Radiative and Multiphonon Relaxation of Rare-Earth Ions inY2O3

Spontaneous-emission probabilities for electric- and magnetic-dipole transitions from excited electronic states of ${\mathrm{Pr}}^{3+}$, ${\mathrm{Nd}}^{3+}$, ${\mathrm{Eu}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Tm}}^{3+}$ impurities in ${\mathrm{Y}}_2$ ${\mathrm{O}}_3$ are calculated using eigenstates in intermediate coupling and experimental intensity parameters. The predicted radiative lifetimes are in good agreement with experimental lifetimes measured using pulsed-selective-excitation techniques for those levels where unit quantum efficiency is expected. Discrepancies do exist, however, which indicate the importance of $J$-state mixing and possible breakdown of the closure approximation used in Judd and Ofelt's treatment. Nonradiative decay rates were determined by subtracting the radiative contribution from the observed lifetime. The rates of multiphonon emission in ${\mathrm{Y}}_2$ ${\mathrm{O}}_3$ exhibit a systematic variation with proximity of the next-lowest level, and contribute significantly to the decay for levels having energy gaps to the next-lowest level of less than 3000 ${\mathrm{cm}}^{-1\mathrm{}}$. Selection-rule restrictions are evident from the reduced relaxation rates for the ${}_{}{}^5{}_{}{}^{}D_J^{}{}_{}{}^{}$ levels of ${\mathrm{Eu}}^{3+}$. The concentration dependence of the excitation spectra and excited-state lifetimes of ${\mathrm{Tm}}^{3+}$ were investigated to establish the importance of ion-pair relaxation; however, these processes were generally avoided.