Bright and Dark States of Two Distant Macrospins Strongly Coupled by Phonons

Abstract

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.