Topological magnon insulator in insulating ferromagnet

In the ferromagnetic insulator with the Dzyaloshinskii-Moriya interaction, we theoretically predict and numerically verify a topological magnon insulator, where the charge-free magnon is topologically protected for transporting along the edge/surface while it is insulating in the bulk. The chiral edge states form a connected loop as a 4π- or 8π-period M\"obius strip in the spin-wave vector space, showing the nontrivial topology of magnonic bands. Using the nonequilibrium Green's function method, we explicitly demonstrate that the one-way chiral edge transport is indeed topologically protected from defects or disorders. Moreover, we show that the topological edge state mainly localizes around edges and leaks into the bulk with oscillatory decay. Although the chiral edge magnons and energy current prefer to travel along one edge from the hot region to the cold one, the anomalous transports are identified in the opposite edge, which reversely flow from the cold region to the hot one. Our findings could be validated within wide energy ranges in various magnonic crystals, such as Lu₂V₂O₇.