Far-infrared Stark and Zeeman splitting of trivalent rare-earth ions in barium, calcium, and cadmium fluorides

We have studied the far-infrared absorption of Ba${\mathrm{F}}_2$, Ca${\mathrm{F}}_2$, and Cd${\mathrm{F}}_2$ doped with Tb, Sm, Nd, Pr, Dy, Ho, Er from room temperature down to 1.4 K. The background absorption induced by the rare-earth ($R$) impurity is too high in the case of Cd${\mathrm{F}}_2$ for any electronic transition to be seen. It is low enough for Ca${\mathrm{F}}_2$- and Ba${\mathrm{F}}_2$- doped crystals. In the case of all Ba${\mathrm{F}}_2$:$R^{3+}$ crystals considered, we have found a common absorption band at 131 ${\mathrm{cm}}^{-1\mathrm{}}$. The structure is explained by localized vibrations of the compensation ${\mathrm{F}}^{-}$ ions, in three different sites: cubic, tetragonal, and trigonal, where the $R$ ions are distributed in different proportions: 4%, 46%, 50%, respectively. We have also found specific bands sensitive to magnetic fields in the case of ${\mathrm{Dy}}^{3+}$ (41.2 ${\mathrm{cm}}^{-1\mathrm{}}$), ${\mathrm{Ho}}^{3+}$ (37 ${\mathrm{cm}}^{-1\mathrm{}}$), and ${\mathrm{Er}}^{3+}$ (69.2 and 70.3 ${\mathrm{cm}}^{-1\mathrm{}}$). The Zeeman effect gives information on the Landé $g$ factors $g_1$ and $g_2$ for ground and excited levels, respectively, and shows that for ${\mathrm{Er}}^{3+}$ the observed lines correspond to two different sites. It is shown that $g_1=g_2=3.6\mathrm{}$ for the trigonal one and $g_1=g_2=0.98\mathrm{}$ for the tetragonal site. For Ba${\mathrm{F}}_2$:${\mathrm{Dy}}^{3+}$, $g_1=3.2\mathrm{}$, $g_2<g_1$; for Ba${\mathrm{F}}_2$: