Stability of Polar Vortex Lattice in Ferroelectric Superlattices

Abstract

A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO/SrTiO. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

Blowing polar skyrmion bubbles in oxide superlattices

“…(a), the polarization vectors rotate continuously inside the PTO layers, which agrees well with the structure from both theoretical calculations and experiment observations[14,15]. The neighboring vortices show theopposite vorticity (indicated by the blue and red regions, as calculated by ), representing the clockwise-counter clockwise geometric arrangement of the vortices.…”

Ferroelectric Relaxor Quantum Crystals

“…Note that the oscillatory instabilities can also occur in the context of faceting of ferroelectric nano-crystals [40][41][42]. These references illustrate some data for a PZT disc ca.…”

“…There are size limits that permit polarization switching, typically between 12 and 15 nm. These size limits may be compared with those in the more recently discovered vortex arrays [39,40]. The size limits remind us that the circular boundary conditions of our disc-shaped ferroelectric films are very important, and the bull's eye spatial patterns (Figures 7d and 8a) approximate first-order Bessel functions (standing waves on a drum head [35][36][37]).…”

“…The present interest is in extending this work from single nonlinear domain instabilities (Figure 7) to arrays of vortex structures [39,40,51]. In addition, the existing theory is limited to two-dimensional structures, and it would be of interest to extend the modelling, for example, from flat [2D] cycloids to low-aspect ratio [3D] helices [52,53].…”

Spatially resolved steady-state negative capacitance

“…We use the superlattices of SrTiO 3 /PbTiO 3 as our model Ferroelectric-Dielectric heterostructure system where a state of negative capacitance is expected to be stabilized in the equilibrium. In such superlattices vortex-like topologies [16][17][18] are observed as the dominant polarization pattern when the periodicity is optimal [19][20][21] . The defining characteristic of these topologies is the gradual suppression of polarization near the center of the vortex.…”