General Formalism for Magnetic Anisotropy Constants

TL;DR

This paper derives finite-temperature expressions for magnetic anisotropy constants from a microscopic perspective, assuming a linear Hamiltonian in magnetization direction, and applies the method to Nd2Fe14B compounds to compute temperature-dependent anisotropy constants.

Contribution

It provides a new formalism for calculating magnetic anisotropy constants at finite temperature from microscopic models, including detailed analysis of the first-order constant and application to real materials.

Findings

Reproduces previous results for the first-order anisotropy constant K_1.

Successfully computes temperature dependencies of K_1, K_2, and K_3 for Nd2Fe14B.

Demonstrates the applicability of the formalism to real magnetic materials.

Abstract

Direct expressions for the magnetic anisotropy constants are given at a finite temperature from microscopic viewpoints. In the present derivation, it is assumed that the Hamiltonian is a linear function with respect to the magnetization direction. We discuss in detail the first-order constant $K_1$ and show that the results reproduce previous results. We also apply our method to Nd$_2$Fe$_{14}$B compounds and demonstrate that the temperature dependencies of the magnetocrystalline anisotropy constants $K_1$, $K_2$, and $K_3$ are successfully computed.