Low temperature acoustic properties of amorphous silica and the tunneling model

Internal friction and speed of sound were measured on a-SiO2 above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, vibrational heating, background losses, and nonlinear effects. Strain amplitudes epsilon(A) = 10(-8) mark the transition between the linear and nonlinear regimes. In the former, agreement with the tunneling model was observed for both internal friction and speed of sound above 25 mK. The observed deviations in the speed of sound below 25 mK can be described with a cutoff energy of Delta(0,min)/k(B) = 6 +/- 0.5 mK. In the nonlinear regime, above 10 mK the behavior was typical for nonlinear harmonic oscillators, while below 10 mK different behavior was found.