Monte Carlo analysis for finite temperature magnetism of Nd$_2$Fe$_{14}$B permanent magnet

TL;DR

This study uses Monte Carlo simulations to analyze how magnetic inhomogeneities and thermal effects influence the magnetic properties of Nd₂Fe₁₄B, revealing deviations from classical laws and insights into magnetization behavior at finite temperatures.

Contribution

It applies a constrained Monte Carlo method to model finite-temperature magnetic properties of Nd₂Fe₁₄B, capturing spin reorientation and anisotropy constants consistent with experiments, and explores deviations from theoretical laws.

Findings

Temperature dependence of anisotropy constants deviates from Callen--Callen law.

The exponent in magnetic field response approaches 2 above room temperature.

Magnetic anisotropy is mainly governed by the $K^{A}_1$ term above the Curie temperature.

Abstract

We investigate the effects of magnetic inhomogeneities and thermal fluctuations on the magnetic properties of a rare earth intermetallic compound, Nd$_2$Fe$_{14}$B. The constrained Monte Carlo method is applied to a Nd$_2$Fe$_{14}$B bulk system to realize the experimentally observed spin reorientation and magnetic anisotropy constants $K^{\rm A}_m (m=1, 2, 4)$ at finite temperatures. % Subsequently, it is found that the temperature dependence of $K^{\rm A}_1$ deviates from the Callen--Callen law, $K^{\rm A}_1(T) \propto M(T)^3$, even above room temperature, $T_{\rm R}\sim 300\rm\, K$, when the Fe (Nd) anisotropy terms are removed to leave only the Nd (Fe) anisotropy terms. This is because the exchange couplings between Nd moments and Fe spins are much smaller than those between Fe spins. % It is also found that the exponent $n$ in the external magnetic field $H_{\rm ext}$ response of barrier height $\mathcal{F}_{\rm B}=\mathcal{F}_{\rm B}^0(1-H_{\rm ext}/H_0)^n$ is less than $2$ in the low-temperature region below $T_{\rm R}$, whereas $n$ approaches $2$ when $T>T_{\rm R}$, indicating the presence of Stoner--Wohlfarth-type magnetization rotation. This reflects the fact that the magnetic anisotropy is mainly governed by the $K^{\rm A}_1$ term in the $T>T_{\rm R}$ region.