An ab-initio theory for the temperature dependence of magnetic anisotropy

TL;DR

This paper develops a first-principles relativistic theory to describe how magnetic anisotropy in metallic ferromagnets varies with temperature, matching experimental trends and providing insights beyond single ion models.

Contribution

It introduces a relativistic generalization of the disordered local moment theory to accurately predict temperature-dependent magnetic anisotropy.

Findings

Magnetic anisotropy K in FePd is proportional to m squared across a broad temperature range.

K in Fe(50)Pt(50) diminishes rapidly from 8 micro-eV to zero as temperature increases.

The theory aligns with experimental data and differs from single ion anisotropy models.

Abstract

We present a first-principles theory of the variation of magnetic anisotropy, K, with temperature, T, in metallic ferromagnets. It is based on relativistic electronic structure theory and calculation of magnetic torque. Thermally induced `local moment' magnetic fluctuations are described within the relativistic generalisation of the `disordered local moment' (R-DLM) theory from which the T dependence of the magnetisation, m, is found. We apply the theory to a uniaxial magnetic material with tetragonal crystal symmetry, L1_0-ordered FePd, and find its uniaxial K consistent with a magnetic easy axis perpendicular to the Fe/Pd layers for all m and proportional to m squared for a broad range of values of m. This is the same trend that we have previously found in L1_0-ordered FePt and which agrees with experiment. This account, however, differs qualitatively from that extracted from a single ion anisotropy model. We also study the magnetically soft cubic magnet, the Fe(50)Pt(50) solid solution, and find that its small magnetic anisotropy constant K_1 rapidly diminishes from 8 micro-eV to zero. K evolves from being proportional to the seventh power of m at low T to the fourth power near the Curie temperature.