Topological Hall Effect in Magnetic Topological Insulator Films

TL;DR

This paper investigates how spin-orbit coupling and disorder influence the topological and anomalous Hall effects in magnetic topological insulator films using numerical simulations and analytical calculations.

Contribution

It provides a detailed numerical and analytical study of the interplay between spin-orbit coupling, disorder, and Hall effects in magnetic topological insulator films, highlighting different behaviors in clean and disordered regimes.

Findings

Spin-orbit coupling affects longitudinal transport mainly in the clean limit.

In the clean limit, spin-orbit coupling has little impact on topological Hall conductance.

In the disordered limit, disorder scattering dominates longitudinal transport, and spin-orbit coupling strongly influences topological Hall conductance.

Abstract

Geometric Berry phase can be induced either by spin-orbit coupling, giving rise to the anomalous Hall effect in ferromagnetic materials, or by chiral spin texture, such as skyrmions, leading to the topological Hall effect. Recent experiments have revealed that both phenomena can occur in topological insulator films with magnetic doping, thus providing us with an intriguing platform to study the interplay between these two phenomena. In this work, we numerically study the anomalous Hall and topological Hall effects in a four-band model that can properly describe the quantum well states in the magnetic topological insulator films by combining Landauer-Buttiker formula and the iterative Green's function method. Our numerical results suggest that spin-orbit coupling in this model plays a different role in the quantum transport in the clean and disordered limits. In the clean limit, spin-orbit coupling mainly influences the longitudinal transport but does not have much effect on topological Hall conductance. Such behavior is further studied through the analytical calculation of scattering cross-section due to skyrmion within the four-band model. In the disordered limit, the longitudinal transport is determined by disorder scattering and spin-orbit coupling is found to affect strongly the topological Hall conductance. This sharp contrast unveils a dramatic interplay between spin-orbit coupling and disorder effect in topological Hall effect in magnetic topological insulator systems.