Unusual polarization patterns in flat epitaxial ferroelectric nanoparticles

A 2D ferroelectric vortex pattern in twisted BaTiO3 freestanding layers

The wealth of complex polar topologies1-10 recently found in nanoscale ferroelectrics results from a delicate balance between the intrinsic tendency of the materials to develop a homogeneous polarization and the electric and mechanical boundary conditions imposed on them. Ferroelectric-dielectric interfaces are model systems in which polarization curling originates from open circuit-like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux-closure11-14 domains that evolve into vortex-like structures at the nanoscale15-17 level. Although ferroelectricity is known to couple strongly with strain (both homogeneous18 and inhomogeneous19,20), the effect of mechanical constraints21 on thin-film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles provides an opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated with the twisting. Furthermore, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding provides opportunities to create two-dimensional high-density vortex crystals that would enable us to explore previously unknown physical effects and functionalities.

Effect of Aspect Ratio of Ferroelectric Nanofilms on Polarization Vortex Stability under Uniaxial Tension or Compression

Mastering the variations in the stability of a polarization vortex is fundamental for the development of ferroelectric devices based on polarization vortex domain structures. Some phase field simulations were conducted on PbTiO3 nanofilms with an initial polarization vortex under uniaxial tension or compression to investigate the conditions of vortex instability and the effects of aspect ratio of nanofilms and temperature on them. The instability of a polarization vortex is strongly dependent on aspect ratio and temperature. The critical compressive stress increases with decreasing aspect ratio under the action of compressive stress. However, the critical tensile stress first decreases and then increases with decreasing aspect ratio, then continues to decrease. There are two inflection points in the curve. In addition, an elevated temperature makes both the critical tensile and compressive stresses decline, and will also cause the aspect ratio corresponding to the inflection point to decrease. These are very important for the design of promising nano-ferroelectric devices based on polarization vortices to improve their performance while maintaining storage density.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Nonvolatile ferroelectric domain wall memory integrated on silicon

Ferroelectric domain wall memories have been proposed as a promising candidate for nonvolatile memories, given their intriguing advantages including low energy consumption and high-density integration. Perovskite oxides possess superior ferroelectric prosperities but perovskite-based domain wall memory integrated on silicon has rarely been reported due to the technical challenges in the sample preparation. Here, we demonstrate a domain wall memory prototype utilizing freestanding BaTiO₃ membranes transferred onto silicon. While as-grown BaTiO₃ films on (001) SrTiO₃ substrate are purely c-axis polarized, we find they exhibit distinct in-plane multidomain structures after released from the substrate and integrated onto silicon due to the collective effects from depolarizing field and strain relaxation. Based on the strong in-plane ferroelectricity, conductive domain walls with reading currents up to nanoampere are observed and can be both created and erased artificially, highlighting the great potential of the integration of perovskite oxides with silicon for ferroelectric domain wall memories.

Integrating ferroelectric perovskite oxides on Si is highly desired for electronic applications but challenging. Here, the authors show emergent in-plane ferroelectricity and promising nonvolatile memories based on resistive domain wall in BaTiO₃/Si.

Phase Diagram of a Strained Ferroelectric Nanowire

Ferroelectric materials manifest unique dielectric, ferroelastic, and piezoelectric properties. A targeted design of ferroelectrics at the nanoscale is not only of fundamental appeal but holds the highest potential for applications. Compared to two-dimensional nanostructures such as thin films and superlattices, one-dimensional ferroelectric nanowires are investigated to a much lesser extent. Here, we reveal a variety of the topological polarization states, particularly the vortex and helical chiral phases, in loaded ferroelectric nanowires, which enable us to complete the strain–temperature phase diagram of the one-dimensional ferroelectrics. These phases are of prime importance for optoelectronics and quantum communication technologies.

