Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

Abstract

Whilst often discussed as non-trivial phases of low-dimensional ferroelectrics, modulated polar phases such as the dipolar maze and the nano-bubble state have been appraised as essentially distinct. Here we emphasize their topological nature and show that these self-patterned polar states, but also additional mesophases such as the disconnected labyrinthine phase and the mixed bimeron-skyrmion phase, can be fathomed in their plurality through the unifying canvas of phase separation kinetics. Under compressive strain, varying the control parameter, i.e., the external electric field, conditions the nonequilibrium self-assembly of domains, and bridges nucleation and spinodal decomposition via the sequential onset of topological transitions. The evolutive topology of these polar textures is driven by the (re)combination of the elementary topological defects, merons and antimerons, into a plethora of composite topological defects such as the fourfold junctions, the bimeron and the target skyrmion. Moreover, we demonstrate that these manipulable defects are stable at room temperature and feature enhanced functionalities, appealing for devising future topological-based nanoelectronics.

Freestanding Ferroelectric Bubble Domains

“…These Néel or Bloch‐type rotations of electric dipoles incur a substantial on‐site and elastic energy cost, which is compensated by the gain in electrostatic energy—providing the local total energy minima needed for polar bubble formation. Our first‐principles based simulations [ 12 ] show that, similar to bubble skyrmions [ 2 ] observed in PTO/STO superlattices, the polar bubbles have a skyrmion topology and are characterized by an integer skyrmion number in each [001] plane. Based on these numerical predictions, the two types [ 2,12 ] of bubble skyrmions share a solenoidal‐like orientation of the outer dipole field lines and are, in fact, homotopy equivalent (i.e., can be continuously transformed one into the other).…”

“…Our first‐principles based simulations [ 12 ] show that, similar to bubble skyrmions [ 2 ] observed in PTO/STO superlattices, the polar bubbles have a skyrmion topology and are characterized by an integer skyrmion number in each [001] plane. Based on these numerical predictions, the two types [ 2,12 ] of bubble skyrmions share a solenoidal‐like orientation of the outer dipole field lines and are, in fact, homotopy equivalent (i.e., can be continuously transformed one into the other). However, unlike bubble domains in PTO‐based materials, our simulations predict that the polar bubbles discussed herein are achiral.…”

“…To understand the observed endurance of FE bubbles we have performed first‐principle based effective Hamiltonian simulations. In a first step, we model the pristine bubble domains by performing a thermal quench of the system from 600 to 300 K [ 12,13 ] under the built‐in bias field E z oriented along p.c. direction and a fixed in‐plane homogeneous strain of −2%.…”

“…The simulation steps described above are done at different values of the built‐in field magnitudes E z in the range from 0 to 2 MV cm −1 . For the pristine state, the chosen combination of the partial screening conditions and misfit strain leads to stable bubble arrays [ 12,13 ] for 0.5 MV cm −1 < E z < 0.9 MV cm −1 . An example of the typical domain structure at E z = 0.7 MV cm −1 is shown in Figure a.…”

“…The intricate and competing correlations among elastic,electrostatic, and gradient energies in ferroelectric (FE)–dielectric (DE)–FE heterostructures create topological objects with complex polar order, such as vortices, bubbles, and skyrmions. [ 1–4 ] The inherent nontrivial electromechanical inhomogeneities in these topological objects promote a plethora of novel physical phenomena such as negative capacitance, [ 5–9 ] flexoelectric effects, [ 10 ] emergent chirality, [ 11 ] and gradual conductivity hysteresis [ 12,13 ] which have tremendous potential in future computing and sensing technologies. The parameter space (epitaxial strain, screening, built‐in field, etc.)…”