Spin Hall effects without spin currents in magnetic insulators

TL;DR

This paper introduces a novel perspective on the spin Hall effect in magnetic insulators, relating it to spin polarization rather than spin currents, and demonstrates this with a modified Kane-Mele model.

Contribution

It proposes an alternative view of the spin Hall effect based on spin polarization, applicable to magnetic insulators, and explores its reciprocal phenomenon and boundary effects.

Findings

Spin Hall effect can occur without spin currents in magnetic insulators.

The effect is related to spin polarization induced by electric fields.

Reciprocal effect involves charge polarization from Zeeman field gradients.

Abstract

The spin Hall effect (SHE) is normally discussed in terms of a spin current, which is ill-defined in strongly spin-orbit-coupled systems because of spin non-conservation. In this work we propose an alternative view of SHE phenomena by relating them to a spin analog of charge polarization induced by an electric field. The spin density polarization is most conveniently defined in insulators, which can have a SHE if they break time-reversal symmetry, i.e. if they are magnetic. The reciprocal of this SHE is a counterpart of the inverse SHE (ISHE), and is manifested in magnetic insulators as a charge polarization induced by a Zeeman field gradient. We use a modified Kane-Mele model to illustrate the magnetic spin Hall effect, and to discuss its bulk-boundary relationship.