Improvements of Electrical Characteristics in Poly-Si Nanowires Thin-Film Transistors with External Connection of a BiFeO3 Capacitor

By a sol–gel method, a BiFeO₃ (BFO) capacitor is fabricated and connected with the control thin film transistor (TFT). Compared with a control thin-film transistor, the proposed BFO TFT achieves 56% drive current enhancement and 7–28% subthreshold swing (SS) reduction. Moreover, the effect of the proposed BiFeO₃ capacitor on I_DS-V_GS hysteresis in the BFO TFT is 0.1–0.2 V. Because dV_int/dV_GS > 1 is obtained at a wide range of V_GS, it reveals that the incomplete dipole flipping is a major mechanism to obtain improved SS and a small hysteresis effect in the BFO TFT. Experimental results indicate that sol-gel BFO TFT is a potential candidate for digital application.

Recent Progress on Topological Structures in Ferroic Thin Films and Heterostructures

Topological spin/polarization structures in ferroic materials continue to draw great attention as a result of their fascinating physical behaviors and promising applications in the field of high-density nonvolatile memories as well as future energy-efficient nanoelectronic and spintronic devices. Such developments have been made, in part, based on recent advances in theoretical calculations, the synthesis of high-quality thin films, and the characterization of their emergent phenomena and exotic phases. Herein, progress over the last decade in the study of topological structures in ferroic thin films and heterostructures is explored, including the observation of topological structures and control of their structures and emergent physical phenomena through epitaxial strain, layer thickness, electric, magnetic fields, etc. First, the evolution of topological spin structures (e.g., magnetic skyrmions) and associated functionalities (e.g., topological Hall effect) in magnetic thin films and heterostructures is discussed. Then, the exotic polar topologies (e.g., domain walls, closure domains, polar vortices, bubble domains, and polar skyrmions) and their emergent physical properties in ferroelectric oxide films and heterostructures are explored. Finally, a brief overview and prospectus of how the field may evolve in the coming years is provided.

Subunit cell-level measurement of polarization in an individual polar vortex

Recently, several captivating topological structures of electric dipole moments (e.g., vortex, flux closure) have been reported in ferroelectrics with reduced size/dimensions. However, accurate polarization distribution of these topological ferroelectric structures has never been experimentally obtained. We precisely measure the polarization distribution of an individual ferroelectric vortex in PbTiO₃/SrTiO₃ superlattices at the subunit cell level by using the atomically resolved integrated differential phase contrast imaging in an aberration-corrected scanning transmission electron microscope. We find, in vortices, that out-of-plane polarization is larger than in-plane polarization, and that downward polarization is larger than upward polarization. The polarization magnitude is closely related to tetragonality. Moreover, the contribution of the Pb─O bond to total polarization is highly inhomogeneous in vortices. Our precise measurement at the subunit cell scale provides a sound foundation for mechanistic understanding of the structure and properties of a ferroelectric vortex and lattice-charge coupling phenomena in these topological ferroelectric structures.

Epitaxial patterned Bi2FeCrO6 nanoisland arrays with room temperature multiferroic properties

Epitaxial multiferroic Bi₂FeCrO₆ nanoisland arrays with a lateral size of ∼100 nm have been successfully fabricated by patterned SiO₂ template-assisted pulsed laser deposition. The as-grown island structure exhibits promising multiferroic properties (i.e. ferroelectric and magnetic) even at nanometer dimensions at room temperature. This work demonstrates an effective strategy to fabricate high-density nonvolatile ferroelectric/multiferroic memory devices.

