Emergence of the Vortex State in Confined Ferroelectric Heterostructures.

The manipulation of charge and lattice degrees of freedom in atomically precise, low-dimensional ferroelectric superlattices can lead to exotic polar structures, such as a vortex state. The role of interfaces in the evolution of the vortex state in these superlattices (and the associated electrostatic and elastic boundary conditions they produce) has remained unclear. Here, the toroidal state, arranged in arrays of alternating clockwise/counterclockwise polar vortices, in a confined SrTiO3 /PbTiO3 /SrTiO3 trilayer is investigated. By utilizing a combination of transmission electron microscopy, synchrotron-based X-ray diffraction, and phase-field modeling, the phase transition as a function of layer thickness (number of unit cells) demonstrates how the vortex state emerges from the ferroelectric state by varying the thickness of the confined PbTiO3 layer. Intriguingly, the vortex state arises at head-to-head domain boundaries in ferroelectric a1 /a2 twin structures. In turn, by varying the total number of PbTiO3 layers (moving from trilayer to superlattices), it is possible to manipulate the long-range interactions among multiple confined PbTiO3 layers to stabilize the vortex state. This work provides a new understanding of how the different energies work together to produce this exciting new state of matter and can contribute to the design of novel states and potential memory applications.