  Coherent conversion of photons to magnons, and back, provides a natural
mechanism for rapid control of interactions between stationary spins with long
coherence times and high-speed photons. Despite the large frequency difference
between optical photons and magnons, coherent conversion can be achieved
through a three-particle interaction between one magnon and two photons whose
frequency difference is resonant with the magnon frequency, as in optomechanics
with two photons and a phonon. The large spin density of a transparent
ferromagnetic insulator (such as the ferrite yttrium iron garnet) in an optical
cavity provides an intrinsic photon-magnon coupling strength that we calculate
to exceed reported optomechanical couplings. A large cavity photon number and
properly selected cavity detuning produce a predicted effective coupling
strength sufficient for observing electromagnetically induced transparency and
the Purcell effect, and even to reach the ultra-strong coupling regime.
