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We theoretically investigate magnon-phonon hybrid excitations intwo-dimensional ferromagnets. The bulk bands of hybrid excitations, which arereferred to as magnon-polarons, are analytically shown to be topologicallynontrivial, possessing finite Chern numbers. We also show that the Chernnumbers of magnon-polaron bands and the number of band-crossing lines can bemanipulated by an external magnetic field. For experiments, we propose to usethe thermal Hall conductivity as a probe of the finite Berry curvatures ofmagnon-polarons. Our results show that a simple ferromagnet on a square latticesupports topologically nontrivial magnon-polarons, generalizing topologicalexcitations in conventional magnetic systems.

Topological Magnon-Phonon Hybrid Excitations in Two-Dimensional Ferromagnets with Tunable Chern Numbers