superlattices*

We investigate via second principles simulations the electrostatics of multi-domain structures in (PbTiO₃)_n/(SrTiO₃)_n superalttices. The relaxed structure corresponds to a polar vortex configuration where counter-rotating vortices lay in between of the c-domains. It is observed that the optimal value of the domain width w, follows diophantically Kittel law for a thickness n assuming straight domains. However, stabilization of other widths different from the optimal are possible within a given range. Studying these limiting cases we could observe that the mechanism for the destruction of domains is the progressive approach of the vortices towards the interface driving the system to a polarization wave directed along x-direction. More interestingly, the generation of new c domains is driven by the nucleation of small polarization regions at the interfaces being encapsulated by pairs of counter-rotating vortices. Moreover, following the dynamics of such structures we detect that the recombination of vortex-antivortex pairs serves as the growth mechanism for the closure and stabilization of the emergent domains