Nonlinear and Hysteretic Ultrasound Propagation in Solid $^4$He: Dynamics of Dislocation Lines and Pinning Impurities

Abstract

We report on the measurements of 9.6 MHz ultrasound propagation down to 15 mK in polycrystalline quantum solid $^4$He containing 0.3 and 20 ppm $^3$He impurities. The attenuation and speed of ultrasound are strongly affected by the dislocation vibration. The observed increase in attenuation from 1.2 K to a peak near 0.3 K is independent of drive amplitude and reflects crossover from overdamped to underdamped oscillation of dislocations pinned at network nodes. Below 0.3 K, amplitude-dependent and hysteretic variations are observed in both attenuation and speed. The attenuation decreases from the peak at 0.3 K to a very small constant value below 70 mK at sufficiently low drive amplitudes of ultrasound, while it remains a high value down to 15mK at the highest drive amplitude. The behaviors at low drive amplitudes can be well described by the effects of the thermal pinning and unpinning of dislocations by the impurities. The binding energy between a dislocation line and a $^3$He atom is estimated to be 0.35 K. The nonlinear and hysteretic behaviors at intermediate drive amplitudes are analyzed in terms of stress-induced unpinning which may occur catastrophically within a network dislocation segment. The relaxation time for pinning at 15 mK is very short ($< 4$ s), while more than 1,000 s is required for unpinning.