Observation of polar vortices in oxide superlattices

In material systems with several interacting degrees of freedom, the complex interplay between these factors can give rise to exotic phases; now superlattices consisting of alternating layers of PbTiO3 and SrTiO3 are found to exhibit an unusual form of ferroelectric ordering in the PbTiO3 layers, in which the electric dipoles arrange themselves into regular, ordered arrays of vortex–antivortex structures. In material systems with several interacting degrees of freedom (such as spin, charge and lattice distortions), the complex interplay between these factors can give rise to exotic phases. A vivid example of such behaviour has been identified by Ramamoorthy Ramesh and colleagues in superlattices consisting of alternating layers of PbTiO3 and SrTiO3. They observe the formation of an unusual form of ferroelectric ordering in the PbTiO3 layers, in which the electric dipoles arrange themselves into regular vortex–antivortex array structures, suggesting potential routes for further tuning and enhancing the properties of these versatile oxide materials. The complex interplay of spin, charge, orbital and lattice degrees of freedom provides a plethora of exotic phases and physical phenomena1,2,3,4,5. In recent years, complex spin topologies have emerged as a consequence of the electronic band structure and the interplay between spin and spin–orbit coupling in materials6,7. Here we produce complex topologies of electrical polarization—namely, nanometre-scale vortex–antivortex (that is, clockwise–anticlockwise) arrays that are reminiscent of rotational spin topologies6—by making use of the competition between charge, orbital and lattice degrees of freedom in superlattices of alternating lead titanate and strontium titanate layers. Atomic-scale mapping of the polar atomic displacements by scanning transmission electron microscopy reveals the presence of long-range ordered vortex–antivortex arrays that exhibit nearly continuous polarization rotation. Phase-field modelling confirms that the vortex array is the low-energy state for a range of superlattice periods. Within this range, the large gradient energy from the vortex structure is counterbalanced by the corresponding large reduction in overall electrostatic energy (which would otherwise arise from polar discontinuities at the lead titanate/strontium titanate interfaces) and the elastic energy associated with epitaxial constraints and domain formation. These observations have implications for the creation of new states of matter (such as dipolar skyrmions, hedgehog states) and associated phenomena in ferroic materials, such as electrically controllable chirality.