Theory of spin Hall effect

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.