Phonon traffic jams slow down erbium spin relaxation at ultralow temperatures

Spin-lattice relaxation in Er³⁺:CaWO₄ was measured at millikelvin temperatures using a superconducting resonator with a small mode volume. At high magnetic fields, relaxation times grow with the number of excited spins and follow a distinctive tanh²(ℏω₀/k_BT) temperature dependence—the hallmark of a phonon bottleneck, where emitted phonons cannot escape the crystal fast enough and are reabsorbed. The finding matters for quantum technologies using rare-earth spin ensembles as quantum memories or transducers, where this bottleneck could degrade or extend coherence depending on the operating regime.