Spin diffusion at finite electric and magnetic fields

Spin-transport properties at finite electric and magnetic fields are studied by using the generalized semiclassical Boltzmann equation. It is found that the spin-diffusion equation for nonequilibrium spin density and spin currents involves a number of length scales that explicitly depend on the electric and magnetic fields. The set of macroscopic equations can be used to address a broad range of the spin-transport problems in magnetic multilayers as well as in semiconductor heterostructure. A specific example of spin injection into semiconductors at arbitrary electric and magnetic fields is illustrated.