Scattering universality classes of side jump in anomalous Hall effect

TL;DR

This paper classifies the side jump contribution in the anomalous Hall effect into three universality classes based on spin scattering characteristics, revealing how their interplay affects Hall conductivity.

Contribution

It introduces a novel classification of scattering processes affecting the side jump in the anomalous Hall effect, highlighting the impact of spin structure on universality classes.

Findings

Three universality classes of scattering identified: spin-independent, spin-conserving, spin-flip.

Side jump contribution varies with the dominant scattering class.

Competition between classes causes the Hall conductivity to flow between different limits.

Abstract

The anomalous Hall conductivity has an important extrinsic contribution known as side jump contribution, which is independent of both scattering strength and disorder density. Nevertheless, we discover that side jump has strong dependence on the spin structure of the scattering potential. We propose three universality classes of scattering for the side jump contribution, having the characters of being spin-independent, spin-conserving and spin-flip respectively. For each individual class, the side jump contribution takes a different unique value. When two or more classes of scattering are present, the value of side jump is no longer fixed but varies as a function of their relative disorder strength. As system control parameter such as temperature changes, due to the competition between different classes of disorder scattering, the side jump Hall conductivity could flow from one class dominated limit to another class dominated limit. Our result indicates that magnon scattering plays a role distinct from normal impurity scattering and phonon scattering in the anomalous Hall effect because they belong to different scattering classes.