Cluster multipole theory for anomalous Hall effect in antiferromagnets

TL;DR

This paper develops a unified theoretical framework using cluster multipole moments to explain the anomalous Hall effect in both ferromagnetic and antiferromagnetic materials, supported by first-principles calculations and experimental comparisons.

Contribution

It introduces the concept of cluster multipole moments to quantify macroscopic magnetization in non-collinear antiferromagnets and links these to the anomalous Hall effect.

Findings

AHE can be explained by cluster multipole order in AFMs.

Application to Mn3Ir and Mn3Z shows agreement with experiments.

Comparison with bcc Fe highlights the role of different multipole moments.

Abstract

We introduce a cluster extension of multipole moments to discuss the anomalous Hall effect (AHE) in both ferromagnetic (FM) and antiferromagnetic (AFM) states in a unified framework. We first derive general symmetry requirements for the AHE in the presence or absence of the spin-orbit coupling, by considering the symmetry of the Berry curvature in k space. The cluster multipole (CMP) moments are then defined to quantify the macroscopic magnetization in non-collinear AFM states, as a natural generalization of the magnetization in FM states. We identify the macroscopic CMP order which induces the AHE. The theoretical framework is applied to the non-collinear AFM states of Mn3Ir, for which an AHE was predicted in a first-principles calculation, and Mn3Z (Z=Sn, Ge), for which a large AHE was recently discovered experimentally. We further compare the AHE in Mn3Z and bcc Fe in terms of the CMP. We show that the AHE in Mn3Z is characterized with the magnetization of a cluster octupole moment in the same manner as that in bcc Fe characterized with the magnetization of the dipole moment.