Disorder effects in the anomalous Hall effect induced by Berry curvature

We describe the charge transport in ferromagnets with spin-orbit coupled Bloch bands by combining the wave-packet evolution equations with the classical Bolzmann equation. This approach can be justified in the limit of smooth disorder potential. Besides the skew scattering contribution, we demonstrate how other effects of disorder appear which are closely linked to the Berry curvature of the Bloch states associated with the wave packet. We show that, although being of the same order of magnitude as the clean limit contribution, generally disorder corrections depend differently on various parameters and can lead to the sign reversal of the Hall current as the function of the chemical potential in systems with a nonconstant Berry curvature in momentum space. Earlier conclusions on the effects of disorder on the anomalous Hall effect depended stricly on the lack of momentum dependence of the Berry curvature in the models studied and generalizations of their findings to other systems with more complicated band structures were unjustified.