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

Abstract

We study cubic ferroelectrics films that become uniaxial with a polar axis perpendicular to the film because of a misfit strain due to the substrate. The main present result is the analytical account for the elastic anisotropy as well as the anisotropy of the electrostriction. They define, in particular, the orientation of the domain boundaries and the stabilizing or destabilizing effect of inhomogeneous elastic strains on the single domain state. We apply the general results to perovskite systems like BaTiO${}_{3}$/SrRuO${}_{3}$/SrTiO${}_{3}$ films and find that, at least not far from the ferroelectric phase transition, the equilibrium domain structure consists of the stripes along the cubic axes or at ${45}^{\ifmmode^\circ\else\textdegree\fi{}}$ to them. We also show that, in this system, the inhomogeneous strains increase stability with regard to small fluctuations of the metastable single domain state, which may exist not very close to the ferroelectric transition. The latter analytical result is in qualitative agreement with the numerical result by Pertsev and Kohlstedt [N. A. Pertsev and H. Kohlstedt, Phys. Rev. Lett. 98, 257603 (2007)] but we show that the effect is much smaller than those authors claim. We find also that under some conditions on the material constants, which are not satisfied in perovskites but are not forbidden, in principle, instead of the striped-like domain structure a checkerboard one can be realized and the polarization-strain coupling decreases the stability of a single domain state instead of increasing it.