| Summary: | We study the collective dynamics of two distant magnets coherently coupled by acoustic phonons that are transmitted through a nonmagnetic spacer. By tuning the ferromagnetic resonances of the two magnets to an acoustic resonance of the intermediate, we control a coherent three-level system. We show that the parity of the phonon mode governs the indirect coupling between the magnets: the resonances with odd (even) phonon modes correspond to out-of-phase (in-phase) lattice displacements at the interfaces, leading to bright (dark) states in response to uniform microwave magnetic fields, respectively. The experimental sample is a trilayer garnet consisting of two thin magnetic films epitaxially grown on both sides of a half-millimeter-thick nonmagnetic single crystal. In spite of the relatively weak magnetoelastic interaction, the long lifetimes of the magnon and phonon modes are the key to unveil strong coupling over a macroscopic distance, establishing the value of garnets as a platform to study multipartite hybridization processes at microwave frequencies.
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