Spin-Hall conductivity of a spin-polarized two-dimensional electron gas with Rashba spin-orbit interaction and magnetic impurities

The Kubo formula is used to calculate the spin-Hall conductivity in a spin-polarized two-dimensional electron system with Rashba-type spin-orbit interaction. As in the case of the unpolarized electron system, spin Hall conductivity is entirely determined by states at the Fermi level, a property that persists in the presence of magnetic impurities. In the clean limit, the spin-Hall conductivity decreases monotonically with the Zeeman splitting, a result of the ordering effect on the electron spins produced by the magnetic field. In the presence of magnetic impurities, the spin-dependent scattering determines a finite renormalization of the static part of the fully dressed vertex correction of the velocity operator that leads to an enhancement of the \sigma_{sH}, an opposite behaviour to that registered in the presence of spin-independent disorder. The variation of \sigma_{sH} with the strength of the Rashba coupling and the Zeeman splitting is studied.