A Landau free energy for the ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$(Ba,Sr${)}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ family is constructed, including the coupling energy between the order parameter and strain tensor. Using group theory, it is demonstrated that the coupling energy can be expressed as a sum of terms linear in the strain and quadratic in the order parameter and should contain a coupling term bilinear in the two order-parameter components. The structural phase transitions (SPT’s) in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$(Ba,Sr${)}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ are discussed on this basis. It is shown that several SPT’s may occur in this system under different conditions. The observations of the influences of applied pressure, doping concentration x, and oxygen deficiency y on the SPT temperature are interpreted quantitatively. Relations connecting spontaneous strain, soft-mode vibrational frequencies, heat capacity, and elastic constants of the lower-temperature phases are derived. The mean-field results of the elastic properties and the results of the scaling analysis are also given. The results of ultrasonic measurements on a ${\mathrm{La}}_{1.88}$${\mathrm{Sr}}_{0.12}$${\mathrm{CuO}}_4$ single crystal are reported. The present and other relevant experimental observations are compared with the obtained theoretical results. The possible effects of structural phase transitions or structural instabilities on the superconductivity of the system are discussed.

• Received 29 March 1993

DOI:https://doi.org/10.1103/PhysRevB.48.16751