Disorder effects in the AHE induced by Berry curvature

TL;DR

This paper investigates how disorder influences the anomalous Hall effect in ferromagnets with spin-orbit coupling, highlighting the role of Berry curvature and showing that disorder can alter the Hall current's sign.

Contribution

It introduces a combined wave-packet and Boltzmann approach to analyze disorder effects on the AHE, accounting for Berry curvature variations and correcting previous assumptions.

Findings

Disorder effects can cause sign reversal of the Hall current.

Berry curvature contributions are comparable to disorder corrections.

Disorder effects depend on system parameters and band structure.

Abstract

We describe the charge transport in ferromagnets with spin orbit coupled Bloch bands by combining the wave-packet evolution equations with the classical Boltzmann equation. This approach can be justified in the limit of smooth disorder potential. Besides the skew scattering contribution, we demonstrate how other effects of disorder appear which are closely linked to the Berry curvature of the Bloch states associated with the wavepacket. We show that, although being of the same order of magnitude as the clean limit Berry curvature contribution, generally disorder corrections depend differently on various parameters and can lead to the sign reversal of the Hall current as the function of the chemical potential in systems with a non-constant Berry curvature in momentum space. Earlier conclusions on the effects of disorder on the anomalous Hall effect depended stricly on the lack of momentum dependence of the Berry curvature in the models studied and generalizations of their findings to other systems with more complicated band structures were unjustified.