Many-body correction to the intrinsic anomalous and spin Hall conductivities

TL;DR

This paper investigates how electron-electron interactions, beyond simple approximations, significantly modify the intrinsic anomalous and spin Hall conductivities in a spin-orbit coupled magnetic 2D electron gas, revealing potential sign reversals.

Contribution

It introduces a method to include local-field corrections in response functions, capturing many-body effects on Hall conductivities beyond the random-phase approximation.

Findings

Electron-electron interactions significantly enhance the anomalous Hall conductivity.

Many-body effects can reverse the sign of the spin Hall conductivity.

The response functions are fully determined by spin-spin correlations in the intrinsic limit.

Abstract

Broken Galilean invariance in a spin-orbit coupled system can amplify many-body effects on its different responses. We study the anomalous Hall and spin Hall conductivities of a magnetic two-dimensional electron gas with Rashba spin-orbit coupling. We show that both of these conductivities in the intrinsic limit are fully specified in terms of the longitudinal and transverse spin-spin response functions. We include the effect of electron-electron interaction in the spin-spin linear response functions, going beyond the random-phase approximation. We do this by incorporating the local-field correction in the response functions, which takes into account the many-body exchange-correlation effects. We observe a significant enhancement of the static anomalous Hall conductivity due to the electron-electron interaction. The many-body correction on the spin Hall effects is more non-trivial, and strong electron-electron interaction can even reverse the sign of the static spin Hall conductivity.