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We study the collective dynamics of two distant magnets coherently coupled byacoustic phonons that are transmitted through an intercalated crystal. Bytuning the ferromagnetic resonances of the two magnets to an acoustic resonanceof the crystal, we control a coherent three levels system. We show that theparity of the phonon mode governs the nature of the indirect coupling betweenthe magnets: the resonances with odd / even phonon modes correspond toout-of-phase / in-phase lattice displacements at the magnets, leading to bright/ dark states in response to uniform microwave magnetic fields, respectively.The sample is a tri-layer garnet consisting of two thin magnetic layersepitaxially grown on both sides of a half-millimeter thick non-magnetic singlecrystal. In spite of the relatively weak magneto-elastic interaction, the longlifetimes of the magnon and phonon modes in the sample are the key to unveilthis long range strong coupling. This demonstrates that garnets are a greatplatform to study multi-partite hybridization process between magnon andphonons at microwave frequencies.

Bright and dark states of two distant macrospins strongly coupled by phonons