Ferromagneticlike Closure Domains in Ferroelectric Ultrathin Films: First-Principles Simulations

We simulate from first principles the energetic, structural, and electronic properties of ferroelectric domains in ultrathin ${\mathrm{SrRuO}}_3/{\mathrm{BaTiO}}_3/{\mathrm{SrRuO}}_3$ ferroelectric capacitors in short circuit. The domains are stabilized down to two unit cells at zero temperature, adopting the form of a domain of closure, common in ferromagnetic thin films. The domains are closed by the in-plane relaxation of the atoms in the first SrO layer of the electrode, which behaves more like SrO in highly polarizable ${\mathrm{SrTiO}}_3$ than in metallic ${\mathrm{SrRuO}}_3$. Even if small, these lateral displacements are very important to stabilize the domains and might provide some hints to explain why some systems break into domains while others remain in a monodomain configuration. An analysis of the electrostatic potential reveals preferential points of pinning for charged defects at the ferroelectric-electrode interface, possibly playing a major role in film fatigue.