Multiphonon Relaxation of Rare-Earth Ions in Yttrium Orthoaluminate

Abstract

Nonradiative relaxation by multiple-phonon emission was investigated for excited electronic states of rare-earth ions in YAl${\mathrm{O}}_3$. Ions studied included ${\mathrm{Nd}}^{3+}$, ${\mathrm{Eu}}^{3+}$, ${\mathrm{Ho}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Tm}}^{3+}$. Rates of multiphonon emission were determined from the difference of measured excited-state lifetimes and calculated radiative lifetimes. Electric dipole transition probabilities were computed using Judd-Ofelt intensity parameters for rare earths in YAl${\mathrm{O}}_3$. Multiphonon decay rates, measured for seventeen different levels with energies to the next-lower level ranging from 1400 to 4700 ${\mathrm{cm}}^{-1\mathrm{}}$, exhibited an approximately exponential dependence on energy gap $\Delta E$ given by $W\left(0\right)\mathrm{}{e}^{-\alpha \Delta E}$, where $W\left(0\right)=5\mathrm{}\times {10}^9$ ${\sec }^{-1\mathrm{}}$ and $\alpha =4.6\mathrm{}\times {10}^{-3\mathrm{}}$ cm. Exceptions to the exponential law occur only when selection rules severely restrict the number of terms in the ion-lattice interaction active in inducing transitions. The phonon frequency distribution and ion-phonon coupling in YAl${\mathrm{O}}_3$ were examined from infrared, Raman, and vibronic spectra. Although phonon energies range up to 750 ${\mathrm{cm}}^{-1\mathrm{}}$, measurements of the temperature dependence of multiphonon emission indicate that phonons of energies $\sim 550-600$ ${\mathrm{cm}}^{-1\mathrm{}}$ make the dominant contribution to the relaxation at temperatures 77-700 °K.