Acoustic Resonances and Non-linearity in Solid 4He

Direct measurements of the low frequency shear modulus of solid He-4 show a remarkable increase below 150 mK, a regime where torsional oscillator (TO) experiments show evidence of mass decoupling. Acoustic resonance measurements at higher frequencies confirm the unusual elastic behavior. A striking feature of both TO and shear modulus measurements is their amplitude dependence-the low temperature anomalies are reduced as the drive amplitudes increase. We have studied the amplitude dependence of acoustic resonances in both standard and isotopically pure He-4 crystals. The resonance peaks shift to lower frequencies as the drive amplitude increases. At high amplitudes the peaks are asymmetric and exhibit both bistability and hysteresis-classic features of nonlinear oscillators. At the lowest amplitudes the peak frequency and shape are independent of drive amplitude and are non-hysteretic. The threshold for nonlinear behavior is lower for the isotopically pure crystal. We also studied the effects of annealing on the acoustic resonances. The nonlinear behavior was qualitatively unchanged but annealing often affected the shape of the resonance peaks, which often had a complicated structure at low temperatures.