Dirac surface states in magnonic analogs of topological crystalline insulators

We propose magnonic analogs of topological crystalline insulators which possess Dirac surface states protected by the combined symmetry of time-reversal and half translation. Constructing models of the topological magnon systems, we demonstrate that the energy current flows through the systems in response to an electric field, owing to the Dirac surface states with the spin-momentum locking. We also propose a realization of the magnonic analogs of topological crystalline insulators in a magnetic compound CrI${}_3$ with a monoclinic structure.