Abstract

We theoretically investigate the topological aspects of the magnon-phonon hybrid excitation in a simple two-dimensional (2D) square-lattice ferromagnet with perpendicular magnetic anisotropy [1]. Several distinguishing features of our model are as follows. Our model is optimized for atomically thin magnetic crystals, i.e., 2D magnets. The recent discovery of magnetism in 2D van der Waals materials opens huge opportunities for investigating unexplored rich physics and future spintronic devices in reduced dimensions [2,3]. In our 2D model, we ignore the nonlocal dipolar interaction, which is not a precondition for a finite Berry curvature in 2D magnets. Moreover, the Berry curvature we find requires neither a special spin asymmetry such as the Dzyaloshinskii-Moriya interaction (DMI) nor a special lattice symmetry: Our 2D model description is applicable for general thin-film ferromagnets. Therefore, we show that even without such long-range dipolar interaction, DMI, or special lattice symmetry, the nontrivial topology of a magnon-phonon hybrid can emerge by taking account of the well-known magnetoelastic interaction originates from the magnetocrystalline anisotropy. Because the magnetocrystalline anisotropy is ubiquitous in ferromagnetic thin-film structures, our result does not rely on specific preconditions and thus is quite generic. Furthermore, we show that the topological structures of the magnon-polaron bands can be manipulated by effective magnetic fields via topological phase transition. We uncover the origin of the nontrivial topological bands by mapping our model to the well-known two-band model for topological insulators [4], where the Chern numbers are read by counting the number of topological textures, called skyrmions, of a certain vector in momentum space. In this picture, the magnon-phonon hybridization induces the chiral texture of the momentum space vector. As an experimental probe for our theory, we propose the thermal Hall conductivity [Fig. 2]. **

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