Strong interactions between a nanomagnet and a microcavity mode

We consider the interaction of a nanomagnet with a single mode of a microcavity in a fully quantum treatment. We derive the interaction Hamiltonian from Maxwell's equations by introducing the fully quantized forms of the spherical electromagnetic solutions. For a nanomagnet acting as a macrospin, within a cavity roughly 1 mm$^3$ in volume, the magnet-microwave mode coupling is $\sim 10^{-7}$eV. Strong coupling can therefore be seen if the quality factor of the cavity exceeds 1000.