Depolarizing field and “real” hysteresis loops in nanometer-scale ferroelectric films

The authors give detailed analysis of the effect of depolarizing field in nanometer-size ferroelectric capacitors studied by Kim et al. [Phys. Rev. Lett. 95, 237602 (2005)]. They calculate a critical thickness of the homogeneous state and its stability with respect to domain formation for strained thin films of BaTiO3 on SrRuO3∕SrTiO3 substrate within the Landau theory. While the former (2.5nm) is the same as given by ab initio calculations, the actual critical thickness is set by the domains at 0.8nm. There is a large Merz’s activation field for polarization relaxation. Remarkably, the results show a negative slope of the “actual” hysteresis loops, a hallmark of the domain structures in ideal thin films with imperfect screening.