Size effects in nanostructured ferroelectrics

The finite size effect in ferroelectrics results in structural instability, imposing a limitation of physical sizes and dimensions of materials in which electric dipoles can be sustained. To evaluate the ultimate limitation of physical sizes for a stable polar phase, the characteristic sizes, i.e., anisotropic correlation lengths of electric dipoles, in a ferroelectric have been examined by considering the surface effect. The size dependence on the Curie temperature in particular is calculated with consideration of crystallographic anisotropy. The mean-field theory shows that the limitation of transverse critical sizes is strongly dependent upon the thickness. In turn, the limitation of the critical thickness is also closely associated with the transverse critical sizes.