Nonvanishing spin Hall currents in the presence of magnetic impurities

TL;DR

This paper investigates the intrinsic spin Hall effect in a 2D electron gas with Rashba coupling, showing that magnetic impurities induce a non-zero spin Hall conductivity influenced by anisotropic interactions and relaxation times.

Contribution

It introduces a detailed calculation of spin Hall conductivity considering anisotropic magnetic impurity interactions and vertex corrections, revealing non-vanishing effects in the presence of magnetic impurities.

Findings

Non-zero spin Hall conductivity depends on impurity interaction anisotropy.

Conductivity varies with momentum relaxation time and spin-orbit splitting.

Clean limit conductivity ranges between e/8π and e/6π.

Abstract

The intrinsic spin Hall conductivity in a two dimensional electron gas with Rashba spin-orbit coupling is evaluated by taking account of anisotropic coupling between magnetic impurities and itinerant electrons. In our calculation Kubo's linear response formalism is employed and the vertex correction is considered. In the semiclassical limit $\mu \gg 1/\tau$, a non-vanishing spin Hall conductivity $\sigma^{}_{sH}$ is found to depend on the momentum relaxation time $\tau$, spin-orbit splitting $\Delta$ and the anisotropic coefficient of interaction between itinerant electrons and magnetic impurities. The clean limit of $\sigma^{}_{sH}$ is in the region of $e/8\pi \sim e/6\pi$, depending on the anisotropic coefficient.