We report on the measurements of 9.6 MHz ultrasound propagation down to 15 mK in polycrystalline quantum solid ${}^4\mathrm{He}$ containing 0.3 and 20 ppm ${}^3\mathrm{He}$ 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 15 mK 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 ${}^3\mathrm{He}$ 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 1000 s is required for unpinning.

中文翻译：

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固态He4中非线性和滞后超声传播：位错线和钉扎杂质的动力学

我们报告了在多晶量子固体中低至15 mK的9.6 MHz超声传播的测量结果 ${}^4他$ 含0.3和20 ppm ${}^3他$杂质。超声波的衰减和速度受位错振动的强烈影响。观察到的从1.2 K到0.3 K附近峰值的衰减增加与驱动幅度无关，并且反映了钉扎在网络节点上的位错从过阻尼振荡到欠阻尼振荡的交叉。低于0.3 K，在衰减和速度上都观察到幅度相关的和滞后的变化。在足够低的超声驱动振幅下，衰减从0.3 K的峰值减小到低于70 mK的很小的恒定值，而在最高的驱动振幅下，衰减保持在高达15 mK的高值。低驱动幅度下的行为可以通过杂质对位错的热钉扎和不钉扎的效果很好地描述。位错线与晶界之间的结合能${}^3他$原子估计为0.35K。根据应力引起的松动，分析了中间驱动振幅下的非线性和滞后行为，应力松动可能在网络位错段内灾难性地发生。固定到15 mK的松弛时间非常短（$<4$ s），而取消固定则需要超过1000 s。