Anomalous Hall effect in metallic collinear antiferromagnets

TL;DR

This paper presents minimal theoretical models of collinear antiferromagnets demonstrating the anomalous Hall effect, highlighting the role of symmetry-breaking and Dzyaloshinskii's invariants in these phenomena.

Contribution

It introduces and analyzes minimal models of Ne9el ordered collinear antiferromagnets showing the anomalous Hall effect, emphasizing the symmetry considerations and microscopic Berry curvature calculations.

Findings

Anomalous Hall effect arises from symmetry-breaking and Dzyaloshinskii's invariants.

Berry curvature calculations confirm the theoretical mechanisms.

Models include 2D square lattice and rutile lattice antiferromagnets.

Abstract

We propose and theoretically study minimal models of N\'{e}el ordered collinear (compensated) antiferromagnets that show the anomalous Hall effect. For simplicity, we first consider two-dimensional models of antiferromagnets with two magnetic sublattices on a square lattice. We provide explicit examples of a N\'{e}el ordered ferrimagnet and a Dzyaloshinskii weak ferromagnet. Then antiferromagnet on the rutile lattice, that belongs to the class of weak ferromagnets, is studied. We analyze Dzyaloshinskii's invariants for the existence of spontaneous magnetization in these N\'{e}el ordered systems. Microscopic calculations of the Berry curvature for the studied systems confirm the validity of these Dzyaloshinskii's invariants. It is shown that the anomalous Hall effect mechanism in these antiferromagnets arises either from the interplay of momentum-dependent exchange interaction of conducting fermions with the N\'{e}el order and the spin-orbit coupling. These physical processes originate from the broken symmetries that permit the Dzyaloshinskii's invariant in the system.