Crystal Field and Site Symmetry of Trivalent Cerium Ions in CaF2: The C4v and C3v Centers with Interstitial-Fluoride Charge Compensator

Abstract

Optical spectra of two ${\mathrm{Ce}}^{3+}$ impurity centers in Ca${\mathrm{F}}_2$ are described. The centers are those with charge compensation by ${\mathrm{F}}^{-}$ ions at the two interstitial sites nearest to the ${\mathrm{Ce}}^{3+}$ ion, one site in the direction of a $C_4$ axis of the lattice and the other site in the direction of a $C_3$ axis. The ultraviolet absorption and fluorescence spectra of the first, $C_{4v}$ center are described and analyzed in terms of crystal-field theory. The four broad absorption bands from the $4f\to 5d$ transitions are assigned to the $e$ and $t_2$ levels, and the splitting in the complete $C_{4v}$ crystal field is used to determine the $5d$ crystal-field parameters. From first-order $4f$ and $5d$ wave functions, the oscillator strength of the lowest-energy absorption band is predicted and is found to agree well with the measured value. The fluorescence spectrum of a low-concentration crystal of Ca${\mathrm{F}}_2$:${\mathrm{Ce}}^{3+}$ at liquid-helium temperture is described and found to arise mostly from transitions from the lowest $5d$ level of the $C_{4v}$ center to the $4f$ levels as split by the $C_{4v}$ crystal field. Vibrational sidebands of several of the zero-phonon lines in fluorescence are found to agree in detail with the vibrational sideband of the lowest-energy absorption line. Six of the seven $4f$ levels of the $C_{4v}$ center are assigned, and from them, in combination with $g$ factors of the ground state, are determined the $4f$ crystal-field parameters and the exact $4f$ wave functions. Transition probabilities predicted from these quantities agree with the observed line strengths in florescence. A very closely spaced pair of lines near 3118.5 Å is observed in some Ca${\mathrm{F}}_2$:${\mathrm{Ce}}^{3+}$ samples and is attributed to the second, $C_{3v}$ center. Support for this comes from the comparison of these lines and their hot band with the corresponding absorption in the oxide-compensated $C_{3v}$ center of Ca${\mathrm{F}}_2$:

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