Hall Voltage with the Spin Hall Effect

TL;DR

This paper predicts that in systems with inhomogeneous electron density, the spin Hall effect produces a measurable Hall voltage, enabling electrical detection of the effect without spin injection.

Contribution

It introduces a novel prediction that inhomogeneous electron density leads to a Hall voltage in the spin Hall effect, distinct from the ordinary Hall effect.

Findings

Hall voltage is quadratic in the longitudinal electric field.

Spin accumulation occurs in the bulk.

Charge accumulation peaks near edges.

Abstract

The spin Hall effect does not generally result in a charge Hall voltage. We predict that in systems with inhomogeneous electron density in the direction perpendicular to main current flow, the spin Hall effect is instead accompanied by a Hall voltage. Unlike the ordinary Hall effect, we find that this Hall voltage is quadratic in the longitudinal electric field for a wide range of parameters accessible experimentally. We also predict spin accumulation in the bulk and sharp peaks of spin-Hall induced charge accumulation near the edges. Our results can be readily tested experimentally, and would allow the electrical measurement of the spin Hall effect in non-magnetic systems and without injection of spin-polarized electrons.