P. Esquinazi

Acoustic properties of amorphous SiO2 and PdSiCu, and of crystalline Ag, NbTi and Ta at very low temperatures

With the vibrating reed and vibrating wire techniques we have investigated the acoustic properties of vitreous silica (SiO2, Suprasil I) and of amorphous PdSiCu as well as of polycrystalline Ag, NbTi and Ta at frequencies of 100 Hz≦ω/2π<6 kHz and at temperatures of 0.1 mK≦T≦1 K. The relative change of sound velocity Δv/v of SiO2 shows saturation effects, strain amplitude dependence, as well as an unexpected temperature dependence below its maximum atT<50 mK. For PdSiCu we observe that below a certain temperature, which depends on the applied strain, the temperature dependence of the sound velocityv deviates from the logarithmic behavior observed at higher temperatures and reaches an almost constant value atT<1 mK. In the same temperature rangeQ−1 does not remain constant but steadily decreases. The acoustic properties of the two amorphous materials at finite strain show substantial deviations from the standard tunneling model. Some of the observed anomalies can be explained taking into account the change of population of the tunneling systems energy states and a nonlinear relaxation absorption. For polycrystalline Ag we find Δv/v αlnT andQ−1αT1/3 over three decades inT atT<100 mK; it shows low-temperature acoustic properties which are strikingly similar to those of amorphous materials. The temperature and strain dependencies of the acoustic properties of polycrystalline superconducting NbTi and Ta resemble those obtained for SiO2. These results indicate that there are basically no differences in the low-temperature acoustic properties of polycrystals and amorphous materials.

What do we learn from vibrating high-temperature superconductors?

This work reviews the theory and experiments of vibrating high-temperature superconductors (period 1988-94). In particular we discuss results on the elastic coupling between the flux line lattice and pinning centres, magnetization measurements, flux diffusion, possible phase transitions and matching effects of the flux line lattice. Special emphasis has been devoted to the comparison of these results with results obtained by more conventional methods such as AC susceptibility, low-frequency torsional oscillators, I-V curves and surface impedance measurements.

Vortex diffusion: An alternative to vortex-glass superconductivity

Abstract I show that the resistive behavior obtained from the characteristic I–V curves reported by Koch et al. (Phys. Rev. Lett. 63, 1151 (1989)) can be interpreted in terms of thermally assisted flux flow and “normal” flux flow resistivities. The so called “vortex-glass-liquid” line is equivalent to the depinning line taken from other measurements.

Nonlinear acoustic properties of vibrating wires at very low temperatures

We have investigated the acoustic properties of superconducting NbTi and Ta wires in vacuum at 1 mK≤T≤1 K and at a few kHz. The temperature dependence of the acoustic properties of the wires is similar to that found in amorphous materials: a maximum in the sound velocity and a plateau in the dissipation at temperatures above it. In addition, we have observed a strong influence of the acoustic power on the measured properties in agreement with recent measurements on amorphous SiO2. This strain dependence can be interpreted by a modification of the tunneling model as a change of populationS of the two-level system energy states in non-crystalline materials. We can explain the strain-dependent anomalies as the superposition of three nonlinear effects: the change of population of the tunneling systems energy states, self-heating of the wire, and a nonlinear restoring force. These effects have a strong influence on the lineshape of the resonance curve. In addition, we have investigated the behavior of vibrating wires in liquid3He and liquid3He-4He solutions atT<100 mK. We can show that in superfluid3He-B atT<0.2 mK or in solutions of3He in4He with a small concentration of3He it is impossible to use a vibrating wire as a viscometer without having exact information about its intrinsic properties.

Thermally activated depinning in an organic superconductor: Universal behavior of the flux-line lattice in layered superconductors

Abstract With the vibrating reed technique we have measured the field dependence of the depinning temperature of the flux-line-lattice (depinning lines) in the organic superconductor κ-(BEDT-TTF)2Cu(NCS)2 for different magnetic field orientations. In a reduced temperature scale the depinning lines are similar to those measured in the high temperature superconductor Bi2Sr2CaCu2O8 in spite of a factor ten difference in the critical temperature. We find that the effective activation barriers for flux motion divided by the thermal energy at the critical temperature are similar for both superconductors. The results can be understood with the thermally activated flux flow model and suggest a rather universal behavior of the thermally activated depinning in layered superconductors. We further show that a small misalignment of the superconducting crystal with the applied magnetic field gives rise to two dissipation peaks; this effect can be quantitatively understood taking into account two diffusivity modes.

The depinning line of a Y(Gd)Ba2Cu30x single crystal

Using a mechanical oscillator we have measured the coupling of the vortex lattice to the atomic lattice of a Y(6% Gd)Ba2 Cu3 06.83 single crystal (Tc= 67 K ) for fields B 1 c-axis. The measured field dependence of the depinning temperature is similar to the dependence obtained from other measurements but shifted to lower reduced temperatures. Our results indicate that the average pinning potential U(B,T) is smaller than in the 90 K (1-2-3) superconductors but has the same field and temperature dependencies.

Thermally activated depinning in superconducting YBa2Cu3O7 a quantitative comparison with the theory of flux diffusion

From the temperature, magnetic-field and angle dependence of the energy dissipation of vibrating Y 1:2:3 high-Tc superconductors and assuming the 3D anisotropic flux diffusion and thermally activated depinning model we obtain the effective activation barriers for flux motion. We show that within this model we can understand quantitatively the dissipation and its dependences, in particular the double and single dissipation peaks observed in single crystals and a 200 nm thin film at angles between field and CuO2 planes 0° < Θ <90°. We further show that the scaling rules for anisotropic superconductors are obeyed for the single crystal in the whole angle range. For the thin film, however, significant deviations from the scaling rules are observed.

Time and temperature dependence of the specific heat of non-crystalline solids within the tunneling model

We propose a new way to introduce the measuring time in the Tunneling Model of non-crystalline solids. We have obtained a time dependent relation for the specific heat which can be used without limits in time or temperature. We prove that under the usual assumptions of the standard Tunneling Model and without free parameters one can understand quantitatively the experimentally observed time and temperature dependence of the specific heat and heat release experiments on vitreous silica over ten orders of magnitude in time. We also discuss the influence of conductions electrons on the time dependent specific heat. Time dependent experiments could provide useful information on the interaction of Tunneling Systems with conduction electrons.

Internal friction and sound velocity of polycrystalline metals at very low temperatures

Abstract We have investigated the acoustical properties of polycrystalline Ag, Al, Cu, Nb, Nb with a Cu-matrix, Nb48Ti52, Pt and Ta at frequencies of 0.1 kHz ⩽ v ⩽ 8 kHz and in the temperature range 0.04 mK ⩽ T ⩽ 1 K. The polycrystalline samples Al, Nb, Nb with a Cu-matrix, NbTi and Ta in the superconducting state as well as normal conducting Ag, Cu and Pt show qualitatively the same acoustical behaviour (with similar strain dependence) as observed for amorphous, dielectric materials. The glass-like “anomalies” can be understood assuming the existence of tunneling systems with a broad spectrum of energy splitting and relaxation rates. When the acoustical intensity is of the order of the thermal energy, non-linear effects are observed. We show and discuss an anomalous time dependence of the sound velocity in Pt as well as a strain-dependent and temperature-independent internal friction in Cu.

Vibrating-wire measurements in vacuum, liquid3He and liquid3He-4He mixtures

In order to overcome the “200µK - barrier” in the refrigeration of liquid3He-4He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of ≤150µK. A vibrating wire which was immersed in pure3He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure3He only in the cell. In superfluid3He-B at T≤0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.