Thickness-dependent polarization of strained BiFeO3 films with constant   tetragonality
  We measure the remnant polarization of ferroelectric domains in BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultra thin films the energetics of near open circuit electrical boundary conditions, i.e. unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to a nanoscale stripe domains, giving rise to an average remnant polarization close to zero as measured by the electron microscopy whilst maintaining the relatively large tetragonal distortion imposed by the non-zero polarization state of each individual domain. 
J. E. Rault, W. Ren, S. Prosandeev, S. Lisenkov, D. Sando, S. Fusil,   M. Bibes, A. Barthelemy, L. Bellaiche, N. Barrett
cond-mat.mtrl-sci