General theory of topological Hall effect in systems with chiral spin textures

TL;DR

This paper develops a comprehensive theory for the topological Hall effect in 2D magnetic systems with chiral spin textures, accounting for asymmetric scattering and different regimes, and explores how various parameters influence THE.

Contribution

It provides a unified theoretical framework describing THE in disordered chiral spin textures, including both adiabatic and non-adiabatic regimes, and analyzes parameter dependencies.

Findings

THE arises from asymmetric scattering on skyrmions in the scattering regime.

The theory describes the crossover between spin and charge regimes of THE.

Dependence of THE resistivity on skyrmion size, Fermi energy, and exchange interaction is analyzed.

Abstract

We present a consistent theory of the topological Hall effect (THE) in 2D magnetic systems with disordered array of chiral spin textures, such as magnetic skyrmions. We focus on the scattering regime when the mean-free path of itinerant electrons exceeds the spin texture size, and THE arises from the asymmetric carrier scattering on individual chiral spin textures. We calculate the resistivity tensor on the basis of the Boltzmann kinetic equation taking into account the asymmetric scattering on skyrmions via the collision integral. Our theory describes both the adiabatic regime, when THE arises from a spin Hall effect and the non-adiabatic scattering when THE is due to purely charge transverse currents. We analyze the dependence of THE resistivity on a chiral spin texture structure,as well as on material parameters. We discuss the crossover between spin and charge regimes of THE driven by the increase of skyrmion size, the features of THE due to the variation of the Fermi energy, and the exchange interaction strength; we comment on the sign and magnitude of THE