Ab initiostudy of the critical thickness for ferroelectricity in ultrathinPt∕PbTiO3∕Ptfilms

The ferroelectricity of single-domain ultrathin PbTiO3 films sandwiched between metallic Pt electrodes has been studied using ab initio density-functional theory (DFT) calculations within the local-density approximation. For stress-free PbTiO3 films with an in-plane lattice constant of the tetragonal bulk phase, we find that the films lose ferroelectricity below a critical thickness of about 4 and 6 unit cells (similar to 16 and 24 A) for PbO- and TiO2-terminated films, respectively. This result is in contradiction to a recent DFT study by Sai, Kolpak, and Rappe [Phys. Rev. B 72, 020101(R) (2005)], in which the persistence of ferroelectricity for Pt/PbTiO3/Pt films down to one unit cell (4 A) has been reported. Careful tests with different types of pseudopotentials and density functionals reveal that this discrepancy is due to insufficiencies of the widely used generalized-gradient approximations PW91 and PBE, which have been employed by Sai for describing perovskite compounds