Paramagnetic Resonance and Relaxation of Trivalent Rare-Earth Ions in Calcium Fluoride. II. Spin-Lattice Relaxation

The temperature dependence of the spin-lattice relaxation time T₁ of trivalent rare-earth impurities in CaF₂ has been measured at 9.6 kMc/sec using pulse saturation techniques. The rare earths investigated include Kramers ions (Ce³⁺, Nd³⁺, Dy³⁺, Er³⁺, Yb³⁺), one non-Kramers ion (Tb³⁺), and one S-state ion (Gd³⁺). The relaxation of ions in lattice sites of cubic, tetragonal, and trigonal crystal-field symmetries have been studied and are found to be different. At liquid-helium temperatures the relaxation usually exhibits a T^-1 temperature dependence; however, the magnitudes are approximately two orders-of-magnitude shorter than estimated single-phonon relaxation times based upon the orbit-lattice interaction. Measurements of the Ce³⁺ relaxation in five samples containing from 0.08 to 1.6% Ce combined with results from other ions show that T₁ decreases with increasing rare-earth concentration. Multiple exponential recoveries from saturation are observed at low temperatures and are discussed with respect to possible cross-relaxation within inhomogeneous spin systems and to other faster relaxing systems. At higher temperatures examples of both Raman and Orbach two-phonon relaxation processes are found. Calculations of two-phonon relaxation times using estimated values of the dynamic crystal fields, energy level structures, and ion wave functions yield coarse order-of-magnitude agreement with experimental values.