Anomalous Hall effect in metallic collinear antiferromagnets
Abstract
We propose and theoretically study minimal models of N\'eel 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\'eel 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\'eel 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\'eel order and the spin-orbit coupling. These physical processes originate from the broken symmetries that permit the Dzyaloshinskii's invariant in the system.
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