Topological Hall effect from strong to weak coupling

TL;DR

This paper provides a unified theoretical framework for the topological Hall effect across strong and weak coupling regimes, incorporating both adiabatic and nonadiabatic spin gauge fields to explain experimental observations.

Contribution

It introduces a comprehensive approach using spin gauge fields that unifies the understanding of THE in different coupling regimes, including a new weak-coupling region.

Findings

Adiabatic contribution dominates in strong coupling.

Nonadiabatic effects cancel part of the adiabatic contribution in weak coupling.

Identifies a new weak-coupling regime where Hall conductivity is proportional to the exchange splitting.

Abstract

Topological Hall effect (THE) of electrons coupled to a noncoplanar spin texture has been studied so far for the strong- and weak-coupling regimes separately; the former in terms of the Berry phase and the latter by perturbation theory. In this letter, we present a unified treatment in terms of spin gauge field by considering not only the adiabatic (Berry phase) component of the gauge field but also the nonadiabatic component. While only the adiabatic contribution is important in the strong-coupling regime, it is completely canceled by a part of the nonadiabatic contribution in the weak-coupling regime, where the THE is governed by the rest of the nonadiabatic terms. We found a new weak-coupling region that cannot be accessed by a simple perturbation theory, where the Hall conductivity is proportional to M, with 2M being the exchange splitting of the electron spectrum.