  Electromagnetic properties of single crystal terbium gallium garnet (TGG) are
characterised from room down to millikelvin temperatures using the whispering
gallery mode method. Microwave spectroscopy is performed at low powers
equivalent to a few photons in energy and conducted as functions of the
magnetic field and temperature. A phase transition is detected close to the
temperature of 3.5 K. This is observed for multiple whispering gallery modes
causing an abrupt negative frequency shift and a change in transmission due to
extra losses in the new phase caused by a change in complex magnetic
susceptibility.
