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We study cubic ferroelectrics films that become uniaxial with a polar axisperpendicular to the film because of a misfit strain due to a substrate. Themain present result is the analytical account for the elastic anisotropy aswell as the anisotropy of the electrostriction. They define, in particular, anorientation of the domain boundaries and stabilizing or destabilizing effect ofinhomogeneous elastic strains on the single domain state. We apply the generalresults to perovskite systems like BaTiO3/SrRuO3/SrTiO3 films and find that atleast not far from the ferroelectric phase transition the equilibrium domainstructure consists of the stripes along the cubic axes or at 45 degrees tothem. We have also showed that in this system the inhomogeneous strainsincrease stability with regards to the small fluctuations of the metastablesingle domain state, which may exist not very close to the ferroelectrictransition. The latter analytical result is in qualitative agreement with thenumerical result by Pertsev and Kohlstedt [Phys. Rev. Lett. 98, 257603 (2007)],but we show that the effect is much smaller than those authors claim. We havefound also that under certain conditions on the material constants, which arenot satisfied in the perovskites but are not forbidden either, a checkerboarddomain structure can be realized instead of the stripe-like one and that thepolarization-strain coupling decreases stability of a single domain stateinstead of increasing it. The single domain state is metastable at certainlarge thicknesses and becomes suitable for memory applications at even largerthicknesses when the lifetime of the metastable state becomes sufficientlylarge.

Effects of anisotropic elasticity in the problem of domain formation and stability of monodomain state in ferroelectric films