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

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.