Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets

TL;DR

This paper introduces an intrinsic second-order anomalous Hall effect linked to Berry-connection polarizability in momentum space, with significant implications for detecting magnetic order in antiferromagnets.

Contribution

It identifies a new intrinsic second-order Hall effect related to band geometry, specifically the Berry-connection polarizability, and demonstrates its application in antiferromagnetic materials.

Findings

The effect is dominant in $ ext{PT}$-symmetric antiferromagnets.

First-principles calculations quantify the effect in Mn$_{2}$Au.

The response depends on the N{é}el vector orientation with $2 ext{ extpi}$ periodicity.

Abstract

Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalous Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property -- the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with $\mathcal{PT}$ symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn$_{2}$Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive dependence on the N\'{e}el vector orientation with a $2\pi$ periodicity, which offers a new route for electric detection of the magnetic order in $\mathcal{PT}$-invariant antiferromagnets.