Analysis of the optical spectrum ofTm3+in LiYF4

Abstract

Absorption and fluorescence spectra of ${\mathrm{Tm}}^{3+}$ in single-crystal LiY${\mathrm{F}}_4$ were recorded at temperatures between 5 and 77 K. The energy levels for the ground configuration were established from these data with the aid of theoretical calculations. Parameters were obtained that gave a least-squares deviation of 16.9 ${\mathrm{cm}}^{-1\mathrm{}}$ between the experimental and calculated energy levels. These calculated levels were obtained by diagonalizing a Hamiltonian that describes the free-ion and crystal-field interactions in a basis of states spanning the $4f^{12}$ configuration. The free-ion parameters are $F_2=462.49\mathrm{}$, $F_4=70.762\mathrm{}$, $F_6=7.6265\mathrm{}$, $\zeta =2652.8\mathrm{}$, $\alpha =23.262\mathrm{}$, $\beta =-761.64\mathrm{}$, $M_0^{\mathrm{}\left(0\right)\mathrm{}}=3.2459\mathrm{}$, $M^{\mathrm{}\left(0\right)\mathrm{}}=1.4608\mathrm{}$, $M^{\mathrm{}\left(2\right)\mathrm{}}=0.8202\mathrm{}$, and $M^{\mathrm{}\left(4\right)\mathrm{}}=0.5572\mathrm{}$, and the crystal-field parameters are $B_{20}=358.7\mathrm{}$, $B_{40}=-607.8\mathrm{}$, $B_{60}=-173.0\mathrm{}$, $B_{44}=844.2\mathrm{}$, and $B_{64}=629.2\mathrm{}$ (all units are ${\mathrm{cm}}^{-1\mathrm{}}$). The calculated and crystal-field-split energy levels were in agreement to within 9 ${\mathrm{cm}}^{-1\mathrm{}}$ after the calculated energy centroids were adjusted. The $S_4$ symmetry property of the ground state was determined to be ${\Gamma }_2$.