Phase diagram and domain splitting in thin ferroelectric films with incommensurate phase

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 modeling of the temperature and thickness dependencies of the period of incommensurate 180° -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 the film thickness, depolarization field contribution, surface and gradient energy. The results may provide insight on the temperature dependence of domain structures in nanosized ferroics with inherent incommensurate phases.