Cavity-mediated coherent coupling of magnetic moments

We demonstrate the long-range strong coupling of magnetostatic modes in spatially separated ferromagnets mediated by a microwave frequency cavity. Two spheres of yttrium iron garnet are embedded in the cavity and their magnetostatic modes probed using a dispersive measurement technique. We find they are strongly coupled to each other even when detuned from the cavity modes, and investigate the dependence of the magnet-magnet coupling on the cavity detuning. Dark states of the coupled magnetostatic modes of the system are observed, and ascribed to mismatches between the symmetries of the modes and the drive field.