Ab initio density-functional theory calculations within the local density approximation were conducted to elucidate whether critical thickness for ferroelectricity intrinsically exists in free-standing polydomain ${\text{PbTiO}}_3$ ultrathin films, where there was no screening effect of electrodes. The ferroelectric polydomain state was found to be energetically favorable over the paraelectric state even in the thinnest film one unit-cell thick, indicating no intrinsic critical thickness existed. The ferroelectric distortions in the film were stabilized by the formation of ferromagneticlike closure domains, because the surface charge, which caused a depolarizing field, was sufficiently screened by the in-plane aligned polarization at the surface. Further analysis of the covalent Pb-O bonding structure, which plays a central role in determining ferroelectricity in ${\text{PbTiO}}_3$, revealed that the closure domain structure consists of the $180°$ as well as $90°$ domain walls.

• Received 26 January 2010

DOI:https://doi.org/10.1103/PhysRevB.81.144116