Spectroscopic analysis of lithium terbium tetrafluoride

Abstract

The absorption spectra of ${\mathrm{Tb}}^{3+}$ in LiTb${\mathrm{F}}_{4}$ have been recorded in the spectral interval from 4000 to 25000 ${\mathrm{cm}}^{\ensuremath{-}1}$ 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. $H=\ensuremath{\Sigma}{\ensuremath{\lambda}}_{i}{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}})}^{i}+\ensuremath{\Sigma}{\ensuremath{\alpha}}_{i}\ensuremath{\Sigma}{B}_{\mathrm{im}}{O}_{\mathrm{im}}$, where the parameters ${\ensuremath{\lambda}}_{i}$ are functions of the spin-orbit parameter $\ensuremath{\zeta}$ and the Slater parameter ${F}_{2}$. The ${O}_{\mathrm{im}}$ and ${\ensuremath{\alpha}}_{i}$ 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. $\ensuremath{\zeta}$ and the six ${B}_{\mathrm{im}}$ were varied to obtain the best agreement with the experimentally observed levels. Keeping ${F}_{2}=434$ ${\mathrm{cm}}^{\ensuremath{-}1}$ fixed, a fit with a standard deviation of 12 ${\mathrm{cm}}^{\ensuremath{-}1}$ was obtained at 10 K with the following parameters: $\ensuremath{\zeta}=1698$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${B}_{20}=445$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${B}_{40}=\ensuremath{-}761$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${B}_{44}=1120$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${B}_{60}=4$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and ${B}_{64}=761+i609$ ${\mathrm{cm}}^{\ensuremath{-}1}$. 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.