Direct and inverse spin Hall effect: Lorentz force and Zeeman energy

TL;DR

This paper explains the mechanisms behind the spin Hall and inverse spin Hall effects using Lorentz and Zeeman forces, linking magnetic forces to spin and charge imbalances in electric currents.

Contribution

It introduces a unified physical explanation for both effects based on magnetic forces acting on electron spins and currents, emphasizing inertial reference frames.

Findings

Magnetic forces account for spin and charge imbalances in spin Hall effects.

The forces on spin sub-bands can be derived from inertial reference frames.

The approach unifies understanding of direct and inverse spin Hall effects.

Abstract

It is shown that magnetic forces as the Lorentz force, exerted on electric currents, and the force {\mu}Div(B), exerted on electron spins at rest, account for both the transverse spin imbalance typical of spin Hall effect and the transverse charge imbalance associated with pure spin currents (inverse spin Hall effect). Considering that for stationary currents the laboratory reference frame and those for which the spin up and spin down carriers are at rest are inertial systems, one can easily find the forces exerted by the lattice on both spin sub-bands, as well as the force between sub-bands.