Coherent backscattering in the topological Hall effect

TL;DR

This paper investigates quantum corrections to the topological Hall effect in 2D magnetic systems, revealing weak localization effects that are experimentally observable in dilute magnetic semiconductors.

Contribution

It provides the first theoretical analysis of quantum corrections to the topological Hall effect, focusing on gradient corrections in 2D systems and their experimental implications.

Findings

Quantum correction to the topological Hall resistivity identified

Weak localization effects are significant in dilute magnetic semiconductors

Theoretical framework for gradient corrections in kinetic equations developed

Abstract

The mutual interplay between electron transport and magnetism has attracted considerable attention in recent years, primarily motivated by strategies to manipulate magnetic degrees of freedom electrically, such as spin-orbit torques and domain wall motion. Within this field the topological Hall effect, which originates from scalar spin chirality, is an example of inter-band quantum coherence induced by real-space inhomogeneous magnetic textures, and its magnitude depends on the winding number and chiral spin features that establish the total topological charge of the system. Remarkably, in the two decades since its discovery, there has been no research on the quantum correction to the topological Hall effect. Here we will show that, unlike the ordinary Hall effect, the inhomogeneous magnetization arising from the spin texture will give additional scattering terms in the kinetic equation, which result in a quantum correction to the topological Hall resistivity. We focus on 2D systems, where weak localization is strongest, and determine the complicated gradient corrections to the Cooperon and kinetic equation. Whereas the weak localization correction to the topological Hall effect is not large in currently known materials, we show that it is experimentally observable in dilute magnetic semiconductors. Our theoretical results will stimulate experiments on the topological Hall effect and fill the theoretical knowledge gap on weak localization corrections to transverse transport.