Nuclear Spin-Lattice Relaxation Associated with Low-Energy Excitations in Glasses

The nuclear $T_1$ has been measured between 1.2 and 300 K on ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{77}{}_{}{}^{}\mathrm{Se}$ in amorphous ${\mathrm{B}}_2$ ${\mathrm{O}}_3$, ${\left({\mathrm{Na}}_2\mathrm{O}\right)}_{0.3}$ ${\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_2\right)}_{0.7}$, ${\mathrm{Na}}_2$ ${\mathrm{B}}_4$ ${\mathrm{O}}_7$, and Se. The measured rates, which for spins $I>\mathrm{}\frac{1}{2}$ are much greater than those observed in corresponding crystalline materials, are nearly field independent and vary as $T^{\alpha }$ with $\alpha \sim 1.3$. Such a quadrupolar relaxation might be explained by a model involving the distribution of two-level systems, as describes the anomalous thermal and ultrasonic-wave properties of similar materials.