Raman spectroscopy of $\mathrm{Ba}{\mathrm{F}}_2$:$R^{3+}$ and $\mathrm{Sr}{\mathrm{F}}_2$:$R^{3+}$ solid solutions between 300 and 1400 K

In this paper we present results of Raman scattering experiments on Ba${\mathrm{F}}_2$ and Sr${\mathrm{F}}_2$ single crystals, doped with trivalent La ions, in the temperature range 300-1400 K. The linewidth of the Raman peaks in heavily doped materials is partly due to time-dependent effects from hopping interstitial fluoride ions, which are present in large numbers because of the excess positive charge of the La ions. From a comparison of experiment with the results of a theoretical treatment we find that the hopping energy of interstitial fluoride ions in a Ba${\mathrm{F}}_2$ crystal doped with 3.1 mol% La${\mathrm{F}}_3$ is 0.60 eV, whereas the corresponding value for a crystal with 7.3 mol% La${\mathrm{F}}_3$ is 0.35 eV. For crystals with higher La concentrations the activation energy is lower. This decrease can be explained in terms of defect-defect interactions.