Logarithmic Temperature Dependence of the Sound Speed in Amorphous Silica at Low Temperatures

The tunneling model has enjoyed considerable success in describing the low temperature properties of glasses. However, departures from the tunneling model have been noted in experiments at very low temperatures (below 100 mK). We have measured the change in the sound speed V/V0 between 1 and 40 mK in an amorphous silica double paddle oscillator oscillating at 14 kHz. Most importantly, the sound speed displayed the logarithmic temperature dependence predicted by the tunneling model to a lower temperature than in previous experiments on amorphous silica. Below 3 mK the sound speed departed from the logarithmic temperature dependence and began to level off. The leveling off can be explained by either an intrinsic effect or thermal decoupling of the sample from the thermometer. By heating the oscillator with a gamma source to determine the thermal resistance of the oscillator, it was found that a relatively large stray heat input (9×10−4 nW) would be needed to cause the leveling off. Further work will be needed to determine whether the leveling off is due to stray heat or intrinsic physics. PACS 61.43.Fs · 62.65.+k