Anomalous Hall Effect in Disordered Multiband Metals

TL;DR

This paper develops a comprehensive microscopic theory for the anomalous Hall effect in disordered multiband ferromagnets, capturing intrinsic and side jump contributions and applicable to ab initio calculations.

Contribution

It introduces a systematic approach to include all scattering-independent contributions to the anomalous Hall effect, handling interband coherence effects.

Findings

Expresses the anomalous Hall effect in terms of band structure for Gaussian disorder

Demonstrates the theory on Rashba and (III,Mn)V models

Applicable to ab initio calculations for ferromagnetic metals

Abstract

We present a microscopic theory of the anomalous Hall effect in metallic multi-band ferromagnets, which accounts for all scattering-independent contributions, i.e., both the intrinsic and the so-called side jump. For a model of Gaussian disorder, the anomalous Hall effect is expressed solely in terms of the electronic band structure of the host material. Our theory handles systematically the interband-scattering coherence effects. We demonstrate the method in the two-dimensional Rashba and three-dimensional ferromagnetic (III,Mn)V semiconductor models. Our formalism is directly amenable to ab initio treatments for a wide range of ferromagnetic metals.