Domain alignment within ferroelectric/dielectric PbTiO3/SrTiO3 superlattice nanostructures

The ferroelectric domain pattern within lithographically defined PbTiO₃/SrTiO₃ ferroelectric/dielectric heteroepitaxial superlattice nanostructures is strongly influenced by the edges of the structures. Synchrotron X-ray nanobeam diffraction reveals that the spontaneously formed 180° ferroelectric stripe domains exhibited by such superlattices adopt a configuration in rectangular nanostructures in which domain walls are aligned with long patterned edges. The angular distribution of X-ray diffuse scattering intensity from nanodomains indicates that domains are aligned within an angular range of approximately 20° with respect to the edges. Computational studies based on a time-dependent Landau-Ginzburg-Devonshire model show that the preferred direction of the alignment results from lowering of the bulk and electrostrictive contributions to the free energy of the system due to the release of the lateral mechanical constraint. This unexpected alignment appears to be intrinsic and not a result of distortions or defects caused by the patterning process. Our work demonstrates how nanostructuring and patterning of heteroepitaxial superlattices allow for pathways to create and control ferroelectric structures that may appear counterintuitive.

Phase coexistence and electric-field control of toroidal order in oxide superlattices

Systems that exhibit phase competition, order parameter coexistence, and emergent order parameter topologies constitute a major part of modern condensed-matter physics. Here, by applying a range of characterization techniques, and simulations, we observe that in PbTiO₃/SrTiO₃ superlattices all of these effects can be found. By exploring superlattice period-, temperature- and field-dependent evolution of these structures, we observe several new features. First, it is possible to engineer phase coexistence mediated by a first-order phase transition between an emergent, low-temperature vortex phase with electric toroidal order and a high-temperature ferroelectric a₁/a₂ phase. At room temperature, the coexisting vortex and ferroelectric phases form a mesoscale, fibre-textured hierarchical superstructure. The vortex phase possesses an axial polarization, set by the net polarization of the surrounding ferroelectric domains, such that it possesses a multi-order-parameter state and belongs to a class of gyrotropic electrotoroidal compounds. Finally, application of electric fields to this mixed-phase system permits interconversion between the vortex and the ferroelectric phases concomitant with order-of-magnitude changes in piezoelectric and nonlinear optical responses. Our findings suggest new cross-coupled functionalities.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.

High-density array of ferroelectric nanodots with robust and reversibly switchable topological domain states

The exotic topological domains in ferroelectrics and multiferroics have attracted extensive interest in recent years due to their novel functionalities and potential applications in nanoelectronic devices. One of the key challenges for these applications is a realization of robust yet reversibly switchable nanoscale topological domain states with high density, wherein spontaneous topological structures can be individually addressed and controlled. This has been accomplished in our work using high-density arrays of epitaxial BiFeO₃ (BFO) ferroelectric nanodots with a lateral size as small as ~60 nm. We demonstrate various types of spontaneous topological domain structures, including center-convergent domains, center-divergent domains, and double-center domains, which are stable over sufficiently long time but can be manipulated and reversibly switched by electric field. The formation mechanisms of these topological domain states, assisted by the accumulation of compensating charges on the surface, have also been revealed. These results demonstrated that these reversibly switchable topological domain arrays are promising for applications in high-density nanoferroelectric devices such as nonvolatile memories.

Topological phase transformations and intrinsic size effects in ferroelectric nanoparticles

Composite materials comprised of ferroelectric nanoparticles in a dielectric matrix are being actively investigated for a variety of functional properties attractive for a wide range of novel electronic and energy harvesting devices. However, the dependence of these functionalities on shapes, sizes, orientation and mutual arrangement of ferroelectric particles is currently not fully understood. In this study, we utilize a time-dependent Ginzburg-Landau approach combined with coupled-physics finite-element-method based simulations to elucidate the behavior of polarization in isolated spherical PbTiO₃ or BaTiO₃ nanoparticles embedded in a dielectric medium, including air. The equilibrium polarization topology is strongly affected by particle diameter, as well as the choice of inclusion and matrix materials, with monodomain, vortex-like and multidomain patterns emerging for various combinations of size and materials parameters. This leads to radically different polarization vs. electric field responses, resulting in highly tunable size-dependent dielectric properties that should be possible to observe experimentally. Our calculations show that there is a critical particle size below which ferroelectricity vanishes. For the PbTiO₃ particle, this size is 2 and 3.4 nm, respectively, for high- and low-permittivity media. For the BaTiO₃ particle, it is ∼3.6 nm regardless of the medium dielectric strength.

