UC Berkeley

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.