The effect of the surface magnetic anisotropy of the neodymium atoms on the coercivity in the neodymium permanent magnet

TL;DR

This study investigates how the surface magnetic anisotropy of neodymium atoms influences the coercivity of Nd-Fe-B magnets, revealing that surface modifications affect coercivity significantly at finite temperatures, with implications for magnetic material design.

Contribution

The paper provides a detailed atomistic analysis of surface anisotropy effects on coercivity at finite temperatures, highlighting the importance of multiple surface layers rather than just the first layer.

Findings

Surface modification of only the first layer has little effect at finite temperatures.

Modifying multiple layers significantly impacts coercivity.

Thermal fluctuations diminish the influence of surface anisotropy changes.

Abstract

The Nd permanent magnet (Nd$_{2}$Fe$_{14}$B) is an indispensable material used in modern energy conversion devices. The realization of high coercivity at finite temperatures is a burning issue. One of the important ingredients for controlling the coercive force is the surface property of magnetic grains. It has been reported by first-principles studies that the Nd atoms in the first (001) surface layer facing the vacuum have in-plane anisotropy perpendicular to the $c$ axis, which may decrease the coercivity. Focusing on the surface anisotropy effect on the coercivity, we examine the coercivity at zero and finite temperatures by using an atomistic model reflecting the lattice structure of the Nd magnet with a stochastic Landau-Lifshitz-Gilbert equation method. We study general three cases, in which the Nd atoms in surface layers have (1) no anisotropy, (2) in-plane anisotropy, and (3) reinforced anisotropy for two types of surfaces, (001) and (100) surfaces. We find that in contrast to the zero-temperature case, due to the thermal fluctuation effect, the modification of only the first surface layer has little effect on the coercivity at finite temperatures. However, the modification of a few layers results in significant effects. We discuss the details of the dependence of the coercivity on temperature, type of surface, and modified layer depth, and also the features of domain growth in magnetization reversal.