Complete elastic constants and giant softening of ${\mathit{c}}_{66}$ in superconducting ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_4$

A novel resonant ultrasound technique is used to measure all elastic constants and their temperature dependence in single-crystal ${\mathrm{La}}_{1.86}$ ${\mathrm{Sr}}_{0.14}$ ${\mathrm{CuO}}_4$. The in-plane shear modulus ${\mathit{c}}_{66}$ drops by nearly half upon cooling to 227 K, an effect attributed to order-parameter fluctuations (of 2D Gaussian character) near the tetragonal-orthorhombic phase boundary. Implications for current models of the structural phase transition are discussed, as well as the effect of domains in the low-temperature orthorhombic state.