Polar Properties and Hysteresis Loops in Multilayered Thin Films Ferroelectric/Virtual Ferroelectric

Abstract

In the framework of Landau--Ginzburg--Devonshire (LGD) phenomenological theory, the influence of misfit strains, surface energy, and finite-size effects on phase diagrams, polar properties, and hysteresis loops has been calculated for multilayered thin films of the type ferroelectric/virtual ferroelectric. The influence of elastic deformations that arise at the interface thin film--substrate owing to a mismatch between the lattice constants in the film and the substrate on the phase diagrams of multilayered thin films virtual ferroelectric SrTiO\(_{3}\)/ferroelectric BaTiO\(_{3}\) has been studied for the first time. In contrast to bulk BaTiO\(_{3}\), in which only four phases (cubic, tetragonal, orthorhombic, and rhombohedral) can exist, it turned out that six thermodynamically stable BaTiO\(_{3}\) phases (paraelectric phase and tetragonal (FEc), two monoclinic (FEaac and FEac), and two orthorhombic (FEa and FEaa) ferroelectric phases) can exist in multilayered SrTiO\(_{3}\)/BaTiO\(_{3}\) films. The main polar properties of hysteresis loops (shape, coercive field, and spontaneous polarization) in thin multilayered SrTiO\(_{3}\)/BaTiO\(_{3}\) films are calculated. It is shown that the system demonstrates a strong dependence of its polar properties on the thickness of SrTiO\(_{3}\) and BaTiO\(_{3}\) layers, as well as on the elastic misfit strains, with SrTiO\(_{3}\) playing the role of dielectric layer: the thicker the layer, the stronger is the depolarization field, which, in its turn, reduces the spontaneous polarization in the BaTiO\(_{3}\) film.