Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3

Conducting atomic force microscopy studies on domain wall currents of Bi5Ti3FeO15 nanodots fabricated by anodic aluminum oxide nanotemplate and sol-gel process

We investigated the local current characteristics of Bi5Ti3FeO15 (BTFO) nanodots on Nb-doped SrTiO3 substrates affected by their ferroelectric domain structures and domain walls. The BTFO nanodots with a diameter of about 50 nm were fabricated by anodic aluminum oxide nanotemplates and a BTFO sol-gel process. Based on a piezoresponse force microscope, it was confirmed that domain walls were formed in the ferroelectric domain structures of the epitaxial BTFO nanodots. Current changes due to ferroelectric tunneling junctions according to ferroelectric polarizations in epitaxial BTFO nanodots were confirmed by conduction atomic force microscopy. In particular, the domain walls formed in the epitaxial BTFO nanodots formed high currents compared to the currents in ferroelectric tunneling junctions due to polarizations. RESEARCH HIGHLIGHTS: Ferroelectric Bi5Ti3FeO15 nanodots with a diameter of 50 nm. Ferroelectric domain structures observed with piezoresponse force microscopy. High domain wall currents observed at domain boundaries observed with conducting atomic force microscopy.

Surface Effect of Thickness-Dependent Polarization and Domain Evolution in BiFeO3 Epitaxial Ultrathin Films

With the trend of device miniaturization, ultrathin ferroelectric films are gaining more and more attention. However, understanding ferroelectricity in this nanoscale context remains a formidable challenge, primarily due to the heightened relevance of surface effects, which often leads to the loss of net polarization. Here, the influence of surface effects on the polarization as a function of thickness in ultrathin BiFeO3 films is investigated using phase-field simulations. The findings reveal a notable increase in ferroelectric polarization with increasing thickness, with a particularly discernible change occurring below the 10 nm threshold. Upon accounting for surface effects, the polarization is marginally lower than the case without such considerations, with the disparity becoming more pronounced at smaller thicknesses. Moreover, the hysteresis loop and butterfly loop of the ultrathin film were simulated, demonstrating that the ferroelectric properties of films remain robust even down to a thickness of 5 nm. Our investigations provide valuable insights into the significance of ferroelectric thin films in device miniaturization.

Surface charge dynamics on air-exposed ferroelectric Pb(Zr,Ti)O3(001) thin films

Probing of the free surface ferroelectric properties of thin polar films can be achieved either by estimating the band bending variance under the top-most layer or by studying the extent of the extrinsic charge accumulated outside the surface. Photoemitted or incoming low-energy electrons can be used to characterize locally both properties in a spectromicroscopic approach. Thin ferroelectric lead zirco-titanate (PZT) is investigated by combining low energy/mirror electron microscopy (LEEM/MEM) with photoemission electron microscopy (PEEM) and high-resolution photoelectron spectroscopy (XPS). Significant extrinsic negative compensation charge is proven to accumulate on the surface of the outward polarized thin film, indicated by high MEM-LEEM transition values, up to 15.3 eV, and is correlated with the surface electrostatic potential, which can be partially screened either by electrons interacting with the sample or by soft X-rays through the ejection of secondary electrons and generation of positive charge under the surface. A radiation-induced surface charge compensation effect is observed. The study indicates that air-exposed high quality ferroelectric thin films show large negative surface potentials, determined locally on the surface, which are nevertheless sensitive to beam damage and molecular desorption. These values represent a confirmation of previously estimated surface potential energy values determined from the LEED data on clean surfaces.

