General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

TL;DR

This paper reveals that generic magnetic insulators can exhibit a nonlinear Hall current proportional to the square of the electric field when inversion symmetry is broken, expanding understanding beyond the quantum anomalous Hall effect.

Contribution

It demonstrates the existence of a nonlinear Hall effect in magnetic insulators due to orbital magnetization, a phenomenon not limited to topological insulators or quantum Hall systems.

Findings

Nonlinear Hall conductivity arises from orbital magnetization induced by virtual interband transitions.

The effect requires inversion symmetry breaking in magnetic insulators.

The nonlinear Hall conductivity vanishes in Landau levels of 2D electron gases.

Abstract

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity and other insulators (with zero Chern number) present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the Integer quantum Hall effect.