Effect of pressure and temperature on energy transfer betweenCr3+andTm3+inY3Al5O12

Abstract

We present variable temperature (15--295 K) and pressure (ambient--102 kbar) studies of energy transfer in ${\mathrm{Cr}}^{3+}:{\mathrm{Tm}}^{3+}:\mathrm{YAG}.$ The ${\mathrm{Cr}}^{3+}\ensuremath{\rightarrow}{\mathrm{Tm}}^{3+}$ energy-transfer rate was observed to increase with increasing temperature and to decrease with increasing pressure. The temperature study permitted us to identify three principal contributions to the overall energy-transfer rate from ${\mathrm{Cr}}^{3+}:$ thermally activated transfer from the ${}^{4}{T}_{2}$ state, thermally activated transfer from the anti-Stokes sidebands of the ${}^{2}E$ state, and temperature independent transfer from the zero phonon and Stokes sideband transitions of the ${}^{2}E$ state. High pressure permitted us to increase the energy of the ${}^{4}{T}_{2}$ state relative to the ${}^{2}E$ state and to eliminate the contribution of the ${}^{4}{T}_{2}$ state to the energy-transfer process. As a result, the contribution of the ${}^{2}E$ state to the energy-transfer process was isolated and evaluated independently. A quantitative model based on F\orster-Dexter theory was used to determine the energy-transfer rates as a function of temperature and pressure. Comparisons of limiting high-pressure and low-temperature energy-transfer rates with the energy-transfer rate at ambient conditions allowed us to separate and determine the relative importance of the three principal energy-transfer processes at ambient conditions. We found that energy transfer from the ${}^{4}{T}_{2}$ state is dominant at ambient conditions despite the fact that it is $\ensuremath{\sim}800{\mathrm{cm}}^{\ensuremath{-}1}$ higher in energy than the ${}^{2}E$ state. Deviations from the Inokuti-Hirayama energy-transfer model observed under low-temperature or high-pressure conditions were shown to be due to preferential energy transfer to nonrandomly distributed ${\mathrm{Tm}}^{3+}$ acceptors. At high-temperature or low-pressure conditions, the overall energy-transfer rate is sufficiently fast to permit efficient transfer to the more numerous randomly distributed ${\mathrm{Tm}}^{3+}$ acceptors. Under these conditions, the Inokuti-Hirayama model becomes a valid description.