Domain wall conductivity in semiconducting hexagonal ferroelectric TbMnO3 thin films

Although enhanced conductivity of ferroelectric domain boundaries has been found in BiFeO3 and Pb(Zr,Ti)O3 films as well as hexagonal rare-earth manganite single crystals, the mechanism of the domain wall conductivity is still under debate. Using conductive atomic force microscopy, we observe enhanced conductance at the electrically-neutral domain walls in semiconducting hexagonal ferroelectric TbMnO3 thin films where the structure and polarization direction are strongly constrained along the c-axis. This result indicates that domain wall conductivity in ferroelectric rare-earth manganites is not limited to charged domain walls. We show that the observed conductivity in the TbMnO3 films is governed by a single conduction mechanism, namely, the back-to-back Schottky diodes tuned by the segregation of defects.

Deciphering the physics and chemistry of perovskites with transmission electron microscopy

Perovskite oxides exhibit rich structural complexity and a broad range of functional properties, including ferroelectricity, ferromagnetism, and superconductivity. The development of aberration correction for the transmission electron microscope and concurrent progress in electron spectroscopy, electron holography, and other techniques has fueled rapid progress in the understanding of the physics and chemistry of these materials. New techniques based on the transmission electron microscope are first surveyed, and the applications of these techniques for the study of the structure, chemistry, electrostatics, and dynamics of perovskite oxides are then explored in detail, with a particular focus on ferroelectric materials.

Low energy consumption spintronics using multiferroic heterostructures

We review the recent progress in the field of multiferroic magnetoelectric heterostructures. The lack of single phase multiferroic candidates exhibiting simultaneously strong and coupled magnetic and ferroelectric orders led to an increased effort into the development of artificial multiferroic heterostructures in which these orders are combined by assembling different materials. The magnetoelectric coupling emerging from the created interface between the ferroelectric and ferromagnetic layers can result in electrically tunable magnetic transition temperature, magnetic anisotropy or magnetization reversal. The full potential of low energy consumption magnetic based devices for spintronics lies in our understanding of the magnetoelectric coupling at the scale of the ferroic domains. Although the thin film synthesis progresses resulted into the complete control of ferroic domain ordering using epitaxial strain, the local observation of magnetoelectric coupling remains challenging. The ability to imprint ferroelectric domains into ferromagnets and to manipulate those solely using electric fields suggests new technological advances for spintronics such as magnetoelectric memories or memristors.

A phase-field study of the scaling law in free-standing ferroelectric thin films

The scaling law for ferroelectric stripe domains is investigated in free-standing BaTiO3 and PbTiO3 thin films via phase-field simulations. The results agree with the Kittel law, where the square of the domain width is found to be proportional to the thin film thickness. After being rescaled by the corresponding domain wall thickness, the generalized scaling law is also demonstrated, with the dimensionless scaling constant M estimated to be ∼3.3 in two ferroelectric materials. Moreover, we predict the effect of the exchange constant which is incorporated in Ginzburg-Landau theory on the equilibrium domain width and the critical thickness of the ferroelectric thin films.

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.

Electronic properties of electrical vortices in ferroelectric nanocomposites from large-scale ab initio computations

An original ab initio procedure is developed and applied to a ferroelectric nanocomposite, in order to reveal the effect of electrical vortices on electronic properties. Such procedure involves the combination of two large-scale numerical schemes, namely, the effective Hamiltonian (to incorporate ionic degrees of freedom) and the linear-scaling three-dimensional fragment method (to treat electronic degrees of freedom). The use of such procedure sheds some light into the origin of the recently observed current that is activated at rather low voltages in systems possessing electrical vortices. It also reveals a novel electronic phenomena that is a systematic control of the type of the band-alignment (i.e., type I versus type II) within the same material via the temperature-driven annihilation/formation of electrical topological defects.

Voltage-controlled ferroelastic switching in Pb(Zr0.2Ti0.8)O3 thin films

We report a voltage controlled reversible creation and annihilation of a-axis oriented ∼10 nm wide ferroelastic nanodomains without a concurrent ferroelectric 180° switching of the surrounding c-domain matrix in archetypal ferroelectric Pb(Zr0.2Ti0.8)O3 thin films by using the piezo-response force microscopy technique. In previous studies, the coupled nature of ferroelectric switching and ferroelastic rotation has made it difficult to differentiate the underlying physics of ferroelastic domain wall movement. Our observation of distinct thresholds for ferroelectric and ferroelastic switching allows us investigate the ferroelastic switching cleanly and demonstrate a new degree of nanoscale control over the ferroelastic domains.

