Anomalous Hall effect in ferromagnetic disordered metals

TL;DR

This paper investigates the anomalous Hall effect in disordered ferromagnetic metals using quantum transport theory, analyzing various mechanisms and the influence of impurity scattering on conductivity.

Contribution

It provides a microscopic model incorporating spin-orbit coupling and impurity effects to calculate Hall conductivity via the Kubo formula, including Berry phase contributions.

Findings

Impurity scattering significantly affects Hall conductivity components.

Different mechanisms like skew scattering, side-jump, and Berry phase are quantitatively evaluated.

Strong impurity scattering alters the relative importance of these mechanisms.

Abstract

The anomalous Hall effect in disordered band ferromagnets is considered in the framework of quantum transport theory. A microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling is used. The Hall conductivity is calculated from the Kubo formula for both, the skew scattering and the side-jump mechanisms. The recently discussed Berry phase induced Hall current is also evaluated within the model. The effect of strong impurity scattering is analyzed and it is found to affect the ratio of the non-diagonal (Hall) and diagonal components of the conductivity as well as the relative importance of different mechanisms.