Theory of Spin Hall Effect: Extension of the Drude Model

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