# A nontrivial crossover in topological Hall effect regimes

## TL;DR

This paper develops an exact theory for the topological Hall effect in systems with magnetic skyrmions, revealing different regimes and a nontrivial transformation into the spin Hall effect with oscillating Hall currents.

## Contribution

It provides an exact solution for electron scattering on skyrmions, clarifies the regimes of THE, and explains the transition to the spin Hall effect.

## Key findings

- Identification of multiple THE regimes.
- Transformation of THE into spin Hall effect with oscillations.
- Differentiation of chirality-driven Hall responses.

## Abstract

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.