Low Frequency Elastic Measurements on Solid $$^{4}$$ 4 He in Vycor Using a Torsional Oscillator

A D Fefferman,A Haziot,J R Beamish,S Balibar

doi:10.1007/s10909-014-1171-z

Abstract

Torsional oscillator experiments involving solid $^{4}$He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium's mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk $^{4}$He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by $^{3}$He impurities. We have used a torsional oscillator (TO) technique to directly measure the shear modulus of the solid $^{4}$He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent torsional oscillator experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.

Highlights

Confinement in porous Vycor glass has long been used to study effects of finite size and disorder on phase transitions in helium
The shear modulus of solid 4He changes [7] below 200 mK, raising the possibility that the observed torsional oscillator (TO) frequency changes were due to elastic stiffening rather than to mass decoupling
Recent analyses [8,9] have shown that in most torsional oscillators the observed frequency changes can be explained by stiffening effects from changes in the shear modulus of the solid helium

Summary

Introduction

Confinement in porous Vycor glass has long been used to study effects of finite size and disorder on phase transitions in helium. We found a small, gradual increase in the system’s shear modulus as it was cooled from 1 K to the lowest temperature (20 mK) This supports the conclusion from recent Vycor TO experiments that the low temperature anomalies seen in previous experiments must have originated in elastic effects in bulk helium in gaps around the Vycor. Confinement in the small pores of Vycor eliminates the dislocation movement responsible for the low temperature modulus changes in bulk solid 4He. The gradual modulus changes we observe in the present experiments appear at lower temperatures than the corresponding stiffening seen in previous ultrasonic measurements at MHz frequencies, as expected for a thermally activated relaxation process in the solid helium in the pores. The modulus changes due to the helium, combined with those due to two-level systems (TLS) in the Vycor [13,20,21], would produce a background temperature dependence in the frequency of a TO containing solid helium-filled Vycor

Experiment

Results and Discussion

64 L κ0 π Dv4y f0