  Resonant photon modes of a 5mm diameter YIG sphere loaded in a cylindrical
cavity in the 10-30GHz frequency range are characterised 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 $C=1.51\pm0.47\times10^7$. Complex modifications beyond a
simple multi-oscillator model, of the photon mode frequencies were observed
between 0 and 0.1 Tesla. Between 0.4 to 1 Tesla, degenerate resonant photon
modes were observed to interact with magnon spin wave resonances with different
couplings 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 Tesla with
Finite Element modelling, a bare dielectric permittivity of $15.96\pm0.02$ of
the YIG crystal has been determined at about $20$ mK.
