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

We study the collective dynamics of two distant magnets coherently coupled by acoustic phonons that are transmitted through an intercalated crystal. By tuning the ferromagnetic resonances of the two magnets to an acoustic resonance of the crystal, we control a coherent three levels system. We show that the parity of the phonon mode governs the nature of the indirect coupling between the magnets: the resonances with odd / even phonon modes correspond to out-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 layers epitaxially grown on both sides of a half-millimeter thick non-magnetic single crystal. In spite of the relatively weak magneto-elastic interaction, the long lifetimes of the magnon and phonon modes in the sample are the key to unveil this long range strong coupling. This demonstrates that garnets are a great platform to study multi-partite hybridization process between magnon and phonons at microwave frequencies.