Spin hall effect in semiconductor structures with spatially inhomogeneous spin relaxation

The extrinsic spin Hall effect in samples with coordinate-dependent relaxation time of the spin was studied. It was shown that the spin Hall effect in this case results in not only spatial separation of electrons with different spin projections, but also in the generation of a certain spin; therefore, the total spin's moment of a sample became nonzero under an electric current. A two-layer structure with different times of spin relaxation in layers and a homogeneous sample with linear behavior of the surface's spin relaxation were considered. An expression for the effective spin's relaxation time, which defines the spin polarization distribution in thin films, was derived. It was shown that the uniform spins polarization parallel to the film plane is possible, if the film thickness amounts to several diffusion lengths of the spin.