Phase Diagrams and Domain Splitting in Thin Ferroelectric Films with Incommensurate Phases

We studied the phase diagram of thin ferroelectric films with incommensurate phases and semiconductor properties within the framework of Landau-Ginzburg-Devonshire theory. We performed both analytical calculations and phase-field modelling of the temperature and thickness dependencies of the period of incommensurate 180 degree domain structures appeared in thin films covered with perfect electrodes. It is found that the transition temperature from the paraelectric into the incommensurate phase as well as the period of incommensurate domain structure strongly depend on film thickness, and surface and gradient energy contributions. The results may provide insight on the temperature dependence of domain structures in nanosized ferroics with inherent incommensurate phases.