Breakdown of chiral edge modes in topological magnon insulators

Topological magnon insulators (TMI) are ordered magnets supporting chiral edge magnon excitations. These edge states are envisioned to serve as topologically protected information channels in low-loss magnonic devices. The standard description of TMI is based on linear spin-wave theory (LSWT), which approximates magnons as free noninteracting particles. However, magnon excitations of TMI are genuinely interacting even at zero temperature, calling into question descriptions based on LSWT alone. Here we perform a detailed nonlinear spin-wave analysis to investigate the stability of chiral edge magnons. We identify three general breakdown mechanisms: (1) The edge magnon couples to itself, generating a finite lifetime that can be large enough to lead to a spectral annihilation of the chiral state. (2) The edge magnon hybridizes with the extended bulk magnons and, as a consequence, delocalizes away from the edge. (3) Due to a bulk-magnon mediated edge-to-edge coupling, the chiral magnons at opposite edges hybridize. We argue that, in general, these breakdown mechanisms may invalidate predictions based on LSWT and violate the notion of topological protection. We discuss strategies how the breakdown of chiral edge magnons can be avoided, e.g., via the application of large magnetic fields. Our results highlight a challenge for the realization of chiral edge states in TMI and in other bosonic topological systems without particle number conservation.