The Kubo formula is used to calculate the spin-Hall conductivity σsH in a spin-polarized two-dimensional electron system with Rashba-type spin– orbit interaction. As in the case of the unpolarized electron system, σsH 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 σsH, an opposite behaviour to that registered in the presence of spin-independent disorder. The variation of σsH with the strength of the Rashba coupling and the Zeeman splitting is studied.
Spin-Hall Conductivity of a Spin-Polarized Two-Dimensional Electron Gas with Rashba Spin-Orbit Interaction and Magnetic ImpuritiesNew Journal of Physics
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