The First Demonstration of Strain-Controlled Periodic Ferroelectric Domains with Superior Piezoelectric Response in Molecular Materials

Achieving a periodic domain structure in ferroelectric materials to tailor the macroscopic properties or realize new functions has always been a hot topic. However, methods to construct periodic domain structures, such as epitaxial growth, direct writing by scanning tips, and the patterned electrode method, are difficult or inefficient to implement in emerging molecular ferroelectrics, which have the advantages of lightweight, flexibility, biocompatibility, etc. An efficient method for constructing and controlling periodic domain structures is urgently needed to facilitate the development of molecular ferroelectrics in nanoelectronic devices. In this work, it is demonstrated that large-area, periodic and controllable needle-like domain structures can be achieved in thin films of the molecular ferroelectric trimethylchloromethyl ammonium trichlorocadmium (TMCM-CdCl₃ ) upon the application of tensile strain. The domain evolution under various tensile strains can be clearly observed, and such processes are accordingly identified. Furthermore, the domain wall exhibits a superior piezoelectric response, with up to fivefold enhancement compared to that of the pristine samples. Such large-area tunable periodic domain structure and abnormally strong piezoresponse are not only of great interests in fundamental studies, but also highly important in the future applications in functional molecular materials.

Squishing Skyrmions: Symmetry-Guided Dynamic Transformation of Polar Topologies Under Compression

Mechanical controllability of recently discovered topological defects (e.g., skyrmions) in ferroelectric materials is of interest for the development of ultralow-power mechano-electronics that are protected against thermal noise. However, fundamental understanding is hindered by the "multiscale quantum challenge" to describe topological switching encompassing large spatiotemporal scales with quantum mechanical accuracy. Here, we overcome this challenge by developing a machine-learning-based multiscale simulation framework─a hybrid neural network quantum molecular dynamics (NNQMD) and molecular mechanics (MM) method. For nanostructures composed of SrTiO₃ and PbTiO₃, we find how the symmetry of mechanical loading essentially controls polar topological switching. We find under symmetry-breaking uniaxial compression a squishing-to-annihilation pathway versus formation of a topological composite named skyrmionium under symmetry-preserving isotropic compression. The distinct pathways are explained in terms of the underlying materials' elasticity and symmetry, as well as the Landau-Lifshitz-Kittel scaling law. Such rational control of ferroelectric topologies will likely facilitate exploration of the rich ferroelectric "topotronics" design space.

Confinement-Driven Inverse Domain Scaling in Polycrystalline ErMnO3

The research on topological phenomena in ferroelectric materials has revolutionized the way people understand polar order. Intriguing examples are polar skyrmions, vortex/anti-vortex structures, and ferroelectric incommensurabilties, which promote emergent physical properties ranging from electric-field-controllable chirality to negative capacitance effects. Here, the impact of topologically protected vortices on the domain formation in improper ferroelectric ErMnO₃ polycrystals is studied, demonstrating inverted domain scaling behavior compared to classical ferroelectrics. It is observed that as the grain size increases, smaller domains are formed. Phase field simulations reveal that elastic strain fields drive the annihilation of vortex/anti-vortex pairs within the grains and individual vortices at the grain boundaries. The inversion of the domain scaling behavior has far-reaching implications, providing fundamentally new opportunities for topology-based domain engineering and the tuning of the electromechanical and dielectric performance of ferroelectrics in general.

Subpicosecond Optical Stress Generation in Multiferroic BiFeO3

Optical excitation leads to ultrafast stress generation in the prototypical multiferroic BiFeO₃. The time scales of stress generation are set by the dynamics of the population of excited electronic states and the coupling of the electronic configuration to the structure. X-ray free-electron laser diffraction reveals high-wavevector subpicosecond-time scale stress generation following ultraviolet excitation of a BiFeO₃ thin film. Stress generation includes a fast component with a 1/e rise time with an upper limit of 300 fs and longer-rise time components extending to 1.5 ps. The contributions of the fast and delayed components vary as a function of optical fluence, with a reduced a fast-component contribution at high fluence. The results provide insight into stress-generation mechanisms linked to the population of excited electrons and point to new directions in the application of nanoscale multiferroics and related ferroic complex oxides. The fast component of the stress indicates that structural parameters and properties of ferroelectric thin film materials can be optically modulated with 3 dB bandwidths of at least 0.5 THz.

