Influence of depolarization field on polarization states in epitaxial ferroelectric thin films with biaxial misfit strains

Depolarization field and misfit strain are two important factors that may greatly influence the properties of ferroelectric thin films. The effect of depolarization field on polarization states of single-domain ferroelectric thin films with nonequally biaxial in-plane misfit strains are studied in the present work by numerically solving three coupled Euler-Lagrange equations, which are derived from the minimization of total free energy. The misfit strain-misfit strain and thickness-misfit strain phase diagrams are constructed for single-domain PbTiO3 thin films grown on tetragonal substrates with and without depolarization field. The depolarization field shifts the phase boundaries in the phase diagrams, leading to the contraction and expansion of the regions of out-of-plane and in-plane phases, respectively. For ferroelectric thin films with nonequally biaxial misfit strains, the depolarization field induces the phase transitions from orthorhombic phases to in-plane tetragonal phases. 10.1103/PhysRevB.77.014104 PHYSICAL REVIEW B 77, 014104 (2008)