A kinetic equation approach to the anomalous Hall effect in a diffusive Rashba two-dimensional electron system with magnetization

TL;DR

This paper develops a kinetic equation approach to analyze the anomalous Hall effect in a magnetized Rashba 2D electron system, revealing intrinsic and disorder-mediated contributions to conductivity.

Contribution

It introduces a two-band kinetic equation method that accounts for impurity scattering and distinguishes intrinsic and disorder-mediated mechanisms in the anomalous Hall effect.

Findings

Intrinsic and disorder-mediated mechanisms contribute to the anomalous Hall conductivity.

The conductivity depends on spin-orbit coupling and magnetization strength.

Numerical results show different behaviors for short- and long-range impurity collisions.

Abstract

We present a two-band kinetic equation method to investigate the anomalous Hall effect in a Rashba two-dimensional electron system subjected to a homogeneous magnetization. The electron-impurity scattering is taken into account in the self-consistent Born approximation. It is demonstrated that the impurity-density-free anomalous Hall conductivity arises from an intrinsic and a disorder-mediated mechanisms, associated respectively with the electron states under and near the Fermi surface. The intrinsic mechanism relates to a dc-field-induced transition process, or in other words, a linear stationary Rabi process. The disorder-mediated one corresponds to a scattering between impurities and the electrons participating in longitudinal transport. Numerically, the dependencies of the anomalous Hall conductivity on the spin-orbit coupling constants and the strength of the magnetization are demonstrated for both the short- and long-range collisions.