Topological Hall effect for electron scattering on nanoscale skyrmions in external magnetic field

We consider topological Hall effect (THE) in thin ferromagnetic films due to electron scattering on nanoscale magnetic skyrmions in the presence of the strong external magnetic field. We account for the effect of the magnetic field on a skyrmion structure and describe the hallmarks of THE differentiating it from ordinary and anomalous Hall effects. We have found that, although in typical ferromagnets the variation of magnetic field substantially affects the skyrmion size, THE changes rather weakly remaining quite robust. Therefore, the magnitude of THE is primarily determined by the skyrmions sheet density n(sk), i.e., for PdFe/Ir(111) it is comparable to the magnitude of the ordinary Hall effect (OHE) at n(sk) = 10(-11) cm(-2). The sign of THE is opposite to that of OHE for skyrmions with positive vorticity, while for antiskyrmions the signs are the same.