TY - JOUR KW - Titanium compounds KW - Phase transitions KW - Ferroelectricity KW - Lead titanate KW - Vortex flow KW - Degrees of freedom (mechanics) KW - High resolution transmission electron microscopy KW - Interface states KW - Strontium titanates KW - Ferroelectric state KW - Ferroelectric superlattice KW - Long range interactions KW - Memory applications KW - Number of unit cells KW - Phase field models KW - Polar structures KW - Vortex state AU - S.-L Hsu AU - M.R McCarter AU - C Dai AU - Z Hong AU - L.-Q Chen AU - C.T Nelson AU - L.W Martin AU - Ramamoorthy Ramesh AB - 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. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim BT - Advanced Materials DO - 10.1002/adma.201901014 LA - eng M1 - 36 N1 - cited By 2 N2 - 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. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim PB - Wiley-VCH Verlag PY - 2019 T2 - Advanced Materials TI - Emergence of the Vortex State in Confined Ferroelectric Heterostructures VL - 31 SN - 09359648 ER -