Anomalous Hall effect in spin-polarized two-dimensional electron gases with Rashba spin-orbit interaction

We present details of the analysis of the effect of disorder on the intrinsic anomalous Hall conductivity ( AHC) in a spin- polarized two-dimensional electron gas with a Rashba- type spin - orbit interaction. We show that the AHC derived by the Kubo formula vanishes when the Fermi energy is larger than the exchange energy unless the lifetime is spin- dependent. Results obtained by numerical integration of the general expressions of the AHC suggest that the AHC could depend on the lifetime, in contrast to previous results.