Large-Scale Domain Engineering in Two-Dimensional Ferroelectric CuInP2S6 via Giant Flexoelectric Effect

Room-temperature ferroelectricity in two-dimensional (2D) materials is a potential for developing atomic-scale functional devices. However, as a key step for the technology implementations of 2D ferroelectrics in electronics, the controllable generation of uniform domains remains challenging at the current stage because domain engineering through an external electric field at the 2D limit inevitably leads to large leakage currents and material breakdown. Here, we demonstrate a voltage-free method, the flexoelectric effect, to artificially generate large-scale stripe domains in 2D ferroelectric CuInP₂S₆ with single domain lateral size at the scale of several hundred microns. With giant strain gradients (∼10⁶ m^-1), we mechanically switch the out-of-plane polarization in ultrathin CuInP₂S₆. The flexoelectric control of polarization is understood with a distorted Landau-Ginzburg-Devonshire double well model. Through substrate strain engineering, the stripe domain density is controllable. Our results highlight the potential of developing van der Waals ferroelectrics-based flexible electronics.

Fractal Analysis on Surface Topography of Thin Films: A Review

The topographies of various surfaces have been studied in many fields due to the significant influence that surfaces have on the practical performance of a given sample. A comprehensive evaluation requires the assistance of fractal analysis, which is of significant importance for modern science and technology. Due to the deep insights of fractal theory, fractal analysis on surface topographies has been widely applied and recommended. In this paper, the remarkable uprising in recent decades of fractal analysis on the surfaces of thin films, an essential domain of surface engineering, is reviewed. By summarizing the methods used to calculate fractal dimension and the deposition techniques of thin films, the results and trends of fractal analysis are associated with the microstructure, deposition parameters, etc. and this contributes profoundly to exploring the mechanism of film growth under different conditions. Choosing appropriate methods of surface characterization and calculation methods to study diverse surfaces is the main challenge of current research on thin film surface topography by using fractal theory. Prospective developing trends are proposed based on the data extraction and statistics of the published literature in this field.

High-precision and linear weight updates by subnanosecond pulses in ferroelectric tunnel junction for neuro-inspired computing

The rapid development of neuro-inspired computing demands synaptic devices with ultrafast speed, low power consumption, and multiple non-volatile states, among other features. Here, a high-performance synaptic device is designed and established based on a Ag/PbZr_0.52Ti_0.48O₃ (PZT, (111)-oriented)/Nb:SrTiO₃ ferroelectric tunnel junction (FTJ). The advantages of (111)-oriented PZT (~1.2 nm) include its multiple ferroelectric switching dynamics, ultrafine ferroelectric domains, and small coercive voltage. The FTJ shows high-precision (256 states, 8 bits), reproducible (cycle-to-cycle variation, ~2.06%), linear (nonlinearity <1) and symmetric weight updates, with a good endurance of >10⁹ cycles and an ultralow write energy consumption. In particular, manipulations among 150 states are realized under subnanosecond (~630 ps) pulse voltages ≤5 V, and the fastest resistance switching at 300 ps for the FTJs is achieved by voltages <13 V. Based on the experimental performance, the convolutional neural network simulation achieves a high online learning accuracy of ~94.7% for recognizing fashion product images, close to the calculated result of ~95.6% by floating-point-based convolutional neural network software. Interestingly, the FTJ-based neural network is very robust to input image noise, showing potential for practical applications. This work represents an important improvement in FTJs towards building neuro-inspired computing systems.

Brain-inspired computing demands high-performance synapses. Here, the authors report a subnanosecond ferroelectric tunnel junction with 256 conductance states, 10⁹ endurance, and 5.3 fJ/bit energy consumption, satisfactory to build synaptic devices.

