Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

TL;DR

This paper investigates how inhomogeneous longitudinal electric fields influence the anomalous Hall conductivity in a ferromagnetic 2D electron gas, revealing a peak in conductivity at specific wave numbers due to inhomogeneity effects.

Contribution

It demonstrates that inhomogeneous electric fields can induce a non-zero anomalous Hall conductivity, with a peak at a wave number related to electron mean free path and spin-exchange length, independent of Rashba energy.

Findings

AHC peaks at a specific wave number related to electron and spin-exchange scales.

Peak AHC can reach the magnitude of the bare-bubble contribution.

Peak position is independent of Rashba energy.

Abstract

It is known that the anomalous Hall conductivity (AHC) in a disordered two dimensional electron system with Rashba spin-orbit interaction and finite ferromagnetic spin-exchange energy is zero in the metallic weak-scattering regime because of the exact cancellation of the bare-bubble contribution by the vertex correction. We study the effect of inhomogeneous longitudinal electric field on the AHC in such a system. We predict that AHC increases from zero (at zero wavenumber), forms a peak, and then decreases as the wavenumber for the variation of electric field increases. The peak-value of AHC is as high as the bare-buble contribution. We find that the wave number, q, at which the peaks occur is the inverse of the geometric mean of the mean free path of an electron and the spin-exchange length scale. Although the Rashba energy is responsible for the peak-value of AHC, the peak position is independent of it.