Tuning the polar states of ferroelectric films via surface charges and flexoelectricity

Using the self-consistent Landau-Ginzburg-Devonshire approach we simulate and analyze the spontaneous formation of the domain structure in thin ferroelectric films covered with the surface screening charge represented by the Bardeen-type surface states. Hence we consider the competition between the screening and the domain formation as alternative ways to reduce the electrostatic energy and reveal unusual peculiarities of distributions of polarization, electric and elastic fields conditioned by the surface screening length and the flexocoupling strength. We have established that the critical thickness of the film and its transition temperature to a paraelectric phase strongly depend on the Bardeen screening length, while the flexocoupling affects the polarization rotation and closure domain structure. Furthermore the flexocoupling induces ribbon-like nano-scale domains in the film depth far from the top open surface, which might be related to the enigmatic polar nanoregions in relaxor ferroelectrics. Thus the joint action of the surface screening (originating from e.g. the adsorption of ambient ions or surface states) and flexocoupling may remarkably modify polar and electromechanical properties of thin ferroelectric films