Energy exponents of avalanches and Hausdorff dimensions of collapse patterns

A simple numerical model to simulate athermal avalanches is presented. The model is inspired by the "porous collapse" process where the compression of porous materials generates collapse cascades, leading to power law distributed avalanches. The energy (E), amplitude (A_{max}), and size (S) exponents are derived by computer simulation in two approximations. Time-dependent "jerk" spectra are calculated in a single avalanche model where each avalanche is simulated separately from other avalanches. The average avalanche profile is parabolic, the scaling between energy and amplitude follows E∼A_{max}^{2}, and the energy exponent is ε = 1.33. Adding a general noise term in a continuous event model generates infinite avalanche sequences which allow the evaluation of waiting time distributions and pattern formation. We find the validity of the Omori law and the same exponents as in the single avalanche model. We then add spatial correlations by stipulating the ratio G/N between growth processes G (linked to a previous event location) and nucleation processes N (with new, randomly chosen nucleation sites). We found, in good approximation, a power law correlation between the energy exponent ε and the Hausdorff dimension H_{D} of the resulting collapse pattern H_{D}-1∼ɛ^{-3}. The evolving patterns depend strongly on G/N with the distribution of collapse sites equally power law distributed. Its exponent ɛ_{topo} would be linked to the dynamical exponent ε if each collapse carried an energy equivalent to the size of the collapse. A complex correlation between ɛ,ɛ_{topo}, and H_{D} emerges, depending strongly on the relative occupancy of the collapse sites in the simulation box.

A numerical study of the statistics of roughness parameters for fluctuating interfaces

Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results show that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.

Universality classes of the domain-wall creep motion driven by spin-transfer torques

With the stochastic Landau-Lifshitz-Gilbert equation, we numerically simulate the creep motion of a magnetic domain wall driven by the adiabatic and nonadiabatic spin-transfer torques induced by the electric current. The creep exponent μ and the roughness exponent ζ are accurately determined from the scaling behaviors. The creep motions driven by the adiabatic and nonadiabatic spin-transfer torques belong to different universality classes. The scaling relation between μ and ζ based on certain simplified assumptions is valid for the nonadiabatic spin-transfer torque, while invalid for the adiabatic one. Our results are compatible with the experimental ones, but go beyond the existing theoretical prediction. Our investigation reveals that the disorder-induced pinning effect on the domain-wall rotation alters the universality class of the creep motion.

Avalanche criticality during ferroelectric/ferroelastic switching

Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ contains complex domains with needles and junction patterns, while BaTiO₃ has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field.

While classical approaches rely on the study of individual ferroelectric domain wall movement on long time scales, the authors consider collective movements of domain walls during short time scales, characterized by discrete jumps, as indicators of avalanches on a broad range of scales.

Domains and domain walls in multiferroics

Multiferroics are materials combining several ferroic orders, such as ferroelectricity, ferro- (or antiferro-) magnetism, ferroelasticity and ferrotoroidicity. They are of interest both from a fundamental perspective, as they have multiple (coupled) non-linear functional responses providing a veritable myriad of correlated phenomena, and because of the opportunity to apply these functionalities for new device applications. One application is, for instance, in non-volatile memory, which has led to special attention being devoted to ferroelectric and magnetic multiferroics. The vision is to combine the low writing power of ferroelectric information with the easy, non-volatile reading of magnetic information to give a “best of both worlds” computer memory. For this to be realised, the two ferroic orders need to be intimately linked via the magnetoelectric effect. The magnetoelectric coupling – the way polarization and magnetization interact – is manifested by the formation and interactions of domains and domain walls, and so to understand how to engineer future devices one must first understand the interactions of domains and domain walls. In this article, we provide a short introduction to the domain formation in ferroelectrics and ferromagnets, as well as different microscopy techniques that enable the visualization of such domains. We then review the recent research on multiferroic domains and domain walls, including their manipulation and intriguing properties, such as enhanced conductivity and anomalous magnetic order. Finally, we discuss future perspectives concerning the field of multiferroic domain walls and emergent topological structures such as ferroelectric vortices and skyrmions.

