  We predict the existence of Einstein-de Haas effect in topological magnon
insulators. Temperature variation of angular momentum in the topological state
shows a sign change behavior, akin to the low temperature thermal Hall
conductance response. This manifests itself as a macroscopic mechanical
rotation of the material hosting topological magnons. We show that an
experimentally observable Einstein-de Haas effect can be measured in the
square-octagon, the kagome, and the honeycomb lattices. Albeit, the effect is
the strongest in the square-octagon lattice. We treat both the low and the high
temperature phases using spin wave and Schwinger boson theory, respectively. We
propose an experimental set up to detect our theoretical predictions. We
suggest candidate square-octagon materials where our theory can be tested.
