Dual Chern Insulators with Electronic and Magnonic Edge States in Two-Dimensional Ferromagnets

Chern insulator (CI) exhibits rich physics with great interest in both theory and experiment. Here, we focus on the honeycomb and kagome ferromagnets and demonstrate that coupling the nontrivial electronic and magnonic bands allows for the dual CIs, where the quantum anomalous Hall effect and its bosonic analogue, i.e., topological magnon insulator, appear simultaneously within one two-dimensional (2D) ferromagnet. Both the tight-binding model and Heisenberg-DM model are constructed to demonstrate the feasibility of attaining the dual CIs and point out the perspectives of dual CIs for spin-orbit coupling and the Dzyaloshinskii-Moriya interaction. Moreover, based on Chern number, topological quantum chemistry, and edge state analysis, we explore the emergence and stability of such dual CIs in realistic 2D ferromagnets, which is expected to draw great experimental attentions.