We examine the anisotropic properties of the exchange stiffness constant $\mathcal{A}$ for a rare-earth permanent magnet, ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$, by connecting analyses with two different scales of length, i.e., Monte Carlo (MC) method with an atomistic spin model and Landau-Lifshitz-Gilbert (LLG) equation with a continuous magnetic model. The atomistic MC simulations are performed on the spin model of ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ constructed from ab initio calculations, and the LLG micromagnetics simulations are performed with the parameters obtained by the MC simulations. We clarify that the amplitude and the thermal property of $\mathcal{A}$ depend on the orientation in the crystal, which are attributed to the layered structure of Nd atoms and weak exchange couplings between Nd and Fe atoms. We also confirm that the anisotropy of $\mathcal{A}$ significantly affects the threshold field for the magnetization reversal (coercivity) given by the depinning process.

• Received 16 April 2018
• Revised 24 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.054418

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

©2018 American Physical Society