Anomalous Temperature Dependence of the Sound Velocity of Amorphous Silica below 3 mK

The sound speed δV/V₀ of amorphous silica between 1 and 30 mK was measured using a double paddle oscillator, cut with a laser from a 0.4 mm thick plate of vitreous silica. The oscillator was operated at four of its resonant modes between 610 Hz and 14 kHz. Above 3 mK and up to the maximum of δV/V₀, the sound speed exhibits the logarithmic temperature dependence predicted by the tunneling model with the slope C = 2.4 × 10⁻⁴, varying by a few percent between the various modes. Below 3 mK, the sound speed departs from the logarithmic dependence and levels off. This can be explained either by a large heat input (>10⁻³ nW/g) of unknown origin or by a low energy cut off, E_min, in the density of tunneling states of 1.5 mK.