Scale-invariant magnetic textures in the strongly correlated oxide NdNiO3

Strongly correlated quantum solids are characterized by an inherently granular electronic fabric, with spatial patterns that can span multiple length scales in proximity to a critical point. Here, we use a resonant magnetic X-ray scattering nanoprobe with sub-100 nm spatial resolution to directly visualize the texture of antiferromagnetic domains in NdNiO₃. Surprisingly, our measurements reveal a highly textured magnetic fabric, which we show to be robust and nonvolatile even after thermal erasure across its ordering temperature. The scale-free distribution of antiferromagnetic domains and its non-integral dimensionality point to a hitherto-unobserved magnetic fractal geometry in this system. These scale-invariant textures directly reflect the continuous nature of the magnetic transition and the proximity of this system to a critical point. The present study not only exposes the near-critical behavior in rare earth nickelates but also underscores the potential for X-ray scattering nanoprobes to image the multiscale signatures of criticality near a critical point.

Periodicity-Doubling Cascades: Direct Observation in Ferroelastic Materials

Very sensitive responses to external forces are found near phase transitions. However, transition dynamics and preequilibrium phenomena are difficult to detect and control. We have observed that the equilibrium domain structure following a phase transition in ferroelectric and ferroelastic BaTiO_{3} is attained by halving of the domain periodicity multiple times. The process is reversible, with periodicity doubling as temperature is increased. This observation is reminiscent of the period-doubling cascades generally observed during bifurcation phenomena, and, thus, it conforms to the "spatial chaos" regime earlier proposed by Jensen and Bak [Phys. Scr. T 9, 64 (1985)PHSTER0281-184710.1088/0031-8949/1985/T9/009] for systems with competing spatial modulations.

Thickness scaling of ferroelectricity in BiFeO3 by tomographic atomic force microscopy

Intrinsic and extrinsic properties of ferroelectric materials are known to have strong dependencies on electrical and mechanical boundary conditions, resulting in finite size effects at length scales below several hundred nanometers. In ferroelectric thin films, equilibrium domain size is proportional to the square root of film thickness, which precludes the use of present tomographic microscopies to accurately resolve complex domain morphologies in submicrometer films. We report a subtractive experimental technique with volumetric resolution below 315 nm³, that allows for three-dimensional, tomographic imaging of materials properties using only an atomic force microscope. Multiferroic BiFeO₃ was chosen as a model system for illustrating the capabilities of tomographic atomic force microscopy due to its technological relevance in low-power, electrically switchable magnetic logic.

Nanometer-scale 3D imaging of materials properties is critical for understanding equilibrium states in electronic materials, as well as for optimization of device performance and reliability, even though such capabilities remain a substantial experimental challenge. Tomographic atomic force microscopy (TAFM) is presented as a subtractive scanning probe technique for high-resolution, 3D ferroelectric property measurements. Volumetric property resolution below 315 nm³, as well as unit-cell-scale vertical material removal, are demonstrated. Specifically, TAFM is applied to investigate the size dependence of ferroelectricity in the room-temperature multiferroic BiFeO₃ across two decades of thickness to below 1 nm. TAFM enables volumetric imaging of ferroelectric domains in BiFeO₃ with a significant improvement in spatial resolution compared with existing domain tomography techniques. We additionally employ TAFM for direct, thickness-dependent measurements of the local spontaneous polarization and ferroelectric coercive field in BiFeO₃. The thickness-resolved ferroelectric properties strongly correlate with cross-sectional transmission electron microscopy (TEM), Landau–Ginzburg–Devonshire phenomenological theory, and the semiempirical Kay–Dunn scaling law for ferroelectric coercive fields. These results provide an unambiguous determination of a stable and switchable polar state in BiFeO₃ to thicknesses below 5 nm. The accuracy and utility of these findings on finite size effects in ferroelectric and multiferroic materials more broadly exemplifies the potential for novel insight into nanoscale 3D property measurements via other variations of TAFM.

