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

Abstract

The temperature dependence of the spin-lattice relaxation time $T_1$ of trivalent rare-earth impurities in Ca${\mathrm{F}}_2$ has been measured at 9.6 kMc/sec using pulse saturation techniques. The rare earths investigated include Kramers ions (${\mathrm{Ce}}^{3+}$, ${\mathrm{Nd}}^{3+}$, ${\mathrm{Dy}}^{3+}$, ${\mathrm{Er}}^{3+}$, ${\mathrm{Yb}}^{3+}$), one non-Kramers ion (${\mathrm{Tb}}^{3+}$), and one $S$-state ion (${\mathrm{Gd}}^{3+}$). 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 $T^{-1\mathrm{}}$ 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 ${\mathrm{Ce}}^{3+}$ relaxation in five samples containing from 0.08 to 1.6% Ce combined with results from other ions show that $T_1$ 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.