Damped Topological Magnons in the Kagom\'{e}-Lattice Ferromagnets*

We demonstrate that interactions can substantially alter the free-band description of magnons in ferromagnets on geometrically frustrated lattices. The anharmonic coupling facilitated by the Dzyaloshinskii-Moriya interaction and a highly-degenerate structure of the two-particle continuum induce a non-perturbative damping of the high-energy magnon modes. We provide a detailed account of the effect for the $S\!=\!1/2$ ferromagnet on the kagom\'e lattice and propose further experiments.