Temperature and Magnetic Field Dependence of the Spin-Lattice Relaxation Rates for ${\mathrm{Er}}^{3+}$, ${\mathrm{Pr}}^{3+}$, and ${\mathrm{Tb}}^{3+}$ in Anhydrous La${\mathrm{Cl}}_3$

Using the plused-saturation technique at 15.4 GHz, we measured the spin-lattice relaxation rates of La${\mathrm{Cl}}_3$:Er, La${\mathrm{Cl}}_3$:Pr, and La${\mathrm{Cl}}_3$:Tb over the temperature range 0.24-4.2°K and analyzed the results within the framework of the Van Vleck—Orbach theory. In addition, from measurements at about 9 GHz made by us and by others on some of the same samples, we obtained information on the magnetic field (or frequency) dependence of the various terms in the relaxation-rate expression. For the erbium and terbium systems, the temperature dependence was consistent with the simple theory. However, for the praseodymium system, a "phonon bottleneck" apparently occurred at low temperatures. The variation of the relaxation rate with the microwave frequency was in agreement with theory for the Kramers ion ${\mathrm{Er}}^{3+}$, and consistent with theory for the bottlenecked non-Kramers ion ${\mathrm{Pr}}^{3+}$. The non-Kramers ion ${\mathrm{Tb}}^{3+}$ has a somewhat unusual frequency dependence, theoretically, due to the splitting of its ground doublet by the La${\mathrm{Cl}}_3$ crystal field. The experimental frequency dependence for this ion was in substantial agreement with theory for the Raman and Orbach rates, but not quite as strong as predicted for the direct rate.