Spectroscopic analysis of lithium terbium tetrafluoride

The absorption spectra of ${\mathrm{Tb}}^{3+}$ in LiTb${\mathrm{F}}_4$ have been recorded in the spectral interval from 4000 to 25000 ${\mathrm{cm}}^{-1\mathrm{}}$ and for temperatures between 2.3 and 150 K. This covers the transitions from the ground multiplet ${}_{}{}^7{}_{}{}^{}F_6^{}{}_{}{}^{}$ to the multiplets ${}_{}{}^7{}_{}{}^{}F_3^{}{}_{}{}^{}$, ${}_{}{}^7{}_{}{}^{}F_2^{}{}_{}{}^{}$, ${}_{}{}^7{}_{}{}^{}F_1^{}{}_{}{}^{}$, ${}_{}{}^7{}_{}{}^{}F_0^{}{}_{}{}^{}$, and ${}_{}{}^5{}_{}{}^{}D_4^{}{}_{}{}^{}$. The transitions were predominantly of electric-dipole nature, but small contributions of magnetic-dipole nature were seen. The crystal-field splitting was temperature dependent—the reason for this is not completely understood. No experimental evidence for a crystallographic phase transition was found. The energy levels of the ground ${}_{}{}^7{}_{}{}^{}F$ term were calculated by diagonalizing an effective spin-orbit and crystal-field Hamiltonian in an $\mathrm{LS}$ basis. $H=\Sigma {\lambda }_i{\left(\overrightarrow{\mathrm{L}}·\overrightarrow{\mathrm{S}}\right)}^i+\Sigma {\alpha }_i\Sigma B_{\mathrm{im}}{O}_{\mathrm{im}}$, where the parameters ${\lambda }_i$ are functions of the spin-orbit parameter $\zeta$ and the Slater parameter $F_2$. The $O_{\mathrm{im}}$ and ${\alpha }_i$ are Racah operators and reduced matrix elements, respectively. The rare-earth site in LiTb${\mathrm{F}}_4$ possesses $S_4$ symmetry, which allows six crystal-field parameters. $\zeta$ and the six $B_{\mathrm{im}}$ were varied to obtain the best agreement with the experimentally observed levels. Keeping $F_2=434\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ fixed, a fit with a standard deviation of 12 ${\mathrm{cm}}^{-1\mathrm{}}$ was obtained at 10 K with the following parameters: $\zeta =1698\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $B_{20}=445\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $B_{40}=-761\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $B_{44}=1120\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $B_{60}=4\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $B_{64}=761+i609\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Although the ground $\mathrm{LS}$ term of ${\mathrm{Tb}}^{3+}$ is rather isolated, the term mixing is significant, which is also the case for the multiplet mixing. Even for the ground multiplet the $J$ mixing cannot be ignored.