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

Abstract

The thickness dependency of the Curie temperature in stress-free $\text{Pb}({\text{Zr}}_{0.5}{\text{Ti}}_{0.5}){\text{O}}_{3}$ 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 $16\text{ }\text{\AA{}}$, 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 $12\text{ }\text{\AA{}}$ while being rather well described by an empirical equation down to $8\text{ }\text{\AA{}}$.