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

TL;DR

This paper investigates the topological Hall effect in thin ferromagnetic films caused by electron scattering on skyrmions under external magnetic fields, highlighting its robustness and dependence on skyrmion density and type.

Contribution

It models the influence of magnetic fields on skyrmion structures and characterizes the topological Hall effect's behavior and sign relative to skyrmion properties.

Findings

THE remains robust despite magnetic field variations.

THE magnitude is primarily determined by skyrmion density.

The sign of THE depends on skyrmion vorticity.

Abstract

We consider topological Hall effect (THE) in thin ferromagnetic films due to electron scattering on magnetic skyrmions in the presence of the relatively 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 in the range 1-5 T 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 $n_{sk}$, being 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.