Vibronic Spectra of Sr${\mathrm{F}}_2$:${\mathrm{Sm}}^{2+}$ and Ba${\mathrm{F}}_2$:${\mathrm{Sm}}^{2+}$

Recent work of Wood and Kaiser has yielded vibronic data on ${\mathrm{Sm}}^{2+}$ doped in two isomorphic crystals, Sr${\mathrm{F}}_2$ and Ba${\mathrm{F}}_2$. The present work proposes a model using Born-von Karmann boundary conditions, which predicts the number of vibronic satellites and the $k=0\mathrm{}$ selection rules. It is shown, however, that the $k=0\mathrm{}$ selection rules are too restrictive to explain the vibronic spectrum and that to obtain a satisfactory explanation one must consider transitions involving vibrations away from $k=0\mathrm{}$. The model, when such transitions are taken into account, is shown to be consistent with the observed data. It is proposed that one of the modes observed in the vibronic spectrum corresponds to vibrations of the transverse optical branch, a second to the longitudinal optical branch, and a third to transitions away from $k=0\mathrm{}$ involving the Raman active branch. This model is able to qualitatively explain the differences observed in the two host lattices. It is contrasted with an $X Y_8$ complex model, proposed by Axe and Sorokin to explain the same data. Raman scattering data have been obtained placing the $F_{2g}$ mode (at $k=0\mathrm{}$) at 280 ${\mathrm{cm}}^{-1\mathrm{}}$ in Sr${\mathrm{F}}_2$ and at 243 ${\mathrm{cm}}^{-1\mathrm{}}$ in Ba${\mathrm{F}}_2$.