Structural and energetic properties of domains in PbTiO 3/ SrTiO 3 superlattices from first principles

We report first-principles calculations, within the density functional theory, on the structural and energetic properties of 180${}^{\ensuremath{\circ}}$ stripe domains in (PbTiO${}_{3}$)${}_{n}$/(SrTiO${}_{3}$)${}_{n}$ superlattices. For the explored periodicities ($n=3$ and 6), we find that the polydomain structures compete in energy with the monodomain phases. Our results suggest the progressive transition, as a function of $n$, from a strong to a weak electrostatic coupling regime between the SrTiO${}_{3}$ and PbTiO${}_{3}$ layers. Structurally, they display continuous rotation of polarization connecting 180${}^{\ensuremath{\circ}}$ domains. A large offset between [100] atomic rows across the domain wall and huge strain gradients are observed. The domain wall energy is very isotropic, depending very weakly on the stripe orientation.