Spectroscopic analysis of LiHo${\mathrm{F}}_4$ and LiEr${\mathrm{F}}_4$

The polarized absorption spectra for ${\mathrm{Ho}}^{3+}$ and ${\mathrm{Er}}^{3+}$ in LiHo${\mathrm{F}}_4$ and LiEr${\mathrm{F}}_4$, respectively, have been recorded in the spectral interval 4000-26 000 ${\mathrm{cm}}^{-1\mathrm{}}$ at 2 K. Parts of the spectra were examined at higher temperatures. The experimental levels for ${\mathrm{Ho}}^{3+}$ and ${\mathrm{Er}}^{3+}$ in LiR${\mathrm{F}}_4$ were close to those found in LiY${\mathrm{F}}_4$. The energy levels of the ground-state term for each ion were calculated by diagonalizing in a term basis an effective Hamiltonian, which takes into account the mixing with other terms due to the spin-orbit coupling. The calculations could not give the correct centers of gravity for the multiplets. After the centers of gravity were matched with the experimental centers, the crystal-field parameters were varied to obtain the best agreement with the experimental observations. For ${\mathrm{Ho}}^{3+}$ the agreement obtained was good, but for ${\mathrm{Er}}^{3+}$ it was not possible to get good agreement for the levels of all the multiplets of the ground-state term. With the crystal-field parameters obtained for ${\mathrm{Er}}^{3+}$ when fitting to the levels of the two lowest multiplets only, all the energy levels below 26 000 ${\mathrm{cm}}^{-1\mathrm{}}$ were calculated by diagonalizing the energy Hamiltonian in a configuration basis. This calculation showed that the term mixing was strong even for the multiplets of the ground-state term. The agreement with the experiments was good for the three lowest terms of ${\mathrm{Er}}^{3+}$. The fitted values for the crystal-field parameters in LiR${\mathrm{F}}_4$ were for ${\mathrm{Ho}}^{3+}$ close to the values reported in LiY${\mathrm{F}}_4$, whereas the parameters differed somewhat in the case of ${\mathrm{Er}}^{3+}$.