Ab initio study of shear strain effects on ferroelectricity at PbTiO ₃ thin films

Ferroelectric thin film with the perovskite ABO ₃ structure have been widely used in technology applications, e.g., actuators in MEMS/NEMS and nonvolatile random access memories (FeRAM). In order to clarify the effect of the shear strain on the ferroelectricity, the PbTiO ₃ thin film as a typical one is chosen. The focus of this study is to put on the PbO-terminated (1 × 1) and c(2 × 2) surfaces and the TiO ₂-terminated (1 × 1) surface. Based on ab initio density functional theory calculations with the local density approximation, we have found out that in both the PbO and TiO ₂-terminated (1 × 1) models, the ferroelectricity in the PbO layers was enhanced under the positive shear strain while it was suppressed under the negative one. For the TiO ₂ layers, the ferroelectricity was slightly enhanced and sharply suppressed under the positive and negative shear strains, respectively. In the PbO-terminated (2 × 2) model, the AFE phase was suppressed by the FE phase under the positive shear strain while the opposite trend was found under the negative shear strain. For the PbO layers, the ferroelectricity was enhanced under the positive and negative shear strains. For the TiO ₂ layers, the influence of the negative shear strain on the ferroelectricity was larger than that of the positive one. In addition, the ideal strength of the PbTiO ₃ thin film with the different terminations was investigated as well.