Poisson noise removal from high-resolution STEM images based on periodic block matching

Scanning transmission electron microscopy (STEM) provides sub-ångstrom, atomic resolution images of crystalline structures. However, in many applications, the ability to extract information such as atom positions, from such electron micrographs, is severely obstructed by low signal-to-noise ratios of the acquired images resulting from necessary limitations to the electron dose. We present a denoising strategy tailored to the special features of atomic-resolution electron micrographs of crystals limited by Poisson noise based on the block-matching and 3D-filtering (BM3D) algorithm by Dabov et al. We also present an economized block-matching strategy that exploits the periodic structure of the observed crystals. On simulated single-shot STEM images of inorganic materials, with incident electron doses below 4 C/cm 2, our new method achieves precisions of 7 to 15 pm and an increase in peak signal-to-noise ratio (PSNR) of 15 to 20 dB compared to noisy images and 2 to 4 dB compared to images denoised with the original BM3D.

Atomic structure and polarity compensation of BaTiO3 (1 1 1) surface

Surfaces of perovskite-type oxides have been attracting increasing interest for their primary importance in various potential applications such as multiferroic thin films, interface electronics and catalysis. However, the (1 1 1) surface of BaTiO3, the most typical ferroelectric, is far from well understood. In this work, the atomic structure and polarity compensation of BaTiO3 (1 1 1) surface have been investigated combining aberration-corrected transmission electron microscopy and first-principle calculations. Depending on the density of oxygen vacancies, the surface shows different degrees of atomic relaxation and electronic charge transfer, which compensates the surface polarity together with the ionic charges associated with the oxygen vacancies. The atomic relaxation and charge transfer would have a direct impact on the ferroelectric and catalytic properties of low-dimensional BaTiO3.

Direct observation of ferroelectric field effect and vacancy-controlled screening at the BiFeO3/LaxSr1-xMnO3 interface

The development of interface-based magnetoelectric devices necessitates an understanding of polarization-mediated electronic phenomena and atomistic polarization screening mechanisms. In this work, the LSMO/BFO interface is studied on a single unit-cell level through a combination of direct order parameter mapping by scanning transmission electron microscopy and electron energy-loss spectroscopy. We demonstrate an unexpected ~5% lattice expansion for regions with negative polarization charge, with a concurrent anomalous decrease of the Mn valence and change in oxygen K-edge intensity. We interpret this behaviour as direct evidence for screening by oxygen vacancies. The vacancies are predominantly accumulated at the second atomic layer of BFO, reflecting the difference of ionic conductivity between the components. This vacancy exclusion from the interface leads to the formation of a tail-to-tail domain wall. At the same time, purely electronic screening is realized for positive polarization charge, with insignificant changes in lattice and electronic properties. These results underline the non-trivial role of electrochemical phenomena in determining the functional properties of oxide interfaces. Furthermore, these behaviours suggest that vacancy dynamics and exclusion play major roles in determining interface functionality in oxide multilayers, providing clear implications for novel functionalities in potential electronic devices.

In situ atom scale visualization of domain wall dynamics in VO2 insulator-metal phase transition

A domain wall, as a device, can bring about a revolution in developing manipulation of semiconductor heterostructures devices at the atom scale. However, it is a challenge for these new devices to control domain wall motion through insulator-metal transition of correlated-electron materials. To fully understand and harness this motion, it requires visualization of domain wall dynamics in real space. Here, domain wall dynamics in VO₂ insulator-metal phase transition was observed directly by in situ TEM at atom scale. Experimental results depict atom scale evolution of domain morphologies and domain wall exact positions in (202) and (040) planes referring to rutile structure at 50°C. In addition, microscopic mechanism of domain wall dynamics and accurate lattice basis vector relationship of two domains were investigated with the assistance of X-ray diffraction, ab initio calculations and image simulations. This work offers a route to atom scale tunable heterostructure device application.

Exploring vertex interactions in ferroelectric flux-closure domains

Using piezoresponse force microscopy, we have observed the progressive development of ferroelectric flux-closure domain structures and Landau-Kittel-type domain patterns, in 300 nm thick single-crystal BaTiO3 platelets. As the microstructural development proceeds, the rate of change of the domain configuration is seen to decrease exponentially. Nevertheless, domain wall velocities throughout are commensurate with creep processes in oxide ferroelectrics. Progressive screening of macroscopic destabilizing fields, primarily the surface-related depolarizing field, successfully describes the main features of the observed kinetics. Changes in the separation of domain-wall vertex junctions prompt a consideration that vertex-vertex interactions could be influencing the measured kinetics. However, the expected dynamic signatures associated with direct vertex-vertex interactions are not resolved. If present, our measurements confine the length scale for interaction between vertices to the order of a few hundred nanometers.

