Spin current, spin accumulation and spin Hall effect

Nonlocal spin transport in nanostructured devices with ferromagnetic injector (F1) and detector (F2) electrodes connected to a normal conductor (N) is studied. We reveal how the spin transport depends on interface resistance, electrode resistance, spin polarization and spin diffusion length, and obtain the conditions for efficient spin injection, spin accumulation and spin current in the device. It is demonstrated that the spin Hall effect is caused by spin-orbit scattering in nonmagnetic conductors and gives rise to the conversion between spin and charge currents in a nonlocal device. A method of evaluating spin-orbit coupling in nonmagnetic metals is proposed.