A first-principles-based scheme is developed to simulate properties of (001) PbO-terminated Pb͑Zr 1−x Ti x ͒O 3 thin films that are under stress-free and open-circuit boundary conditions. Their low-temperature spontaneous polarization never vanishes down to the minimal thickness, and continuously rotates between the in-plane ͗010͘ and ͗110͘ directions when varying the Ti composition around x = 0.50. Such rotation dramatically enhances piezoelectricity and dielectricity. Furthermore, the order of some phase transitions changes when going from bulk to thin films.

The thickness dependency of the Curie temperature in stress-free Pb͑Zr 0.5 Ti 0.5 ͒O 3 ultrathin films under open-circuit conditions is revealed from the computation of some nontrivial statistical quantities ͑such as fourth-order cumulants͒, via a first-principles-based technique. For thicknesses above 16 Å, this dependency follows the usual finite-size scaling law with a critical exponent that is consistent with the one associated with the three-dimensional-random-Ising universality class. On the other hand, the Curie temperature-versus-film's thickness curve deviates from this scaling law below 12 Å while being rather well described by an empirical equation down to 8 Å.

We report first-principles-based calculations, combined with an efficient Monte Carlo technique, that undoubtedly show that Pb(Zr0.5Ti0.5)O3, one of the most important ferroelectrics to date, adopts critical behavior that strongly deviates from the classical mean-field approach while being, in fact, consistent with the 3D-random Ising universality class.

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