Metal-ferroelectric supercrystals with periodically curved metallic layers

Simultaneous manipulation of multiple boundary conditions in nanoscale heterostructures offers a versatile route to stabilizing unusual structures and emergent phases. Here, we show that a stable supercrystal phase comprising a three-dimensional ordering of nanoscale domains with tailored periodicities can be engineered in PbTiO₃-SrRuO₃ ferroelectric-metal superlattices. A combination of laboratory and synchrotron X-ray diffraction, piezoresponse force microscopy, scanning transmission electron microscopy and phase-field simulations reveals a complex hierarchical domain structure that forms to minimize the elastic and electrostatic energy. Large local deformations of the ferroelectric lattice are accommodated by periodic lattice modulations of the metallic SrRuO₃ layers with curvatures up to 10⁷ m^-1. Our results show that multidomain ferroelectric systems can be exploited as versatile templates to induce large curvatures in correlated materials, and present a route for engineering correlated materials with modulated structural and electronic properties that can be controlled using electric fields.