Ultrathin Films of Ferroelectric Solid Solutions under a Residual Depolarizing Field

A first-principles-derived approach is developed to study the effects of depolarizing electric fields on the properties of $\mathrm{P}\mathrm{b}(\mathrm{Z}\mathrm{r},\mathrm{T}\mathrm{i}){\mathrm{O}}_3$ ultrathin films for different mechanical boundary conditions. A rich variety of ferroelectric phases and polarization patterns is found, depending on the interplay between strain and the amount of screening of surface charges. Examples include triclinic phases, monoclinic states with in-plane and/or out-of-plane components of the polarization, homogeneous and inhomogeneous tetragonal states, as well as peculiar laminar nanodomains.