Unusual polarization patterns in flat epitaxial ferroelectric nanoparticles.

We investigate the effects of a lattice misfit strain on a ground state and polarization patterns in flat perovskite nanoparticles (nanoislands of BaTiO3 and PZT) with the use of an ab initio derived effective Hamiltonian. We show that the strain strongly controls the balance between the depolarizing field and the polarization anizotropy in determining the equilibrium polarization patterns. Compressive strain favors 180 degrees stripe or tweed domains while a tensile strain leads to in-plane vortex formation, with the unusual intermediate phase(s) where both ordering motifs coexist. The results may allow us to explain contradictions in recent experimental data for ferroelectric nanoparticles.