Multiphonon Relaxation of Rare-Earth Ions in Yttrium Orthoaluminate

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 ${\mathrm{cm}}^{\ensuremath{-}1}$, exhibited an approximately exponential dependence on energy gap $\ensuremath{\Delta}E$ given by $W(0){e}^{\ensuremath{-}\ensuremath{\alpha}\ensuremath{\Delta}E}$, where $W(0)=5\ifmmode\times\else\texttimes\fi{}{10}^{9}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ and $\ensuremath{\alpha}=4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ 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 ${\mathrm{cm}}^{\ensuremath{-}1}$, measurements of the temperature dependence of multiphonon emission indicate that phonons of energies $\ensuremath{\sim}550\ensuremath{-}600$ ${\mathrm{cm}}^{\ensuremath{-}1}$ make the dominant contribution to the relaxation at temperatures 77-700 \ifmmode^\circ\else\textdegree\fi{}K.