  Recent experimental results demonstrate that in thin films ferroelectricity
persists down to film thickness of a few unit cells. This finding opens an
avenue for novel electronic devices based on ultathin ferroelectrics, but also
raises questions about factors controlling ferroelectricity and the nature of
the ferroelectric state at the nanoscale. Here we report a first-principles
study of KNbO3 ferroelectric thin films placed between two metal electrodes,
either SrRuO3 or Pt. We show that the bonding at the ferroelectric-metal
interface imposes severe constraints on the displacement of atoms, destroying
the bulk tetragonal soft mode in thin ferroelectric films. This does not,
however, quench local polarization. If the interface bonding is sufficiently
strong the ground state represents a ferroelectric double-domain structure,
driven by the intrinsic oppositely-oriented dipole moments at the two
interfaces. Although the critical thickness for the net polarization of KNbO3
film is finite - about 1 nm for Pt and 1.8 nm for SrRuO3 electrodes - local
polarization persists down to thickness of a unit cell.
