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

Abstract

The ferroelectricity of single-domain ultrathin ${\mathrm{PbTiO}}_{3}$ 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 ${\mathrm{PbTiO}}_{3}$ 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 ($\ensuremath{\sim}16$ and $24\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$) for $\mathrm{PbO}$- and ${\mathrm{TiO}}_{2}$-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 $\mathrm{Pt}∕{\mathrm{PbTiO}}_{3}∕\mathrm{Pt}$ films down to one unit cell $(4\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$ 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 et al. for describing perovskite compounds.