Low-symmetry ferroelectric phases stabilized by anisotropic misfit strain

The complete thermodynamic potential of (111) ferroelectric thin films including anisotropic in-plane misfit strain, in-plane shear strain, and external stress is developed based on the Landau-Ginzburg-Devonshire thermodynamic theory. Anisotropic strain-tuned low-symmetry equilibrium phases in (111) single-domain ferroelectric $\mathrm{PbTi}{\mathrm{O}}_{3}$ films were investigated via the developed nonlinear thermodynamic potential and the misfit strain--misfit strain phase diagram was constructed. It was found that the anisotropic epitaxial strain can effectively control the orientations of polarization vectors, which determine the symmetry of equilibrium phases, and their functionalities. In particular, two types of low-symmetry triclinic phases, disappearing under isotropic strain states, can be stabilized by anisotropic strains. Low-symmetry monoclinic and triclinic ferroelectric phases and field-induced phase transitions were also analyzed in depth. It was indicated that the monoclinic (${M}_{A}^{1}$) symmetry rhombohedral-like--tetragonal-like transition and triclinic (${T}_{\mathrm{r}}^{1}$)-monoclinic (${M}_{B}^{1}$) phase transition would give rise to the superior piezoelectric properties as compared to other structure phase transitions. Electric field-enhanced piezoelectric response in triclinic structure originates from the elastic softening that is related to the shear ${u}_{5}$. These results provide guidance for interpreting and understanding more experimental observations as well as the designing of high-performance piezoelectric films.