The torsional modulus of ${\mathrm{Y}}_1{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{9-x}$, measured by the composite oscillator method, shows a softening of ≃1% on cooling through the superconducting transition. The change is 3 to 4 orders of magnitude larger than that in an average modulus for a typical superconductor. For the high symmetry implied by our polycrystalline sample, furthermore, no change is allowed by symmetry for this mode at the superconducting (or any Landau-type) transition. The decrease in modulus is accompanied by an increase in damping.

• Received 26 May 1987

DOI:https://doi.org/10.1103/PhysRevB.36.2411