Phase diagram of ferroelectric BaTiO3 ultrathin films under open-circuit conditions

Using a first-principles-based Monte Carlo approach, we investigate the strain-temperature phase diagram of BaTiO3 ultrathin film without any surface charge screening. Although the depolarizing field has little effect on the phase types, a unique stripe domain structure with periodic out-of-plane polarization forms in the ultrathin films to minimize the energy of the depolarizing field under the constraint of the boundary condition, which leads to an unusual characteristic of the phase diagram. As a result, the total out-of-plane polarization remains zero at any strain and temperature. The film thickness has obvious effects on the phase diagram, e. g. the Curie temperature decreases and the strain moves to more negative values when the film thickness decreases. It is found that the compressive strain plays a decisive role in the characterization of ferroelectric polarization in such films, which suppresses the in-plane polarization while supporting the out-of-plane polarization, and thus drives the polarization to rotate from the in-plane to the normal direction.