Defect-related lattice strain and the transition temperature in ferroelectric thin films

We propose an extension to the phenomenological thermodynamic Landau-Devonshire theory to include the contribution of inhomogeneous strains caused by lattice defects to the Gibbs free energy. The model yields correction terms for dielectric and ferroelectric quantities as a function of both elastic misfit strain and defect-related strain that can be measured by x-ray-diffraction techniques. We compare the correction in Curie-Weiss temperature due to elastic and inhomogeneous strain in pristine, W and Mn 1% doped Ba_0.6Sr_0.4TiO₃ thin films grown on the LaAlO₃ substrate. If the contribution of inhomogeneous strain is included, the agreement with measurements markedly improves.