  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.

Mesoscale and Nanoscale Physics