Three-dimensional topological magnon systems

We propose a class of models for a magnonic analog of topological insulators in three dimensions. The models have pseudo-time-reversal symmetry which ensures the existence of bosonic Kramers pairs. We define a set of $\mathbb{Z}_2$ topological invariants that characterizes different topological phases and determines the presence or absence of surface Dirac cones. This is demonstrated by considering a bosonic counterpart of the Fu-Kane-Mele model on a diamond lattice. The model is found to exhibit three distinct phases analogous to strong topological, weak topological, and trivial insulator phases of the original fermionic model. We also discuss a possible realization of the thermal Hall effect of surface magnons in the presence of a magnetic field in proximity to a normal ferromagnet.