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

We report measurements of the spin-lattice relaxation rate T₁^-1 for several magnetically dilute rare-earth ions in the temperature range 1.2^∘T5^∘K, using the transient recovery of the microwave paramagnetic resonance in the frequency range 8ν18 Gc/sec. Data are given for Sm³⁺ and Dy³⁺ in the double nitrate La₂{Mg}₂(NO₃)₁₂.24H₂O; for Pr³⁺, Sm³⁺, and Er³⁺ in the ethyl sulfate La(C₂H₅SO₄)₃.9H₂O; and for Ce³⁺, Nd³⁺, Pr³⁺, Sm³⁺, Er³⁺, and Tb³⁺ in the ethyl sulfate Y(C₂H₅SO₄)₃.9H₂O. We observe the temperature dependence for the direct process T₁^-1∝T; for the Orbach process T₁^-1∝exp(-ΔT); and for the Raman process T₁^-1∝T⁷ or T⁹. 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 Tb^-1∝T² rather than the direct process. In several cases the Orbach process determines a previously unknown value of the crystal-field splitting Δ, while in some cases it shows that the value of Δ in the dilute salt is significantly different from the value determined optically in the concentrated salt.