Resonance Modes at Defects in Crystalline Quartz

Abstract

The Raman spin-lattice relaxation time $T_{1R}$ for the oxygen divacancy (${E_1}^{\prime }$) center in synthetic crystalline quartz measured in applied magnetic fields of 3 kOe is accurately given by $\frac{1}{T_{1R}}=B\frac{e^{x_1}}{{(e^{x_1}-1)}^2}+C\frac{e^{x_2}}{{(e^{x_2}-1)}^2}+D{e}^{-x_3},$ where $B=0.25\mathrm{}$ ${\sec }^{-1\mathrm{}}$, $C=250\mathrm{}$ ${\sec }^{-1\mathrm{}}$, and $D=300\mathrm{}000$ ${\sec }^{-1\mathrm{}}$, and the characteristic frequencies have the corresponding temperatures of $x_{1}T=20\mathrm{}\pm 2°$K, $x_{2}T=125\mathrm{}\pm 10°$K, and $x_{3}T=1400\mathrm{}\pm 300°$K. The two lower frequencies are interpreted in terms of mechanical resonances localized at each center and having large resonant amplitudes. The highest frequency is tentatively associated with some of the optical modes of the Si${\mathrm{O}}_2$ lattice. There is no evidence for relaxation by the acoustic modes having the normal Debye cutoff.