  We propose a new theory of the topological Hall effect (THE) in systems with
chiral magnetization vortices such as magnetic skyrmions. We solve the problem
of electron scattering on a magnetic skyrmion exactly, for an arbitrary
strength of exchange interaction and the skyrmion size. We report the existence
of different regimes of THE and resolve the apparent contradiction between the
adiabatic Berry phase theoretical approach and the perturbation theory for THE.
We traced how the topological charge Hall effect transforms into the spin Hall
effect upon varying the exchange interaction strength or the skyrmion size.
This transformation has a nontrivial character: it is accompanied by an
oscillating behavior of both charge and spin Hall currents. This hallmark of
THE allows one to differentiate the chirality driven contribution to Hall
response in the experiments.
