We investigate the origin of a resonant period drop of a torsional oscillator (TO) containing solid ${}^4\mathrm{He}$ by inspecting its relation to a change in elastic modulus. To understand this relationship directly, we measure both phenomena simultaneously using a TO with a pair of concentric piezoelectric transducers inserted in its annulus. We confirm experimentally that both anomalies are directly related. Although the temperature, ${}^3\mathrm{He}$ concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid ${}^4\mathrm{He}$ connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.

• Received 14 March 2016
• Revised 17 May 2016

DOI:https://doi.org/10.1103/PhysRevB.93.214512