Spin-Lattice Relaxation in Some Rare-Earth Salts at Helium Temperatures; Observation of the Phonon Bottleneck

By observing the transient recovery of microwave paramagnetic resonance signals at $\nu \approx 9.3$ kMc/sec and $\nu \approx 34$ kMc/sec, we measure the spin-lattice relaxation rate ${T_1}^{-1\mathrm{}}$ for the rare earth ions Nd, Pr, and Sm in the double nitrate [${\mathrm{La}}_2$ ${\mathrm{Mg}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·24${\mathrm{H}}_2$O] and for Ce and Nd in the ethyl sulfate [La${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$·9${\mathrm{H}}_2$O] in the temperature range $1.4°<T<\mathrm{}5\mathrm{}°$K. We observe the direct process, ${T_1}^{-1\mathrm{}}\propto T$; the Orbach process, ${T_1}^{-1\mathrm{}}\propto \exp (-\frac{\Delta }{\mathrm{kT}})$; and the Raman process, ${T_1}^{-1\mathrm{}}\propto T^7$ and $T^9$. The measured relaxation rates are in good agreement with simple theoretical estimates based on Orbach's phenomenological approach. For example, for 1% Nd in the ethyl sulfate with $z\perp H$ at $\nu =9.3\mathrm{}$ kMc/sec we measure ${T_1}^{-1\mathrm{}}=1.7T+3.6\mathrm{}\times {10}^{-4\mathrm{}}{T}^9$ ${\sec }^{-1\mathrm{}}$, as compared to the theoretical estimate, ${T_1}^{-1\mathrm{}}=1.4T+1.3\mathrm{}\times {10}^{-4\mathrm{}}{T}^9$ ${\sec }^{-1\mathrm{}}$. The data, together with similar measurements by others, lead to the over-all conclusion that spin-lattice relaxation at low temperatures in rare earth salts is reasonably well understood.