Effect of mechanical loads on stability of nanodomains in ferroelectric ultrathin films: towards flexible erasing of the non-volatile memories

Intensive investigations have been drawn on nanoscale ferroelectrics for their prospective applications such as developing memory devices. In contrast with the commonly used electrical means to process (i.e., read, write or erase) the information carried by ferroelectric domains, at present, mechanisms of non-electrical processing ferroelectric domains are relatively lacking. Here we make a systematical investigation on the stability of 180° cylindrical domains in ferroelectric nanofilms subjected to macroscopic mechanical loads, and explore the possibility of mechanical erasing. Effects of domain size, film thickness, temperature and different mechanical loads, including uniform strain, cylindrical bending and wavy bending, have been revealed. It is found that the stability of a cylindrical domain depends on its radius, temperature and film thickness. More importantly, mechanical loads have great controllability on the stability of cylindrical domains, with the critical radius nonlinearly sensitive to both strain and strain gradient. This indicates that erasing cylindrical domain can be achieved by changing the strain state of nanofilm. Based on the calculated phase diagrams, we successfully simulate several mechanical erasing processes on 4 × 4 bits memory devices. Our study sheds light on prospective device applications of ferroelectrics involving mechanical loads, such as flexible memory devices and other micro-electromechanical systems.

The stabilization of a single domain in free-standing ferroelectric nanocrystals

High resolution electron microscopy, electron diffraction and electron holography were used to study individual free-standing ∼ 30 nm barium titanate nanocrystals. Large unidirectional variations in the tetragonal distortion were mapped across the smaller nanocrystals, peaking to anomalously large values of up to 4% at the centers of the nanocrystals. This indicated that the nanocrystals consist of highly strained single ferroelectric domains. Simulations using an effective Hamiltonian for modeling a nanocrystal under a small depolarizing field and negative pressure qualitatively confirm this picture. These simulations, along with the development of a phenomenological model, show that the tetragonal distortion variation is a combined effect of: (i) electrostrictive coupling between the spontaneous polarization and strain inside the nanocrystal, and (ii) a surface-induced effective stress existing inside the nanodot. As a result, a 'strain skin layer', having a smaller tetragonal distortion relative to the core of the nanocrystal, is created.

Coherent Bragg nanodiffraction at the hard X-ray Nanoprobe beamline

Bragg coherent diffraction with nanofocused hard X-ray beams provides unique opportunities for quantitative in situ studies of crystalline structure in nanoscale regions of complex materials and devices by a variety of diffraction-based techniques. In the case of coherent diffraction imaging, a major experimental challenge in using nanoscale coherent beams is maintaining a constant scattering volume such that coherent fringe visibility is maximized and maintained over the course of an exposure lasting several seconds. Here, we present coherent Bragg diffraction patterns measured from different nanostructured thin films at the Sector 26 Nanoprobe beamline at the Advanced Photon Source and demonstrate that with nanoscale positional control, coherent diffraction patterns can be measured with source-limited fringe visibilities more than 50% suitable for imaging by coherent Bragg ptychography techniques.

Determination of polarization-fields across polytype interfaces in InAs nanopillars

Polarization fields within InAs nanopillars with zincblende(ZB)/wurtzite(WZ) polytype stacking are quantified. The displacement of charged ions inside individual tetrahedra of WZ regions is measured at the atomic scale. The variations of spontaneous polarization along the interface normal are related to strain at interfaces of different polytypes. Thus, direct correlation between local atomic structure and electric properties is demonstrated.

Effects of a rotating electric field on the properties of epitaxial (001) Pb(Zr,Ti)O3 ultrathin film: a first-principles-based study

Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions and subjected to an electric field rotating in the (1¯10) plane are investigated via the use of an effective Hamiltonian, for different magnitudes of this field. Varying the direction and magnitude of the electric field leads to specific reorganization of dipoles into original configuration states, whose microstructures and macroscopic properties are revealed. In particular, a novel (direction of the electric field-versus-magnitude of the electric field) phase diagram is reported here. The field-induced correlation between the polar distortions and the oxygen octahedral tilting is also discussed.

Achieving single domain relaxor-PT crystals by high temperature poling

Single domain relaxor-PT crystals are important from both fundamental and application viewpoints.

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.

