Spin Hall effects in diffusive normal metals

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Abstract
We consider spin and charge flow in normal metals. 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. Using the quasiclassical approximation, we derive diffusion equations which include contributions from skew scattering, side-jump scattering, and the anomalous spin-orbit induced velocity. We compute the magnitude of various spin Hall effects in experimental relevant geometries and discuss when the different scattering mechanisms are important.
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