Critical lateral size for ferroelectricity in ultrathin film of PbTiO3

We investigated the atomic structures and ferroelectrics of ultrathin film of PbTiO3, whose ferroelectric polarization is parallel to the surface, through first-principles pseudopotential total-energy calculations. We examined the atomic displacements and found that, on TiO2-terminated surface, Ti, O-n, and O-p atoms are displaced dominantly along the direction normal to the surface, while on PbO-terminated surface, Pb and O atoms are displaced dominantly along the polarization direction parallel to the surface. Around the TiO2-terminated surface, the Pb-O hybrid bonding (one of the characteristics of ferroelectric lattice distortion) is weakened, while on the PbO-terminated surface it is enhanced. It is remarkable that the ferroelectric polarization is reduced around TiO2-terminated surface and, rather, enhanced on PbO-terminated surface. The surface effect is significant only within the layers of one lattice constant.