We present a theory of electron scattering on a magnetic Skyrmion for the case when the exchange interaction is moderate so that the adiabatic approximation and the Berry phase approach are not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic Skyrmions, the special importance of which is its applicability to dilute magnetic semiconductors with a weak exchange interaction.

• Received 12 February 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.027202