Asymmetric scattering and tunneling of electrons due to spin-orbit and exchange interaction

We consider a transverse electrical and spin current response to a longitudinal electric field in a metallic or semiconductor system characterized by various types of chirality. Using the similar theoretical approach we study a skew scattering on magnetic skyrmions leading to topological Hall effect, tunneling anomalous Hall effect (TAHE) of electrons and holes across an interface between magnetic semiconductors and electron scattering on a magnetic center in a semiconductor. We demonstrate how the chiral symmetry of the system manifests itself in the Hall response and its dependence on the electron spin polarization.