Effects of the depolarization field in a perforated film of the biaxial ferroelectric

Official URL: http://dx.doi.org/10.1134/S1063783412110170

The domain structure in a biaxial ferroelectric layer perforated by cylindrical channels has been investigated using the numerical simulation based on the phenomenological theory of ferroelectricity and the equations of electrostatics in the framework of the Gauss-Seidel iterative method. Both polar axes lie in the plane of the film, which is characteristic of thin epitaxial films of BaTiO3 and (Ba1-xSrx )TiO3 on a MgO substrate. The calculations have been performed using the parameters of BaTiO3, which does not matter because of the qualitative character of the results: the electrostatic problem is two-dimensional and formally applies to infinitely thick layers rather than to thin layers. The primary attention has been paid to the systems containing sixteen channels. Two different orientations of the polar axes with respect to the lattice channels have been considered. It has been shown that, for these orientations, the domain structure has a different character: when the line with the minimum distance between the channels is perpendicular to the bisector of the angle between the polar axes, this structure contains a single channel in the repeating motif and a polarization vortex; when one of the polar axes is perpendicular to the line with the minimum distance between the channels, the situation is less clear. There are indications that the repeating motif of the domain structure in a system of many channels contains two channels and does not contain vortices. The strong influence of the electrodes on the domain structure in this case has been noted.