Unconventional lattice stiffening in superconducting ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ single crystals

Ultrasonic and specific-heat measurements have been performed on single crystals of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ (LSCO) with x=0.09, 0.14, and 0.19 across the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$. We observed jumplike decreases in the longitudinal elastic moduli at ${\mathit{T}}_{\mathit{c}}$, as are seen in conventional superconductors. Anisotropic strain dependence of ${\mathit{T}}_{\mathit{c}}$ was estimated from both the jump in the elastic moduli and specific heat at ${\mathit{T}}_{\mathit{c}}$ via the Ehrenfest relation. With further lowering temperature below ${\mathit{T}}_{\mathit{c}}$, we found a pronounced lattice stiffening in the elastic moduli of LSCO, which contrasts with the continuous softening observed in most of the conventional superconductors. Thermodynamic analysis revealed that the stiffening originates from the change in the superconducting condensation energy under the lattice strain. This unusual lattice stiffening in the superconducting state is possibly a common character of the high-${\mathit{T}}_{\mathit{c}}$ copper oxides.