Ferroelectric properties and piezoresponse force micoroscopy study of Bi3TaTiO9 thin films

We investigate the ferroelectric properties and crystal structures of Bi₃TaTiO₉ (BTTO) thin films deposited on single-crystal Nb-doped (100) SrTiO₃ substrates via pulsed laser deposition. The BTTO films exhibited either a (001)-epitaxial crystalline structure or a mixed a- and c-oriented polycrystalline structure depending on the substrate temperature. The ferroelectric polarization and piezoelectric coefficient of the mixed a- and c-oriented film were larger than those of the (001)-epitaxial film because its polar axis was perpendicular to the c-axis. Vertical and lateral piezoresponse force microscopy studies indicate that the ferroelectric domains of the (001)-epitaxial film were all parallel to the in-plane orientation, whereas the mixed a- and c-oriented film comprised both square grains with in-plane-oriented ferroelectric domains and longish grains with ferroelectric domains out of orientation with the plane.

Large anisotropy of ferroelectric and pyroelectric properties in heteroepitaxial oxide layers

Epitaxial PbZr_0.52Ti_0.48O₃ (PZT) layers were integrated on Si(001) with single PZT {001} orientation, mosaïcity below 1° and a majority of a-oriented ferroelectric domains (∼65%). Ferroelectric and pyroelectric properties are determined along both the out-of-plane and in-plane directions through parallel-plate capacitor and coplanar interdigital capacitor along the <100>_PZT direction. A large anisotropy in these properties is observed. The in-plane remnant polarization (21.5 µC.cm⁻²) is almost twice larger than that measured along the out-of-plane direction (13.5 µC.cm⁻²), in agreement with the domain orientation. Oppositely, the in-plane pyroelectric coefficient (−285 µC.m⁻².K⁻¹) is much lower than that measured out-of-plane (−480 µC.m⁻².K⁻¹). The pyroelectric anisotropy is explicated in term of degree of structural freedom with temperature. In particular, the low in-plane pyroelectric coefficient is explained by a two-dimensional clamping of the layers on the substrate which induces tensile stress (from thermal expansion), competing with the decreasing tetragonality of a-domains (shortening of the polar c-axis lattice parameter). Temperature-dependent XRD measurements have revealed an increased fraction of a-domains with temperature, attesting the occurrence of a partial two-dimensional clamping. These observed properties are of critical importance for integrated pyroelectric devices.

Surface-screening mechanisms in ferroelectric thin films and their effect on polarization dynamics and domain structures

For over 70 years, ferroelectric materials have been one of the central research topics for condensed matter physics and material science, an interest driven both by fundamental science and applications. However, ferroelectric surfaces, the key component of ferroelectric films and nanostructures, still present a significant theoretical and even conceptual challenge. Indeed, stability of ferroelectric phase per se necessitates screening of polarization charge. At surfaces, this can lead to coupling between ferroelectric and semiconducting properties of material, or with surface (electro) chemistry, going well beyond classical models applicable for ferroelectric interfaces. In this review, we summarize recent studies of surface-screening phenomena in ferroelectrics. We provide a brief overview of the historical understanding of the physics of ferroelectric surfaces, and existing theoretical models that both introduce screening mechanisms and explore the relationship between screening and relevant aspects of ferroelectric functionalities starting from phase stability itself. Given that the majority of ferroelectrics exist in multiple-domain states, we focus on local studies of screening phenomena using scanning probe microscopy techniques. We discuss recent studies of static and dynamic phenomena on ferroelectric surfaces, as well as phenomena observed under lateral transport, light, chemical, and pressure stimuli. We also note that the need for ionic screening renders polarization switching a coupled physical-electrochemical process and discuss the non-trivial phenomena such as chaotic behavior during domain switching that stem from this.

