Effect of Rotation on Elastic Moduli of Solid $^4$He

TL;DR

This study investigates how unidirectional rotation affects the elastic moduli of solid helium-4, revealing that rotation weakens dislocation pinning by helium-3 impurities, especially under shear strains exceeding a critical threshold.

Contribution

It provides direct measurements of shear and Young's moduli of solid helium-4 under rotation, demonstrating the rotation-induced unpinning of dislocations from helium-3 impurities.

Findings

Rotation suppresses shear modulus below 80 mK at high shear strains.

Rotation decreases the probability of helium-3 impuriton pinning on dislocations.

Rotation-induced anisotropy affects impuriton motion, reducing pinning efficiency.

Abstract

We report measurements of elastic moduli of hcp solid $^4$He down to 15 mK when the samples are rotated unidirectionally. Recent investigations have revealed that the elastic behavior of solid $^4$He is dominated by gliding of dislocations and pinning of them by $^3$He impurities, which move in the solid like Bloch waves (impuritons). Motivated by the recent controversy of torsional oscillator studies, we have preformed direct measurements of shear and Young's moduli of annular solid $^4$He using pairs of quarter-circle shape piezoelectric transducers (PZTs) while the whole apparatus is rotated with angular velocity $\Omega$ up to 4 rad/s. We have found that shear modulus $\mu$ is suppressed by rotation below 80 mK, when shear strain applied by PZT exceeds a critical value, above which $\mu$ decreases because the shear strain unbinds dislocations from $^3$He impurities. The rotation - induced decrement of $\mu$ at $\Omega = 4$ rad/s is about 14.7 (12.3) % of the total change of temperature dependent $\mu$ for solid samples of pressure 3.6 (5.4) MPa. The decrements indicate that the probability of pinning of $^3$He on dislocation segment, $G$, decreases by several orders of magnitude. We propose that the motion of $^3$He impuritons under rotation becomes strongly anisotropic by the Coriolis force, resulting a decrease in $G$ for dislocation lines aligning parallel to the rotation axis.