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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. We investigate the dependence of the magnet-magnet coupling on the cavity detuning $Δ$, and find a $1/Δ$ dependence also characteristic of cavity-coupled superconducting qubits. 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.