Interplay between lattice softening and high-${\mathit{T}}_{\mathit{c}}$ superconductivity in ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_4$

High-resolution ultrasonic measurements have been performed on single-crystalline ${\mathrm{La}}_{1.86}$ ${\mathrm{Sr}}_{0.14}$ ${\mathrm{CuO}}_4$ in magnetic fields H up to 14 T. We found that by reducing temperature the transverse elastic constant (${\mathit{C}}_{11}$-${\mathit{C}}_{12}$)/2 starts to soften from about 50 K and continues to soften down to ${\mathit{T}}_{\mathit{c}}$(H), even when ${\mathit{T}}_{\mathit{c}}$(H) is reduced to 14 K by magnetic field. The softening turns to rapid hardening by the emergence of superconductivity. This behavior of C${(}_{11}$-${\mathit{C}}_{12}$)/2 is a consequence of the structural instability of the orthorhombic phase and disappearance of the instability caused by emergence of the superconducting state.