Measurement of up-conversion energy-transfer probabilities in Ho:Y3Al5O12 and Tm:Y3Al5O12

Abstract

The probabilities for up-conversion involving two nearest-neighbor ${\mathrm{Ho}}^{3+}$ ${(}^5$ ${\mathit{I}}_7$) ions and ${\mathrm{Tm}}^{3+}$ ${(}^3$ ${\mathit{F}}_4$) ions in ${\mathrm{Y}}_3$ ${\mathrm{Al}}_5$ ${\mathrm{O}}_{12}$ have been determined. The final states are ${}_{}{}^5{}_{}{}^{}$ ${\mathit{I}}_5$ and ${}_{}{}^5{}_{}{}^{}$ ${\mathit{I}}_6$ for ${\mathrm{Ho}}^{3+}$ and ${}_{}{}^3{}_{}{}^{}$ ${\mathit{H}}_4$ and ${}_{}{}^3{}_{}{}^{}$ ${\mathit{H}}_5$ for ${\mathrm{Tm}}^{3+}$. A rate-equation model has been used to obtain an expression for the concentration dependence of the up-conversion-rate constant in the migration-limited regime. We have also measured the reverse cross-relaxation probabilities for two of the processes with ${\mathrm{Ho}}^{3+}$ ${(}^5$ ${\mathit{I}}_5$) and ${\mathrm{Tm}}^{3+}$ ${(}^3$ ${\mathit{H}}_4$) as donors. The results fit well to the energy-gap law for phonon-assisted energy transfer. They also show evidence that there may be a correlation between the deviations from the energy-gap law for opposite processes.