Self-similar nested flux closure structures in a tetragonal ferroelectric

In specific solid-state materials, under the right conditions, collections of magnetic dipoles are known to spontaneously form into a variety of rather complex geometrical patterns, exemplified by vortex and skyrmion structures. While theoretically, similar patterns should be expected to form from electrical dipoles, they have not been clearly observed to date: the need for continued experimental exploration is therefore clear. In this Letter we report the discovery of a rather complex domain arrangement that has spontaneously formed along the edges of a thin single crystal ferroelectric sheet, due to surface-related depolarizing fields. Polarization patterns are such that nanoscale "flux-closure" loops are nested within a larger mesoscale flux closure object. Despite the orders of magnitude differences in size, the geometric forms of the dual-scale flux closure entities are rather similar.

Atomic-scale measurement of structure and chemistry of a single-unit-cell layer of LaAlO3 embedded in SrTiO3

A single layer of LaAlO3 with a nominal thickness of one unit cell, which is sandwiched between a SrTiO3 substrate and a SrTiO3 capping layer, is quantitatively investigated by high-resolution transmission electron microscopy. By the use of an aberration-corrected electron microscope and by employing sophisticated numerical image simulation procedures, significant progress is made in two aspects. First, the structural as well as the chemical features of the interface are determined simultaneously on an atomic scale from the same specimen area. Second, the evaluation of the structural and chemical data is carried out in a fully quantitative way on the basis of the absolute image contrast, which has not been achieved so far in materials science investigations using high-resolution electron microscopy. Considering the strong influence of even subtle structural details on the electronic properties of interfaces in oxide materials, a fully quantitative interface analysis, which makes positional data available with picometer precision together with the related chemical information, can contribute to a better understanding of the functionality of such interfaces.

Prospects for Ferroelectrics: 2012–2022

A review is given of more than a dozen subtopics within the general study of ferroelectrics, with emphasis upon controversies, unsolved problems, and prospects for the next decade, including pure science and industrial applications. The review emphasizes work over the past two years, from 2010 to 2012.

Following strain-induced mosaicity changes of ferroelectric thin films by ultrafast reciprocal space mapping

We investigate coherent phonon propagation in a thin film of ferroelectric PbZr(0.2)Ti(0.8)O(3) (PZT) by ultrafast x-ray diffraction experiments, which are analyzed as time-resolved reciprocal space mapping in order to observe the in- and out-of-plane structural dynamics, simultaneously. The mosaic structure of the PZT leads to a coupling of the excited out-of-plane expansion to in-plane lattice dynamics on a picosecond time scale, which is not observed for out-of-plane compression.

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.

Novel complex phenomena in ferroelectric nanocomposites

A first-principles-based effective Hamiltonian is used to investigate finite-temperature properties of ferroelectric nanocomposites made of periodic arrays of ferroelectric nanowires embedded in a matrix formed by another ferroelectric material. Novel transitions and features related to flux-closure configurations are found. Examples include (i) a vortex core transition, that is characterized by the change of the vortex cores from being axisymmetric to exhibiting a 'broken symmetry'; (ii) translational mode of the vortex cores; (iii) striking zigzag dipolar chains along the vortex core axis; and (iv) phase-locking of ferroelectric vortices accompanied by ferroelectric antivortices. These complex phenomena are all found to coexist with a spontaneous electrical polarization aligned along the normal of the plane containing the vortices.

Flexible pyroelectric nanogenerators using a composite structure of lead-free KNbO(3) nanowires

Pyroelectric nanogenerators fabricated using a lead-free KNbO(3) nanowire-PDMS polymer composite are reported for the first time. The voltage/current output of the nanogenerators can be controlled by electric fields and enhanced by increasing the rate of change in temperature. The fabricated nanogenerators can be used to harvest energy from sunlight illumination and have potential applications in self-powered nanodevices and nanosystems.

Depinning phase transition in the two-dimensional clock model with quenched randomness

With Monte Carlo simulations, we systematically investigate the depinning phase transition in the two-dimensional driven random-field clock model. Based on the short-time dynamic approach, we determine the transition field and critical exponents. The results show that the critical exponents vary with the form of the random-field distribution and the strength of the random fields, and the roughening dynamics of the domain interface belongs to the new subclass with ζ≠ζ(loc)≠ζ(s) and ζ(loc)≠1. More importantly, we find that the transition field and critical exponents change with the initial orientations of the magnetization of the two ordered domains.

