Size Effects in Ferroelectric Thin Films: The Role of 180 degree domains
  The depolarization fields set up to due to uncompensated surface charges in a ferroelectric thin film can suppress the ferroelectric phase below a critical size. Recent experiments show that 180 degree domain structures can help to stabilize ferroelectricity in films as thin as 3 unit cells. We study the influence of domain structures on the size-dependent properties of ferroelectric thin films using time-dependent Ginzburg-Landau theory. The model incorporates the effect of depolarization field by considering non-ferroelectric passive layers at the top and bottom surfaces. We show that the 180 degree domain size decreases as the film thickness is reduced and the film abruptly becomes paraelectric below a critical size. The 180 degree domains appear during polarization switching causing a time-dependent relaxation of the remnant polarization, consistent with recent experiments. The depolarization-induced domain wall motion significantly alters the shape of the polarization versus electric field (P-E) loops at small thicknesses. 
Rajeev Ahluwalia and David J. Srolovitz