We study features of mobile carriers' skew scattering in nonmagnetic semiconductors emerging due to a combination of spin-orbit coupling in a crystal band structure and a nontrivial inner structure of impurities. In particular, we show that a nonzero magnetic moment of the impurity generally leads to the anomalous Hall effect (AHE) in the absence of the spin polarization of the mobile carriers, the effect arising from spin-independent scattering asymmetry due to exchange interaction. We analyze the skew scattering in bulk zinc-blende semiconductors for both electron and hole states and emphasize the crucial role of the impurity spin polarization for the emergent AHE for the valence band holes. We also revisit the skew scattering in quantum wells showing that the cancellation of the extrinsic contribution to the AHE common for two-dimensional systems can be lifted off depending on both the electron wave function and the impurity structure.

• Received 27 March 2022
• Revised 18 July 2022
• Accepted 18 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.085203