Negative longitudinal piezoelectricity in epitaxial perovskite ferroelectric films

In this paper, we investigate the underlying mechanisms of the universal and intrinsic negative piezoelectricity in perovskite thin film ferroelectrics by using our developed thermodynamic theory of single domain (310) oriented films. Perovskite ferroelectric $\mathrm{Pb}(\mathrm{Z}{\mathrm{r}}_{1--x}\mathrm{T}{\mathrm{i}}_{x}){\mathrm{O}}_{3}$ (PZT) is analyzed in detail as a typical example, but the theory can be applied to any other perovskite piezoelectrics. Consistent with recent experimental work [O. Paull et al., Nat. Mater. 21, 74 (2022)], our theory also indicates that there exists a strong coupling between ${P}_{2}$ (along the [1--30] direction) and ${P}_{3}$ (along the [310] direction) allowed by the 2/$m$ point group symmetry of the paraelectric state. From the calculated composition--misfit strain and misfit strain--misfit strain phase diagrams of $\mathrm{Pb}(\mathrm{Z}{\mathrm{r}}_{1--x}\mathrm{T}{\mathrm{i}}_{x}){\mathrm{O}}_{3}$, it can be seen that isomorphic transitions of 1 symmetry between three triclinic states (${a}_{1}{a}_{2}c, {a}_{1}c$, and ${a}_{1}{a}_{2}$) take place near morphotropic phase boundary composition and under both isotropic tensile strain and anisotropic tensile strain. The negative piezoelectric coefficient ${d}_{33}$ appears in the quasi-${a}_{1}{a}_{2}$ phase under tensile strain, which stems from the very approximate energies between ${a}_{1}{a}_{2}c$ and ${a}_{1}{a}_{2}$ under tensile strain due to the strong coupling between ${P}_{2}$ and ${P}_{3}$ caused by symmetry breaking. Moreover, this coupling leads to negative partial differentiation of longitudinal strain on longitudinal polarization in the quasi-${a}_{1}{a}_{2}$ phase, which also gives rise to negative ${d}_{33}$. We also demonstrate the longitudinal negative piezoelectricity in (210) and (410) PZT thin films. The results are consistent with those of (310) films due to their same symmetry. This paper will deepen understanding about the anomalous negative piezoelectricity of perovskite ferroelectric materials, and provide strategies for discovering materials with novel electromechanical properties.