The Anomalous Hall Effect in Magnetic Topological Insulators

TL;DR

This paper provides a comprehensive theoretical analysis of the anomalous Hall effect in magnetic topological insulators, demonstrating how various parameters influence the effect and aligning with recent experimental findings.

Contribution

It introduces a modified semi-classical framework that systematically treats all three contributions to the AHE and derives analytical expressions for conductivities.

Findings

AHE can change sign with magnetization orientation, impurity concentration, and chemical potential.

Each contribution to AHE can be independently turned off by parameter adjustments.

Theoretical results agree with recent experimental observations.

Abstract

The anomalous Hall effect (AHE) is studied on the surface of a 3D magnetic topological insulator. By applying a modified semi-classical framework, all three contributions to the AHE, the intrinsic Berry phase curvature effect, the side-jump effect and the skew scattering effects are systematically treated, and analytical expressions for the conductivities are obtained in terms of the Fermi level, the spatial orientation of the surface magnetization and the concentration of magnetic and non-magnetic impurities. We demonstrate that the AHE can change sign by altering the orientation of the surface magnetization, the concentration of the impurities and also the position of the chemical potential, in agreement with recent experimental observations. Hence, each contribution to the AHE, or even the whole AHE, can be turned off by properly adjusting the given parameters. For example, one can turn off the anomalous hall conductivity in a system with in-plane magnetization by pushing the system into the fully metallic regime.