Direct, Orbach, and Raman Relaxation in Dilute Cerous Magnesium Nitrate

Paramagnetic-relaxation measurements are reported for ${\mathrm{Ce}}^{3+}$ present as a dilute impurity in ${\mathrm{La}}_2$ ${\mathrm{Mg}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·24${\mathrm{H}}_2$O. Intrinsic direct relaxation rates are observed at Zeeman frequencies low enough to avoid a phonon bottleneck. At higher frequencies, where a substantial bottleneck is present, the intrinsic direct rate is obtained by a special technique. Direct and Raman rates obey the expected frequency and temperature variations, and the Orbach process depends on Zeeman frequency in a way we ascribe to a phonon bottleneck at the Orbach frequency. We find $T_1^{}{}_{}{}^{-1\mathrm{}}=6.02\mathrm{}\times {10}^{-39\mathrm{}}{\nu }^{4}T+0.09\mathrm{}{T}^9+\exp (logB-\frac{\Delta }{T})$, where $\nu$ is the Zeeman frequency in cps and $T$ the temperature. The argument of the Orbach rate depends on Zeeman frequency. All of the parameters are found to agree well with the accepted theoretical model.