Phonon-bottlenecked spin relaxation of Er³⁺:Y₂SiO₅at sub-kelvin temperatures

We report on electron spin relaxation measurements of Er3+ dopants in a Y2SiO5 crystal using an electron paramagnetic resonance spectrometer based on a Josephson bifurcation amplifier. We observed the change in the induced flux as a function of time for two spin transitions (at different crystallographic sites) after an excitation microwave pulse or a change in the static magnetic field. Low-microwave-power measurements showed relaxation times of approximately 10 h at 20 mK, and 1/T1 followed a T2 dependence between 30 and 200 mK. We observed no difference in behavior between the two transitions. The microwave power and temperature dependences suggest that a phonon-bottleneck-like process limits relaxation.