Electron-spin-lattice relaxation in ${\mathrm{Yb}}^{3+}$-doped silicate glass

Relaxation rates of ${\mathrm{Yb}}^{3+}$ ions incorporated in low concentrations into a host silicate glass have been measured using a pulse saturation and recovery technique at 9.5 GHz over the temperature range 1.5–7.0 K. Compared with similar measurements made on crystalline material, the temperature dependence of the recovery rates for the two-phonon Raman process is anomalously weak (${\mathit{T}}^6$ instead of ${\mathit{T}}^9$). This anomaly suggests the need to modify the Debye density of states. Fractal models have been suggested for the thermal properties of glasses and for similarly anomalous spin-relaxation behavior in proteins. This model is discussed as well as other models of phonon localization in glasses. An estimate for the localization frequency or crossover frequency between extended and localized phonon regimes can be extracted from fits of the data from the sample with the lowest Yb concentration.