Topological Hall Response from Canted Antiferromagnetic Order in $d$-Electron Kagome Systems

Abstract

In a two-dimensional kagome monolayer, a nontrivial intrinsic Berry curvature may arise in the $d$-electron system from the interaction with a non-collinear spin order induced by an underlying antiferromagnetic exchange. This opens the route for a quantum anomalous Hall effect in the multi-orbital system, even without an external magnetic field, explicit spin-orbit coupling or relativistic effects. For spin orders with an out-of-plane component, the scalar spin chirality is finite, and the integration of the Berry curvature over the Brillouin zone may yield integer Hall conductivities in units of $e^2/h$. For a Fermi level within a nontrivial gap, the canted configuration offers, at least in principle, the possibility of a maximal Chern number, $C=\pm 5$. Candidate materials are considered in this paper. In existing materials, the electron hopping is generally highly anisotropic, leading to a quantum anomalous Hall effect with smaller Chern numbers. A topological phase transition between Hall plateaus of opposite $C$ can be driven by flipping the out-of-plane component of the spin order, alluding to the potential of this system to applications in quantum information.