Phase field modeling of flexoelectric effects in ferroelectric epitaxial thin films

The flexoelectric effect which is defined as the coupling between strain gradient and polarization has long been neglected because it is insignificant in bulk ferroelectrics. However, at nanoscale, the strain gradient can be dramatically increased leading to giant flexoelectric effects. In the present study, the flexoelectric effects in epitaxial nano thin films of a 180° multi-domain structure, which are subjected to a compressive in-plane misfit strain, are investigated by the phase field method. Unlike the case of a single domain structure where the strain gradient is mainly attributed to the formation of dislocation which relaxes the misfit strain, in a multi-domain structure, it is attributed to many factors, such as surface and interface effects, misfit relaxation and domain wall structure. The results obtained show that relatively large flexoelectricity-induced electric fields are produced near the domain wall region. The induced field will not only influence the domain structure of the thin film, but also the hysteresis loops when it is under an applied electric field.