Spin imbalance of charge carriers induced by an electric current

TL;DR

This paper investigates how inhomogeneous magnetic fields generated by electric currents influence the spin Hall effect in metals, highlighting a relativistic correction that can be as significant as spin-orbit interactions.

Contribution

It introduces the analysis of current-induced magnetic fields' impact on the spin Hall effect, emphasizing a relativistic correction that does not rely on heavy elements.

Findings

Magnetic field inhomogeneities cause spin accumulation at edges.

Relativistic effects can rival spin-orbit contributions.

Induced spins are oriented normal to the metal surface.

Abstract

We analyze the contribution of the inhomogeneous magnetic field induced by an electrical current to the spin Hall effect in metals. The Zeeman coupling between the field and the electron spin leads to a spin dependent force, and to spin accumulation at the edges. We compare the effect of this relativistic correction to the electron dynamics to the features induced by the spin-orbit interaction. The effect of current induced magnetic fields on the spin Hall effect can be comparable to the extrinsic contribution from the spin-orbit interaction, although it does not require the presence of heavy elements with a strong spin-orbit interaction. The induced spins are oriented normal to the metal slab.