Dirac surface states in topological crystalline magnon insulators

The physics of topologically nontrivial magnon states provides a new perspective on transport phenomena in magnetic materials. However, few topological magnon materials in three-dimensions are considered. This is partly because it is difficult to find out symmetries that would protect the surface state topologically due to Bose statistics.
In this study, we propose magnetic models having magnon surface states with Dirac dispersion. The magnon surface states are topologically protected by the combined symmetry of time reversal and half translation, which is naturally satisfied in antiferromagnets with a stacked structure. The models we proposed are, thus, examples of magnonic analogs of topological crystalline insulators [1]. In addition, we show that the energy current flows through the system in response to an electric field. We propose a realization of magnonic analogs of topological crystalline insulators in a magnetic compound CrI₃ [2] with a monoclinic structure.
[1] L. Fu, Phys. Rev. Lett. 106, 106802 (2011).
[2] M. A. McGuire, H. Dixit, V. R. Cooper, and B. C. Sales, Chemistry of Materials 27, 612-620 (2015).