Paramagnetic Resonance and Relaxation of Trivalent Rare-Earth Ions in Calcium Fluoride. I. Resonance Spectra and Crystal Fields

Abstract

The energy level structures arising from the crystal-field splitting of the free-ion ground states of trivalent rare-earth ions in Ca${\mathrm{F}}_2$ are determined from a survey of the optical and electron paramagnetic resonance spectra. The predicted ground states are in agreement with existing paramagnetic resonance data. Estimates are made of the magnitude of the cubic crystal-field parameters and their variation throughout the rare-earth series. Axial crystal fields of tetragonal and trigonal symmetries, due to nearest-neighbor charge compensation, are found to cause large perturbations on the cubic-field energy levels. The paramagnetic resonance spectra of all rare-earth ions are reviewed and new resonances for ${\mathrm{Ce}}^{3+}$, ${\mathrm{Sm}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Yb}}^{3+}$ are reported. Expressions for the calculation of crystal-field matrix elements in terms of $3-j$ and $6-j$ symbols and their relationship to the operator equivalent approach are given in an Appendix.