Static and dynamic electro-optical properties of liquid crystals mediated by ferroelectric polymer films

Liquid crystals (LC) can reveal the fractal dimension of multi-domain ferroelectric films (FF) while these films can control the switching time of FF–LC hybrids.

Nanoscale Bubble Domains and Topological Transitions in Ultrathin Ferroelectric Films

Observation of a new type of nanoscale ferroelectric domains, termed as "bubble domains"-laterally confined spheroids of sub-10 nm size with local dipoles self-aligned in a direction opposite to the macroscopic polarization of a surrounding ferroelectric matrix-is reported. The bubble domains appear in ultrathin epitaxial PbZr_0.2 Ti_0.8 O₃ /SrTiO₃ /PbZr_0.2 Ti_0.8 O₃ ferroelectric sandwich structures due to the interplay between charge and lattice degrees of freedom. The existence of the bubble domains is revealed by high-resolution piezoresponse force microscopy (PFM), and is corroborated by aberration-corrected atomic-resolution scanning transmission electron microscopy mapping of the polarization displacements. An incommensurate phase and symmetry breaking is found within these domains resulting in local polarization rotation and hence impart a mixed Néel-Bloch-like character to the bubble domain walls. PFM hysteresis loops for the bubble domains reveal that they undergo an irreversible phase transition to cylindrical domains under the electric field, accompanied by a transient rise in the electromechanical response. The observations are in agreement with ab-initio-based calculations, which reveal a very narrow window of electrical and elastic parameters that allow the existence of bubble domains. The findings highlight the richness of polar topologies possible in ultrathin ferroelectric structures and bring forward the prospect of emergent functionalities due to topological transitions.

Recoverable Self-Polarization in Lead-Free Bismuth Sodium Titanate Piezoelectric Thin Films

Bismuth sodium titanate, Bi_0.5Na_0.5TiO₃ (BNT), is a promising lead-free ferroelectric material. However, its potential applications have not been fully explored, mainly because of the complex domain structure arising from its intricate phase transitions. A deep and thorough study of its domain structure and polarization switching behavior will greatly help with understanding the polarization nature and with promoting future applications. In this work, we demonstrate that BNT polycrystalline films possess a highly ordered out-of-plane polarization (self-polarization) and randomly oriented in-plane polarizations. Interestingly, the inherent nature of polarization in the BNT films does not allow for the nonvolatile domain writing, as the switched polarization spontaneously and rapidly reverses to the initial orientation state once the external poling electric field is removed, making the self-polarization recoverable. Such a stable self-polarization vanishes gradually with temperature increasing over 150 °C but starts to recover to its initial state upon cooling down to 250 °C, and entirely recovers once the temperature is reduced to below 200 °C. Such interesting properties of BNT films are attributed to the combined effects of the free charges at the Pt electrode, (detected) cation vacancies at the oxide/Pt interface and the defects in oxide lattices. Our results make a step closer to fully understand the nature of polarization and related piezoelectricity in BNT. Such films with recoverable self-polarization are of great interest for applications as sensors, actuators, and transducers that can operate particularly under high temperatures and high electric field conditions.

Terahertz-Range Polar Modes in Domain-Engineered BiFeO_{3}

The dielectric permittivity and properties of electrically active lattice resonances in nanotwinned BiFeO_{3} crystals have been studied theoretically using an earlier established interatomic potential. The results suggest that an array of 71° domain walls with about 2-5 nm spacing enhances the static permittivity of BiFeO_{3} by more than an order of magnitude. This enhancement is associated with an electrically active excitation, corresponding to a collective vibration of pinned domain walls at a remarkably high frequency of about 0.3 THz.

