Hall effect driven by non-collinear magnetic polarons in diluted magnetic semiconductors

In this letter we develop the theory of Hall effect driven by non-collinear magnetic textures (topological Hall effect - THE) in diluted magnetic semiconductors (DMS). We show that a carrier spin-orbit interaction induces a chiral magnetic ordering inside a bound magnetic polaron (BMP). The inner structure of non-collinear BMP is controlled by the type of spin-orbit coupling, allowing to create skyrmion- (Rashba) or antiskyrmion-like (Dresselhaus) configurations. The asymmetric scattering of itinerant carriers on polarons leads to the Hall signal which exists in weak external magnetic fields and low temperatures. We point out that DMS-based systems allow one to investigate experimentally the dependence of THE both on a carrier spin polarization and on a non-collinear magnetic texture shape.