the relaxation time is 1 s.

• Received 3 June 2020
• Accepted 17 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.020413

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