Ferroelastic domains in bilayered ferroelectric thin films

We investigate theoretically ferroelastic domain fractions in a heteroepitaxial bilayer consisting of (001) tetragonal PbZrxTi1-xO3 and (001) rhombohedral PbZr1-xTixO3 on a thick (001) passive substrate as a function of the lattice misfit strain between layers and the substrate. By considering the self-strain in each layer and the indirect elastic interaction between the layers, we provide a numerical analysis of the relative domain fractions in the tetragonal layer of a (001)PbZr0.2Ti0.8O3/(001)PbZr0.8Ti0.2O3 and (001)PbZr0.4Ti0.6O3/(001)PbZr0.6Ti0.4O3 bilayer structure as a function of the tetragonal layer thickness on (001)LaAlO3, (001)SrTiO3, and (001) MgO. It is found that the elastic coupling between the tetragonal and rhombohedral layers leads to an excess elastic energy in the tetragonal layer, resulting in a two to three times increase in the ferroelastic domain volume fraction of the tetragonal layer compared to single-layer films of similar thickness. These results show alternate ways of engineering ferroelastic domain structures in ferroelectric thin films.