Polarization scaling in ultrathin epitaxial ferroelectric heterostructures: First-principles results

To resolve the apparent inconsistency between the high c/a and the low measured switchable polarization of ultrathin Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ (PZT) films \footnote{V. Nagarajan {\it et al.}, previous abstract}, we have carried out first-principles effective hamiltonian simulations. The epitaxial strain constraints and the thickness dependent residual depolarization field $\mathcal{E}$$_d$, arising from an incomplete screening of the dipole surface density by real metallic electrodes, \footnote{ J. Junquera and Ph. Ghosez, Nature {\bf 422}, 506 (2003)} are properly included. As the thickness decreases below 150\AA, the increase of $\mathcal{E}$$_d$ in the uniformly polarized state drives a phase transition to a state with 180$^o$ stripe domains, similar to that observed for PbTiO$_3$ films on insulating substrates \footnote{D. D. Fong {\it et al.}, Science, {\bf 304} 1650 (2004)}. Although the net polarization is zero, each domain exhibits the bulk strained polarization and tetragonality, 1.25 \% larger than in the unstrained sample, yielding a consistent interpretation of the experimental data. Work supported by DOE Grant DE-FG02-01ER45937