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
C
3
symmetry, the phase factor ± ϕ
caused by the next nearest-neighbor Dzyaloshinskii–Moriya interaction
breaks the pseudo-spin time-reversal symmetry
scriptT
, which leads
to the split of magnon bands,
i.e., the emergence of TMIs with a nonzero Chern number of
scriptC
=
prefix−
1
, in experimentally feasible
candidates
of MoI3, CrSiTe3, and CrGeTe3 monolayers.
Moreover, protected by the
C
3
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.