Topological Magnon-Phonon Hybrid Bands in Ferromagnetic Skyrmion Crystals

We investigate magnon-phonon (MP) excitations in a Neel-type two-dimensional ferromagnetic skyrmion crystal (SkX) stabilized on a triangular spin lattice by Dzyaloshinskii-Moriya interaction (DMI). Although the lowest two magnon bands of the bare SkX are topologically trivial, we show that coupling to lattice vibrations reconstructs the low-energy sector and generates topological MP hybrid bands. Starting from a spin-lattice Hamiltonian in which phonons couple to magnons through fluctuations of the DMI vectors, we derive the bosonic Hamiltonian for the SkX and compute the hybrid band structure by Bogoliubov diagonalization. MP coupling opens gaps at low-energy magnon-phonon crossings, lifts phonon degeneracies associated with supercell folding, and yields nontrivial Chern numbers for the lowest hybrid bands. The resulting low-energy topology and associated edge states remain robust under magnetic-field variation, while higher-energy hybrid bands can undergo field-driven topological phase transitions. These results extend topological magnon-phonon hybridization to noncoplanar SkXs.