Anomalous Hall Effect in Metallic Collinear Antiferromagnets

We propose and theoretically study minimal models of Néel 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 Néel 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 Néel 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 from the interplay of momentum-dependent exchange interaction of conducting fermions with the Néel order and the spin-orbit coupling. These physical processes originate from the broken symmetries that permit the Dzyaloshinskii’s invariant in the system.