"Phase Diagram" of the Spin Hall Effect

TL;DR

This paper derives analytical formulas for the frequency-dependent spin-Hall conductivity in a 2DEG with impurities, spin-orbit coupling, and magnetic field, revealing how different mechanisms influence the effect under various conditions.

Contribution

It provides the first analytical formulas for the frequency-dependent spin-Hall conductivity considering multiple mechanisms and external parameters in a 2DEG.

Findings

D.c. spin Hall conductivity vanishes without magnetic field.

Magnetic field restores skew-scattering and side-jump contributions.

Mechanisms can be tuned by frequency, magnetic field, and temperature.

Abstract

We obtain analytic formulas for the frequency-dependent spin-Hall conductivity of a two-dimensional electron gas (2DEG) in the presence of impurities, linear spin-orbit Rashba interaction, and external magnetic field perpendicular to the 2DEG. We show how different mechanisms (skew-scattering, side-jump, and spin precession) can be brought in or out of focus by changing controllable parameters such as frequency, magnetic field, and temperature. We find, in particular, that the d.c. spin Hall conductivity vanishes in the absence of a magnetic field, while a magnetic field restores the skew-scattering and side-jump contributions proportionally to the ratio of magnetic and Rashba fields.