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Broken Galilean invariance in a spin-orbit coupled system can amplifymany-body effects on its different responses. We study the anomalous Hall andspin Hall conductivities of a magnetic two-dimensional electron gas with Rashbaspin-orbit coupling. We show that both of these conductivities in the intrinsiclimit are fully specified in terms of the longitudinal and transverse spin-spinresponse functions. We include the effect of electron-electron interaction inthe spin-spin linear response functions, going beyond the random-phaseapproximation. We do this by incorporating the local-field correction in theresponse functions, which takes into account the many-body exchange-correlationeffects. We observe a significant enhancement of the static anomalous Hallconductivity due to the electron-electron interaction. The many-body correctionon the spin Hall effects is more non-trivial, and strong electron-electroninteraction can even reverse the sign of the static spin Hall conductivity.

Many-body correction to the intrinsic anomalous and spin Hall conductivities