Frequency shifts and dissipation of a compound torsional oscillator induced by solid 4 He samples containing 3 He impurity concentrations (x3 = 0.3, 3, 6, 12 and 25 in units of 10 −6 ) have been measured at two resonant mode frequencies (f1 = 493 and f2 = 1164 Hz) at temperatures (T ) between 0.02 and 1.1 K. The fractional frequency shifts of the f1 mode were much smaller than those of the f2 mode. The observed frequency shifts continued to decrease as T was increased above 0.3 K, and the conventional non-classical rotation inertia fraction was not well defined in all samples with x3 ≥ 3 ppm. Temperatures where peaks in dissipation of the f2 mode occurred were higher than those of the f1 mode in all samples. The peak dissipation magnitudes of the f1 mode was greater than those of the f2 mode in all samples. The activation energy and the characteristic time (τ0) were extracted for each sample from an Arrhenius plot between mode frequencies and inverse peak temperatures. The average activation energy among all samples was 430 mK, and τ0 ranged from 2×10 −7 s to 5×10 −5 s in samples with x3 = 0.3 to 25 ppm. The characteristic time increased with increasing x3. Observed temperature dependence of dissipation were consistent with those expected from a simple Debye relaxation model if the dissipation peak magnitude was separately adjusted for each mode. Observed frequency shifts were greater than those expected from the model. The discrepancies between the observed and the model frequency shifts increased at the higher frequency mode.
Measurements on hysteretic response of compound torsional oscillator containing annular-shaped solid 4 He samples were carried out by varying the oscillator drive amplitude starting from high to low and then back up to the initial high value. Hysteresis in the oscillator frequency and amplitudes were observed only below an onset temperature. The hysteresis onset temperature (T H ) did not depend on the oscillator frequency, width of the sample annulus, annealing and refreezing after melting. A systematic increase in T H was observed as the 3 He impurity concentration in solid 4 He samples was increased. The dependence of T H on 3 He impurity concentration followed approximately that of the dissipation peak temperatures. Possible relationships of the observed hysteresis phenomena with models of solid 4 He dynamics based on freezing of a vortex liquid and dislocation motion are discussed.
We describe the first observations on the time-dependent dissipation when the drive level of a torsional oscillator containing solid (4)He is abruptly changed. The relaxation of dissipation in solid (4)He shows rich dynamical behavior including exponential and logarithmic time-dependent decays, hysteresis, and memory effects.
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