Anomalous Hall effect in a two-dimensional electron system: unified analysis of side-jump and skew scattering mechanisms

摘要

We present a unified kinetic equation approach to analyze the side-jump and skew scattering anomalous Hall contributions in a two-dimensional electron system with extrinsic spin-orbit coupling and also spin-orbit coupling induced directly by the driving electric field. Considering long-range electron-impurity scattering up to the second Born approximation, we derive the side-jump and skew scattering contributions to the anomalous Hall conductivity on an equal basis. Our numerical analysis shows that in a typical two-dimensional semiconductor with magnetization, both the side-jump and skew anomalous Hall conductivities are of the same order of magnitude. For an attractive electron-impurity scattering potential, their signs are the same as that of the ordinary Hall conductivity. Also, we make it clear that the anomalous Hall effect is relatively small in comparison with the ordinary one in the diffusive regime.