Nonthermalization and Large Variation in Multiphonon Relaxation Rate among Rare-Earth-Ion Stark Levels

In $^{5}D_{1}$ of YV${\mathrm{O}}_{4}$:${\mathrm{Eu}}^{3+}$ at 2.0 $^{\mathrm{o}}\mathrm{K}$, multiphonon relaxation occurs from the Stark level because it is not in thermal equilibrium with the lower of the two levels in the manifold. The energy levels of $^{5}D_{1}$ were simple enough to allow the construction of a detailed mathematical model which provided an excellent fit to the temperature-dependent multiphonon relaxation rate. The two Stark levels of $^{5}D_{1}$ also differ in multiphonon relaxation rate by factor of about 15. The Eu $^{5}D_{1}$ fluorescence was too weak in YAs${\mathrm{O}}_{4}$ and YP${\mathrm{O}}_{4}$ for these systems to be investigated for these effects. Similar effects appear also with ${\mathrm{Ho}}^{3+} E(^{5}S_{2},^{5}F_{4})$ in YV${\mathrm{O}}_{4}$ and YAs${\mathrm{O}}_{4}$.