The ferroelectric properties of disorder $\mathrm{Pb}\left({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}\right){\mathrm{O}}_3$ thin films are investigated with Monte Carlo simulations on the basis of a first-principles-derived Hamiltonian. It is found that there exists a critical thickness of about three unit cells $(\sim 12\mathrm{\AA })$ below which the ferroelectricity disappears under the condition that the in-plane polarizations are suppressed by sufficient clamping effect. Above the critical thickness, periodic 180° stripe domains with out-of-plane polarizations are formed in the systems in order to minimize the energy of the depolarizing field. The stripe period increases with increasing film thickness. The microscopic mechanism responsible for these phenomena is discussed.

• Received 9 June 2004

DOI:https://doi.org/10.1103/PhysRevB.70.104108