Theory of spin Hall effect

TL;DR

This paper extends the Drude model to include spin and spin-orbit interactions, deriving an expression for spin Hall conductivity that matches experimental data for metals and semiconductors.

Contribution

It introduces a new theoretical framework for the spin Hall effect that accounts for spin-orbit coupling without depending on scattering mechanisms.

Findings

Derived an expression for spin Hall conductivity independent of scattering.

Established a relation between spin and charge conductivities in cubic metals.

Theoretical predictions agree with experimental measurements.

Abstract

An extension of Drude model is proposed that accounts for spin and spin-orbit interaction of charge carriers. Spin currents appear due to combined action of the external electric field, crystal field and scattering of charge carriers. The expression for spin Hall conductivity is derived for metals and semiconductors that is independent of the scattering mechanism. In cubic metals, spin Hall conductivity $\sigma_s$ and charge conductivity $\sigma_c$ are related through $\sigma_s = [2 \pi \hbar/(3mc^2)]\sigma_c^2$ with $m$ being the bare electron mass. Theoretically computed value is in agreement with experiment.