Thickness dependency of 180° stripe domains in ferroelectric ultrathin films: A first-principles-based study

A first-principles-based scheme is used to investigate the thickness dependency of domain width of 180° stripe domains in Pb(Zr,Ti)O3 ultrathin films. Our study shows that (1) more metastable states with energy closer to the 180° stripe domain ground state occur in thicker films, (2) the Kittel law is valid for 180° stripe domains when the film thickness is above 1.6nm, and (3) below 1.2nm, the Kittel law cannot be applied anymore due to the disappearance of domains. The thickness dependency of the domain morphology is also discussed.