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.

At the lowest temperatures, where the direct process dominates, we observe in the double nitrate several instances of a spin-bath relaxation rate ${T_b}^{-1\mathrm{}}$ which is not the direct spin-lattice (i.e., spin-phonon) process, but rather a slower phonon-limited "bottle-neck" process, with a temperature dependence ${T_b}^{-1\mathrm{}}\propto T^2$. This dependence along with that on crystal size and paramagnetic ion concentration is in good agreement with simple theoretical expectations. The data indicate that the hot phonon-bath relaxation time is the time taken by sound waves to traverse the crystal half-thickness. For 1% Pr in the double nitrate at 1.4°K the bottleneck is severe, the observed rate ${T_b}^{-1\mathrm{}}$ being ∼${10}^3$ times smaller than the true direct rate ${T_1}^{-1\mathrm{}}$.

• Received 19 February 1962

DOI:https://doi.org/10.1103/PhysRev.127.32