Topological magnon insulator in insulating ferromagnet

TLDR

Chiral edge states form a Möbius‑strip loop in spin‑wave vector space, indicating nontrivial magnon band topology. The study predicts and verifies a topological magnon insulator in a ferromagnetic insulator with Dzyaloshinskii‑Moriya interaction, where charge‑free magnons are protected along edges but insulating in the bulk. Using nonequilibrium Green’s function calculations, the authors demonstrate that one‑way chiral edge transport is topologically protected against defects and can be validated across wide energy ranges in magnonic crystals such as Lu₂V₂O₇. The topological edge state localizes at the edges with oscillatory bulk decay, and chiral magnons preferentially move from hot to cold along one edge while anomalous transport flows oppositely on the other edge.

Abstract

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 $4\ensuremath{\pi}$- or $8\ensuremath{\pi}$-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 Lu${}_{2}$V${}_{2}$O${}_{7}$.