Phonon-bottlenecked spin relaxation of Er${}^{3+}$:CaWO${}_4$ at milliKelvin temperatures

Abstract

We study spin-lattice relaxation times of electron spins in Er${}^{3+}$:CaWO${}_4$ at millikelvin temperature, detected via their coupling to a low-mode volume superconducting resonator. At large magnetic field supporting strong phonon-emission rates, we observe a noticeable increase in relaxation times with increasing spin-excitations, which exhibit a unique $[\tanh (\hslash {\omega }_0/k_{\text{B}}T){]}^2$ temperature dependence. These observations are typical of a phonon-bottlenecked spin relaxation, and have implications for quantum technologies that exploit rare-earth spin ensembles as coherent resources.

9 pages, 10 figures including supplementary information