Anomalous domain periodicity observed in ferroelectric PbTiO3 nanodots having 180° stripe domains

Nanometer-scale ferroelectric dots and tubes have received a great deal of attention owing to their potential applications to nonvolatile memories and multi-functional devices. As for the size effect of 180° stripe domains in ferroelectric thin films, there have been numerous reports on the thickness-dependent domain periodicity. All these studies have revealed that the domain periodicity (w) of 180° stripe domains scales with the film thickness (d) according to the classical Landau-Lifshitz-Kittel (LLK) scaling law (w ∝ d^1/2) down to the thickness of ~2 nm. In the case of PbTiO₃ nanodots, however, we obtained a striking correlation that for the thickness less than a certain critical value, d_c (~35 nm), the domain width even increases with decreasing thickness of the nanodot, which surprisingly indicates a negative value in the LLK scaling-law exponent. On the basis of theoretical considerations of d_c, we attributed this anomalous domain periodicity to the finite lateral-size effect of a ferroelectric nanodot with an additional effect possibly coming from the existence of a thin non-ferroelectric surface layer.

Discovery of stable skyrmionic state in ferroelectric nanocomposites

Non-coplanar swirling field textures, or skyrmions, are now widely recognized as objects of both fundamental interest and technological relevance. So far, skyrmions were amply investigated in magnets, where due to the presence of chiral interactions, these topological objects were found to be intrinsically stabilized. Ferroelectrics on the other hand, lacking such chiral interactions, were somewhat left aside in this quest. Here we demonstrate, via the use of a first-principles-based framework, that skyrmionic configuration of polarization can be extrinsically stabilized in ferroelectric nanocomposites. The interplay between the considered confined geometry and the dipolar interaction underlying the ferroelectric phase instability induces skyrmionic configurations. The topological structure of the obtained electrical skyrmion can be mapped onto the topology of domain-wall junctions. Furthermore, the stabilized electrical skyrmion can be as small as a few nanometers, thus revealing prospective skyrmion-based applications of ferroelectric nanocomposites.

Controllability of vortex domain structure in ferroelectric nanodot: fruitful domain patterns and transformation paths

Ferroelectric vortex domain structure which exists in low-dimensional ferroelectrics is being intensively researched for future applications in functional nanodevices. Here we demonstrate that adjusting surface charge screening in combination with temperature can provide an efficient way to gain control of vortex domain structure in ferroelectric nanodot. Systematical simulating experiments have been conducted to reveal the stability and evolution mechanisms of domain structure in ferroelectric nanodot under various conditions, including processes of cooling-down/heating-up under different surface charge screening conditions, and increasing/decreasing surface charge screening at different temperatures. Fruitful phase diagrams as functions of surface screening and temperature are presented, together with evolution paths of various domain patterns. Calculations discover up to 25 different kinds of domain patterns and 22 typical evolution paths of phase transitions. The fruitful controllability of vortex domain structure by surface charge screening in combination with temperature should shed light on prospective nanodevice applications of low-dimensional ferroelectric nanostructures.

Manipulating ferroelectric domains in nanostructures under electron beams

Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90° domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net polarizations. Not only does this explain the puzzling patterns that have been observed in TEM studies of ferroelectric nanodots, but also suggests how to manipulate ferroelectric domain patterns via electron beams.

