Ultrahigh cooperativity interactions between magnons and resonant photons in a YIG sphere

Resonant photon modes of a 5-mm-diameter yttrium iron garnet (YIG) sphere loaded in a cylindrical cavity in the 10-30-GHz frequency range are characterized as a function of applied dc magnetic field at millikelvin temperatures. The photon modes are confined mainly to the sphere and exhibited large mode filling factors in comparison to previous experiments, allowing ultrastrong coupling with the magnon spin-wave resonances. The largest observed coupling between photons and magnons is 2g/2 pi = 7.11 GHz for a 15.5-GHz mode, corresponding to a cooperativity of C = 1.51 +/- 0.47 x 10(7). Complex modifications, beyond a simple multioscillator model, of the photon mode frequencies were observed between 0 and 0.1 T. Between 0.4 and 1 T, degenerate resonant photon modes were observed to interact with magnon spin-wave resonances with different coupling strengths, indicating time-reversal symmetry breaking due to the gyrotropic permeability of YIG. Bare dielectric resonator mode frequencies were determined by detuning magnon modes to significantly higher frequencies with strong magnetic fields. By comparing measured mode frequencies at 7 T with finite element modeling, a bare dielectric permittivity of 15.96 +/- 0.02 of the YIG crystal has been determined at about 20 mK.