Magnetic field threshold for nucleation and depinning of domain walls in the neodymium permanent magnet Nd2Fe14B

The Nd magnet ${\mathrm{Nd}}₂{\mathrm{Fe}}₁₄\mathrm{B}$ is an indispensable permanent magnet for high-technology commercial products. We study magnetization reversal in hard-soft-hard magnet systems of the atomistic model of the Nd magnet at zero and room temperatures. We present the nucleation and pinning fields as a function of the strength of the anisotropy energy of the soft magnet, estimated by using the stochastic Landau-Lifshitz-Gilbert equation. In the Nd magnet, reflecting the lattice structure, the properties of domain walls (DWs) depend on their moving directions. Bloch and N\'eel DWs move along the $a$ (or $b$) and $c$ axes, respectively. We investigate the difference in the nucleation and pinning fields between the Bloch and N\'eel DWs. We also analyze the dependence of the threshold fields on the thickness of the soft magnet. We find that the thermal fluctuation effect affects the threshold fields in the Nd magnet model more significantly than those in the simple anisotropic Heisenberg model [Mohakud et al., Phys. Rev. B 94, 054430 (2016)]. We also find that the strength of the anisotropy energies of the soft magnet phase is not so important for the pinning field, while it is essential for the nucleation field, etc. We discuss the detailed features of the dependencies and their microscopic mechanisms.