Vortex domain structure in ferroelectric nanoplatelets and control of its transformation by mechanical load

Vortex domain patterns in low-dimensional ferroelectrics and multiferroics have been extensively studied with the aim of developing nanoscale functional devices. However, control of the vortex domain structure has not been investigated systematically. Taking into account effects of inhomogeneous electromechanical fields, ambient temperature, surface and size, we demonstrate significant influence of mechanical load on the vortex domain structure in ferroelectric nanoplatelets. Our analysis shows that the size and number of dipole vortices can be controlled by mechanical load, and yields rich temperature-stress (T-S) phase diagrams. Simulations also reveal that transformations between “vortex states” induced by the mechanical load are possible, which is totally different from the conventional way controlled on the vortex domain by the electric field. These results are relevant to application of vortex domain structures in ferroelectric nanodevices, and suggest a novel route to applications including memories, mechanical sensors and transducers.

Toroidal ferroelectricity in PbTiO3 nanoparticles

We report from first-principles-based atomistic simulations that ferroelectricity can be sustained in PbTiO(3) nanoparticles of only a few lattice constants in size as a result of a toroidal ordering. We find that size-induced topological transformations lead to the stabilization of a ferroelectric bubble by the alignment of vortex cores along a closed path. These transformations, which are driven by the aspect ratio of the nanostructure, change the topology of the polarization field, producing a rich variety of polar configurations. For sufficiently flat nanostructures, a multibubble state bridges the gap between 0D nanodots and 2D ultrathin films. The thermal properties of the ferroelectric bubbles indicate that this state is suitable for the development of nanometric devices.

Goldstone-like states in a layered perovskite with frustrated polarization: a first-principles investigation of PbSr2Ti2O7

With the help of first-principles-based computational techniques, we demonstrate that Goldstone-like states can be artificially induced in a layered-perovskite ferroelectric compound with frustrated polarization, resulting in the emergence of a variety of interesting physical properties that include large, tunable dielectric constants and an ability to easily form vortex polar states in a nanodot geometry. In a similar fashion to the well-known perovskite materials with morphotropic phase boundaries (MPBs), these states manifest themselves as polarization rotations with almost no energy penalty, suggesting that the existence of an MPB is actually yet another manifestation of the Goldstone theorem in solids.

SrTiO(3):Cr nanocrystalline powders: size effects and optical properties

The crystal structure, optical absorption, and photoluminescence of chromium impurity centers were studied in nanocrystalline SrTiO(3):Cr (0.1 mol%) powders with average particle size within the range 13-100 nm prepared by the Pechini-type polymeric sol-gel method. Only the presence of a cubic perovskite phase of O(h)(1) symmetry was proved for the powders at room temperature, by means of x-ray diffraction. The lattice constant a = 3.910 Å, larger than that of bulk SrTiO(3) crystals (a = 3.905 Å), was found for nanoparticles with the size about 20 nm. The optical absorption edge and the zero-phonon R-line ([Formula: see text]) of luminescence of the octahedral Cr(3+) centers shifted to higher energies with decreasing nanoparticle size. These size effects were regarded as intrinsic to SrTiO(3). An unusual and large temperature shift of the R-line position very similar to the 'dielectric related' one of the bulk crystals was observed for all powders, evidencing their quantum paraelectric behavior. However, the powders with the average particle size about 13 and 20 nm did not reveal completely reproducible behavior of the R-line position at low temperatures. This instability was considered a possible manifestation of a low-temperature phase transition in small enough SrTiO(3) nanoparticles.

Vortex polarization states in nanoscale ferroelectric arrays

Two-dimensional arrays of ferroelectric lead zirconate titanate (PZT) nanodots were fabricated using pulsed laser deposition through ultrathin anodic aluminum oxide membrane stencil masks. The static distribution of polarization configurations was investigated using in- and out-of-plane piezoresponse force microscopy (PFM). The observed presence of an in-plane polarization component in nominally (001) oriented PZT suggests the existence of a significant deviation from the regular tetragonal structure that allows the formation of complex core-polarization states. Core-polarization states may indicate the presence of quasi-toroidal polarization ordering. The experimental results are compared with a theoretical model to determine the fingerprint of a vortex polarization state in PFM.