Spin Hall effects in diffusive normal metals.

We study transport in normal metals in an external magnetic field. We employ the Keldysh formalism to find transport equations in the presence of the spin-orbit interaction, interaction with magnetic impurities, and nonmagnetic impurity scattering. 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. 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 a 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.