Coupled Electronic and Magnonic Topological States in Two-Dimensional Ferromagnets.

Magnetic materials offer a fertile playground for fundamental physics discovery, with not only electronic but also magnonic topological states intensively explored. However, one natural material with both electronic and magnonic nontrivial topologies is still unknown. Here, we demonstrate the coexistence of first-order topological magnon insulators (TMIs) and electronic second-order topological insulators (SOTIs) in 2D honeycomb ferromagnets, giving rise to the nontrivial corner states being connected by the charge-free magnonic edge states. We show that, with C3 symmetry, the phase factor ± ϕ caused by the next nearest-neighbor Dzyaloshinskii-Moriya interaction breaks the pseudo-spin time-reversal symmetry T, which leads to the split of magnon bands, i.e., the emergence of TMIs with a nonzero Chern number of C=-1, in experimentally feasible candidates of MoI3, CrSiTe3, and CrGeTe3 monolayers. Moreover, protected by the C3 symmetry, the electronic SOTIs characterized by nontrivial corner states are obtained, bridging the topological aspect of fermions and bosons with a high possibility of innovative applications in spintronics devices.