Large Chern-Number Quantum Anomalous Hall Effect from Canted Antiferromagnetic Order in $d$-Electron System on Kagome Lattice

Electrons of $d$-symmetry interacting with a localized non-collinear antiferromagnetic spin order on a kagome lattice are considered. Even in the absence of an external magnetic field, spin-orbit coupling or relativistic effects, the spin texture produces a non-trivial intrinsic Berry curvature. This opens the route for a quantum anomalous Hall effect in the $d$-system. 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 $e^2/h$. This canted configuration gives rise to the maximal possible Chern number, $C=\pm 5$ when the Fermi level is within nontrivial gap. The effect is best understood for -- but not limited to -- isotropic $d$-electron hopping and degenerate $d$-levels. In this case, analytic expressions are available and point to a topological origin for the manifestation of the maximal $C$. Numerical calculations show that these findings are robust to some anisotropy in the hopping integrals and to moderate splittings of the $d$ levels. The $C=\pm 5$ plateau can be split into Chern peaks with smaller integers by varying the onsite energies. The 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 quantum information.