Spin-Lattice Relaxation in Some Rare-Earth Salts. I. Temperature Dependence

We report measurements of the spin-lattice relaxation rate ${T_1}^{-1\mathrm{}}$ for several magnetically dilute rare-earth ions in the temperature range $1.2°\leqq T\leqq 5°$K, using the transient recovery of the microwave paramagnetic resonance in the frequency range $8\leqq \nu \leqq 18$ Gc/sec. Data are given for ${\mathrm{Sm}}^{3+}$ and ${\mathrm{Dy}}^{3+}$ in the double nitrate ${\mathrm{La}}_2$${\mathrm{Mg}}_2$${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$.24${\mathrm{H}}_2$O; for ${\mathrm{Pr}}^{3+}$, ${\mathrm{Sm}}^{3+}$, and ${\mathrm{Er}}^{3+}$ in the ethyl sulfate La${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$.9${\mathrm{H}}_2$O; and for ${\mathrm{Ce}}^{3+}$, ${\mathrm{Nd}}^{3+}$, ${\mathrm{Pr}}^{3+}$, ${\mathrm{Sm}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Tb}}^{3+}$ in the ethyl sulfate Y${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$.9${\mathrm{H}}_2$O. We observe the temperature dependence for the direct process ${T_1}^{-1\mathrm{}}\propto T$; for the Orbach process ${T_1}^{-1\mathrm{}}\propto \exp (-\frac{\Delta }{T})$; and for the Raman process ${T_1}^{-1\mathrm{}}\propto T^7 or T^9$. The magnitudes of the processes are in reasonable agreement with simple theoretical estimates. The observed rates are shown to be independent of paramagnetic ion concentration in the range 0.1 to 1%. For Pr in the ethyl sulfate, we observe, as expected, a phonon bottleneck rate ${T_b}^{-1\mathrm{}}\propto T^2$ rather than the direct process. In several cases the Orbach process determines a previously unknown value of the crystal-field splitting $\Delta$, while in some cases it shows that the value of $\Delta$ in the dilute salt is significantly different from the value determined optically in the concentrated salt.