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

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