Coulomb corrections to the extrinsic spin-Hall effect of a two-dimensional electron gas

We develop the microscopic theory of the extrinsic spin Hall conductivity of a two-dimensional electron gas, including skew-scattering, side-jump, and Coulomb interaction effects. We find that while the spin-Hall conductivity connected with the side-jump is independent of the strength of electron-electron interactions, the skew-scattering term is reduced by the spin-Coulomb drag, so the total spin current and the total spin-Hall conductivity are reduced for typical experimental mobilities. Further, we predict that in paramagnetic systems the spin-Coulomb drag reduces the spin accumulations in two different ways: (i) directly through the reduction of the skew-scattering contribution (ii) indirectly through the reduction of the spin diffusion length. Explicit expressions for the various contributions to the spin Hall conductivity are obtained using an exactly solvable model of the skew-scattering.