Low Temperature Acoustic Properties of Amorphous Silica and the Tunneling Model

Abstract

Internal friction and speed of sound of a-SiO2 was measured above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, non-linear effects, and clamping losses. Strain amplitudes ǫA = 10 −8 mark the transition between the linear and non-linear regime. In the linear regime, excellent agreement with the Tunneling Model was observed for both the internal friction and speed of sound, with a cut-off energy of ∆o,min/kB = 6.6 mK. In the non-linear regime, two different behaviors were observed. Above 10 mK the behavior was typical for non-linear harmonic oscillators, while below 10 mK a different behavior was found. Its origin is not understood.PACS numbers: 61.43. Fs, 62.54.+k, 63.50.+x The low temperature acoustic, thermal, and dielectric properties of amorphous solids have long been successfully described by the phenomenological Tunneling Model (TM). In this model, the low energy localized vibrational excitations, a common feature of amorphous solids, are described by non-interacting two-level defects which are thought to be caused by tunneling of atoms or groups of atoms between nearly degenerate potential minima. The excitation energy between the two lowest states of the double well potential, E = ∆ 2 + ∆ 2 o , is determined by the asymmetry, ∆ and the tunneling splitting, ∆ o [1]. Low temperature internal friction and speed of sound measurements on a-SiO 2 using the torsional oscillator technique between 66 and 160 kHz above 50 mK have shown excellent agreement with the TM [2,3]. However, several acoustic and dielectric experiments have indicated deviations from this model below 100 mK [4][5][6][7][8] and have been interpreted as evidence for tunneling defect interactions [9,10]. This discrepancy provided the impetus for the present study in which we extended the acoustic measurements to 6 mK.In low temperature acoustic measurements, a major cause of uncertainty are thermal decoupling caused by spurious heat input and self heating, non-linear effects resulting from moderate strain amplitudes, and lack of knowledge of the influence of mounting [2,5,6,8,10]. Taking particular care to control these problems, we report here measurements in the extended temperature range which are in excellent agreement with the predictions of the TM with a low energy cut-off in the tunneling state spectrum, ∆ o,min /k B = 6.6 mK. These results emphasize the extreme care with which low temperature acoustic work must be carried out.

Intrinsic dissipation in high-frequency micromechanical resonators

“…Similar saturation of ␦ f / f , which is related to the shift in the sound velocity, has also been observed in both dielectric constant and sound velocity [46][47][48][49] of glasses, typically below 100 mK. Acoustic dissipation and dielectric relaxation in these systems are understood by the tunneling model of TLS, 50 as tunneling becomes important at temperatures below 1 K. Phenomenologically, the observation of saturation suggests a low-energy cutoff in the tunnel parameters arising perhaps from an additional mechanism outside the framework of the tunneling model.…”

Energy Transport Induced by an External Alternating Field in Strongly Disordered Media

“…One can think that these effects may explain the quantitative disagreement between the theoretical predictions of papers [7] and the experimental data available [10]. On the other hand, the results of paper [11], corresponding to the extremely low strain field amplitude, show no anomalies in the low temperature behavior of the internal friction. Possibly, this negative result is an indirect evidence in favor of the influence of the strong alternating field on the relaxation rate reported in Ref.…”

“…Consider the relation of the results obtained with our previous works [7] and experimental data available [10,11].…”

“…In addition, the frequency used in Ref. [11] is much larger than the frequencies used in [10] and the many-body contribution into the internal friction could be suppressed at such high frequency [7,8].…”

“…The results obtained manifest that the relaxation properties are vastly influenced by the field. We argue for new treatment for a wide range of anomalous properties in glasses discovered during the past decade [9][10][11].Consider an ensemble of two-level systems. The Schrödinger equation for a single excitation can be presented in the form ͑h 1͒…”