Domain structure in ultrathin ferroelectric films: Analysis with a free energy model

Experiments have shown that the transition temperature of 4-75-unit-cell-thick PbTiO3 films grown on an insulating SrTiO3 substrate range between 550 and 980 K. At high temperatures (below T-c), the films are in a 180 degrees stripe domain state, polarized perpendicular to the surface, and transform at about room temperature to a single macroscopic domain. This transition is curious because the strong depolarizing field is expected to quench the spontaneous polarization. Indeed, a 10-unit-cell-thick BaTiO3 film grown on the same substrate was found to remain in the paraelectric state even at room temperature. To understand these phenomena, we present a free energy model based on the bulk perovskite ferroelectricity model that we have previously developed. The model takes into account two interacting order parameters, the average spontaneous local off-center displacements (pseudospins) and the condensed soft mode. The model shows that at high temperatures the PbTiO3 films should be in the stripe domain state and predicts in reasonable quantitative agreement with experiment the stripe period as a function of temperature and film thickness. It further predicts that at about room temperature the films would transform into a single domain state with vanishing electrical polarization but with large ionic displacements. Finally, the model explains why the properties of PbTiO3 and BaTiO3 are so different from each other.