Spin Hall effect, Hall effect and spin precession in diffusive normal metals

TL;DR

This paper investigates the interplay of spin Hall effect, Hall effect, and spin precession in diffusive normal metals under magnetic fields, revealing how these phenomena influence spin and charge transport in thin films.

Contribution

It derives diffusion equations for spin and charge flow in normal metals under magnetic fields and numerically analyzes the effects in realistic thin film geometries, highlighting the suppression and maximization of spin Hall potentials.

Findings

Out-of-plane spin Hall potential is suppressed at high Larmor frequencies.

In-plane spin Hall potential peaks at a finite magnetic field.

Spin precession causes decay of spin-injection-induced Hall effects.

Abstract

We study transport in normal metals in an external magnetic field. This system exhibits an interplay between a transverse spin imbalance (spin Hall effect) caused by the spin-orbit interaction, a Hall effect via the Lorentz force, and spin precession due to the Zeeman effect. Diffusion equations for spin and charge flow are derived. The spin and charge accumulations are computed numerically in experimentally relevant thin film geometries. The out-of-plane spin Hall potential is suppressed when the Larmor frequency is larger than the spin-flip scattering rate. The in-plane spin Hall potential vanishes at zero magnetic field and attains its maximum at a finite magnetic field before spin precession starts to dominate. Spin-injection via ferromagnetic contacts creates a transverse charge Hall effect that decays in a finite magnetic field due to spin precession.