Magnetocrystalline Anisotropy Energy of a Transition Metal Monolayer: A Non-perturbative Theory

TL;DR

This paper presents a non-perturbative theoretical calculation of magnetocrystalline anisotropy energy in transition metal monolayers, revealing its proportionality to the square of spin-orbit coupling and the significance of degeneracy lifting near the Fermi level.

Contribution

It introduces a fully convergent tight-binding method including $s$-$d$ hybridization and treats spin-orbit interaction non-perturbatively, clarifying the origin of anisotropy energy.

Findings

$E_{anis}$ is proportional to $\lambda_{so}^2$

Degeneracy lifting near the Fermi level significantly contributes to $E_{anis}$

Anisotropy energy decreases with increasing temperature

Abstract

The magnetocrystalline anisotropy energy $E_{anis}$ for a monolayer of Fe and Ni is determined using a fully convergent tight-binding calculation including $s$-$d$ hybridization. The spin-orbit interaction $\lambda_{so}$ is treated non-perturbatively. Remarkably, we find $E_{anis}\propto\lambda_{so}^2$ and important contributions to $E_{anis}$ due to the lifting of degeneracies near the Fermi-level. This is supported by the calculated decrease of the anisotropy energy with increasing temperature on a scale of several hundred K. Our results clarify the present debate on the origin of $E_{anis}$.