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The anomalous Hall effect in ferromagnetic metals is classified into twobased on the mechanism. The first one is the intrinsic Hall effect due to theBerry curvature in momentum space; this is a Hall effect that solely arisesfrom the band structure of solids. On the other hand, another contribution tothe Hall effect, so-called extrinsic mechanism, comes from impurity scatteringssuch as skew scattering and side jump; for the extrinsic mechanism, thespin-orbit interaction of the impurity ions is often required. These twomechanisms are often discussed separately; the intrinsic Hall effect isdominant in the intermediate resistivity region while the latter, i.e., skewscattering, becomes important in the clean limit. In this work, it is showntheoretically that the non-commutative nature of the real-space coordinates inthe presence of the Berry curvature causes the skew scattering by thenonmagnetic impurity without relativistic spin-orbit interactions, in sharpcontrast to the conventional cases.

Noncommutative quantum mechanics and skew scattering in ferromagnetic metals