Size effect in ferroelectrics is treated as a competition between the geometrical symmetry of the ferroelectric sample and its crystalline symmetry. Polarization rotation is shown to be a clear finite size effect that results from this competition, which can be induced by all types of driving forces that are coupled with the sample geometry, such as electrical, mechanical and/or thermal. The concept is illustrated with the Landau theory analysis of the polarization state of a cylindrical nanowire of the prototypical ferroelectric PbTiO${}_3$ having its axis parallel to [111] direction. It is shown that this system exhibits a polarization rotation driven by variations of the wire radius or/and temperature. An additional feature of the system is the occurrence of the rhombohedral phase which does not exist in bulk PbTiO${}_3$.

• Received 25 November 2010

DOI:https://doi.org/10.1103/PhysRevB.83.014104