Phase transitions and ferroelectricity in very thin films: Homogeneous and inhomogeneous (domain) states

We discuss ferroelectric phase transitions into single- and multidomain states in very thin films using continuous theory. We 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 (2.5 nm) is the same as given by ab-initio calculations, the actual critical thickness is set by the domains at 1.6 nm. 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. The conclusion that domains always form in thin films is valid almost irrespective of the nature of electrodes (metallic or semiconducting) and whether or not the screening carriers may be present in the ferroelectric itself. In particular, crossover from second to first order phase transition with thickness, envisaged by Batra et al. (1972), is not possible, since it is being preempted by formation of domain structure.