Dependence of Curie temperature on the thickness of an ultrathin ferroelectric film

The thickness dependency of the Curie temperature in stress-free Pb(Zr0.5Ti0.5)O₃ ultrathin films under open-circuit conditions is revealed from the computation of some nontrivial statistical quantities (such as fourth-order cumulants), via a first-principles-based technique. For thicknesses above 16, 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 while being rather well described by an empirical equation down to 8.