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

摘要

It is known that the anomalous Hall conductivity (AHC) in a disordered twodimensional electron system with Rashba spin-orbit interaction and finiteferromagnetic spin-exchange energy is zero in the metallic weak-scatteringregime because of the exact cancellation of the bare-bubble contribution by thevertex correction. We study the effect of inhomogeneous longitudinal electricfield on the AHC in such a system. We predict that AHC increases from zero (atzero wavenumber), forms a peak, and then decreases as the wavenumber for thevariation of electric field increases. The peak-value of AHC is as high as thebare-buble contribution. We find that the wave number, q, at which the peaksoccur is the inverse of the geometric mean of the mean free path of an electronand the spin-exchange length scale. Although the Rashba energy is responsiblefor the peak-value of AHC, the peak position is independent of it.