We propose a concept of three-dimensional topological magnon systems which are the magnonic analog of topological insulators in three dimensions. 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. The validity of the classification scheme based on these ${\mathbb{Z}}_2$ invariants is demonstrated by considering three concrete examples. One of them is a bosonic counterpart of the Fu-Kane-Mele model on a diamond lattice, which 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. The topological characterization in this paper can also be applied to other systems, such as spin liquids or paramagnets, described by Schwinger bosons.

• Received 9 July 2019
• Revised 1 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.144401