Ferroelectric order in individual nanometre-scale crystals

Ferroelectricity in finite-dimensional systems continues to arouse interest, motivated by predictions of vortex polarization states and the utility of ferroelectric nanomaterials in memory devices, actuators and other applications. Critical to these areas of research are the nanoscale polarization structure and scaling limit of ferroelectric order, which are determined here in individual nanocrystals comprising a single ferroelectric domain. Maps of ferroelectric structural distortions obtained from aberration-corrected transmission electron microscopy, combined with holographic polarization imaging, indicate the persistence of a linearly ordered and monodomain polarization state at nanometre dimensions. Room-temperature polarization switching is demonstrated down to ~5 nm dimensions. Ferroelectric coherence is facilitated in part by control of particle morphology, which along with electrostatic boundary conditions is found to determine the spatial extent of cooperative ferroelectric distortions. This work points the way to multi-Tbit/in(2) memories and provides a glimpse of the structural and electrical manifestations of ferroelectricity down to its ultimate limits.

Electrostatic coupling and local structural distortions at interfaces in ferroelectric/paraelectric superlattices

The performance of ferroelectric devices is intimately entwined with the structure and dynamics of ferroelectric domains. In ultrathin ferroelectrics, ordered nanodomains arise naturally in response to the presence of a depolarizing field and give rise to highly inhomogeneous polarization and structural profiles. Ferroelectric superlattices offer a unique way of engineering the desired nanodomain structure by modifying the strength of the electrostatic interactions between different ferroelectric layers. Through a combination of X-ray diffraction, transmission electron microscopy, and first-principles calculations, the electrostatic coupling between ferroelectric layers is studied, revealing the existence of interfacial layers of reduced tetragonality attributed to inhomogeneous strain and polarization profiles associated with the domain structure.

Conduction at domain walls in insulating Pb(Zr0.2 Ti0.8)O3 thin films

Domain wall conduction in insulating Pb(Zr(0.2) Ti(0.8))O(3) thin films is demonstrated. The observed electrical conduction currents can be clearly differentiated from displacement currents associated with ferroelectric polarization switching. The domain wall conduction, nonlinear and highly asymmetric due to the specific local probe measurement geometry, shows thermal activation at high temperatures, and high stability over time.

Unexpected controllable pair-structure in ferroelectric nanodomains

The imminent inability of silicon-based memory devices to satisfy Moore's Law is approaching rapidly. Controllable nanodomains of ferroic systems are anticipated to enable future high-density nonvolatile memory and novel electronic devices. We find via piezoresponse force microscopy (PFM) studies on lead zirconate titanate (PZT) films an unexpected nanostructuring of ferroelectric-ferroelastic domains. These consist of c-nanodomains within a-nanodomains in proximity to a-nanodomains within c-domains. These structures are created and annihilated as pairs, controllably. We treat these as a new kind of vertex-antivertex pair and consider them in terms of the Srolovitz-Scott 4-state Potts model, which results in pairwise domain vertex instabilities that resemble the vortex-antivortex mechanism in ferromagnetism, as well as dislocation pairs (or disclination pairs) that are well-known in nematic liquid crystals. Finally, we show that these nanopairs can be scaled up to form arrays that are engineered at will, paving the way toward facilitating them to real technologies.

Polarization closure in PbZr((0.42))Ti((0.58))O(3) nanodots

Domain states in PbZr((0.42))Ti((0.58))O(3) single-crystal ferroelectric nanodots, formed on cooling through the Curie temperature, were imaged by transmission electron microscopy. In the majority of cases, 90° stripe domains were found to form into four distinct "bundles" or quadrants. Detailed analysis of the dipole orientations in the system was undertaken, using both dark-field imaging and an assumption that charged domain walls were energetically unfavorable in comparison to uncharged walls. On this basis, we conclude that the dipoles in these nanodots are arranged such that the resultant polarizations, associated with the four quadrant domain bundles, form into a closed loop. This "polarization closure" pattern is reminiscent of the flux-closure already commonly observed in soft ferromagnetic microdots but to date unseen in analogous ferroelectric dots.

Mesoscale flux-closure domain formation in single-crystal BaTiO3

Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields,and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Flux-closure patterns are rarely observed in ferroelectric materials and almost exclusively form at the nanoscale. McQuaid et al. report mesoscopic dipole closure patterns formed in free-standing single-crystal lamellae of BaTiO₃, thought to result from an unusual set of experimental conditions.

Epitaxial Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions

The temperature-versus-misfit-strain phase diagram of Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions is simulated via the use of an effective Hamiltonian. Two novel phases, both exhibiting dipolar nanodomains and oxygen octahedral tilting, are discovered. The interplay between dipolar, antiferrodistortive, alloying, and strain degrees of freedom induces several striking features in these two phases, such as the chemical pinning of domain walls, the enhancement of oxygen octahedral tilting near the domain walls, and the existence of dipolar waves and cylindrical dipolar chiral bubbles.