The mutual interactions between a structural transition and a ferroelectric transition are analyzed for different strain states in a pseudocubic (100) $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ film by examining the equilibrium solutions of the total free energy as a function of polarization, strain and structural order parameter. The range of possible ferroelectric transition temperatures and the possible ferroelectric states of a strained $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ film are determined with respect to the variation in the reported properties of bulk $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ single crystals. The ferroelectric and structural domain morphologies at a biaxial tensile strain $e_0=0.94\%$ were predicted using phase-field simulations. It is shown that variations in the reported values of bulk properties and in the Landau energy coefficients from different literature sources lead not only to a wide range of possible transition temperatures at a given strain, but also to different ferroelectric states (e.g., polarization along the pseudocubic ⟨110⟩ vs ⟨100⟩ directions) thus different domain structures under a biaxial tensile strain. Both optical second harmonic generation and confocal scanning optical microscopy measurements demonstrate that the domain states in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ films strained at $e_0=0.94\%$ and 1.16% exhibit polar directions along the pseudocubic ⟨110⟩ directions within the pseudocubic (001) plane of the film.

• Received 4 January 2006

DOI:https://doi.org/10.1103/PhysRevB.73.184112