Tetragonal CH3NH3PbI3 is ferroelectric

Halide perovskite (HaP) semiconductors are revolutionizing photovoltaic (PV) solar energy conversion by showing remarkable performance of solar cells made with HaPs, especially tetragonal methylammonium lead triiodide (MAPbI3). In particular, the low voltage loss of these cells implies a remarkably low recombination rate of photogenerated carriers. It was suggested that low recombination can be due to the spatial separation of electrons and holes, a possibility if MAPbI3 is a semiconducting ferroelectric, which, however, requires clear experimental evidence. As a first step, we show that, in operando, MAPbI3 (unlike MAPbBr3) is pyroelectric, which implies it can be ferroelectric. The next step, proving it is (not) ferroelectric, is challenging, because of the material's relatively high electrical conductance (a consequence of an optical band gap suitable for PV conversion) and low stability under high applied bias voltage. This excludes normal measurements of a ferroelectric hysteresis loop, to prove ferroelectricity's hallmark switchable polarization. By adopting an approach suitable for electrically leaky materials as MAPbI3, we show here ferroelectric hysteresis from well-characterized single crystals at low temperature (still within the tetragonal phase, which is stable at room temperature). By chemical etching, we also can image the structural fingerprint for ferroelectricity, polar domains, periodically stacked along the polar axis of the crystal, which, as predicted by theory, scale with the overall crystal size. We also succeeded in detecting clear second harmonic generation, direct evidence for the material's noncentrosymmetry. We note that the material's ferroelectric nature, can, but need not be important in a PV cell at room temperature.

Controlled Charging of Ferroelastic Domain Walls in Oxide Ferroelectrics

Conductive domain walls (DWs) in ferroic oxides as device elements are a highly attractive research topic because of their robust and agile response to electric field. Charged DWs possessing metallic-type conductivity hold the highest promises in this aspect. However, their intricate creation, low stability, and interference with nonconductive DWs hinder their investigation and the progress toward future applications. Here, we find that conversion of the nominally neutral ferroelastic 90° DWs into partially charged DWs in Pb(Zr_0.1Ti_0.9)O₃ thin films enables easy and robust control over the DW conductivity. By employing transmission electron microscopy, conductive atomic force microscopy and phase-field simulation, our study reveals that charging of the ferroelastic DWs is controlled by mutually coupled DW bending, type of doping, polarization orientation and work-function of the adjacent electrodes. Particularly, the doping outweighs other parameters in controlling the DW conductivity. Understanding the interplay of these key parameters not only allows us to control and optimize conductivity of such ferroelastic DWs in the oxide ferroelectrics but also paves the way for utilization of DW-based nanoelectronic devices in the future.

BiFeO3 nanorings synthesized via AAO template-assisted pulsed laser deposition and ion beam etching

Well-ordered BiFeO₃ nanorings with epitaxial structure, strong ferroelectricity and polarization reversal have been fabricated using this novel and facile method.

Polarization curling and flux closures in multiferroic tunnel junctions

Formation of domain walls in ferroelectrics is not energetically favourable in low-dimensional systems. Instead, vortex-type structures are formed that are driven by depolarization fields occurring in such systems. Consequently, polarization vortices have only been experimentally found in systems in which these fields are deliberately maximized, that is, in films between insulating layers. As such configurations are devoid of screening charges provided by metal electrodes, commonly used in electronic devices, it is wise to investigate if curling polarization structures are innate to ferroelectricity or induced by the absence of electrodes. Here we show that in unpoled Co/PbTiO₃/(La,Sr)MnO₃ ferroelectric tunnel junctions, the polarization in active PbTiO₃ layers 9 unit cells thick forms Kittel-like domains, while at 6 unit cells there is a complex flux-closure curling behaviour resembling an incommensurate phase. Reducing the thickness to 3 unit cells, there is an almost complete loss of switchable polarization associated with an internal gradient.

Ferroelectric vortex-type structures have only been seen in isolated films, leaving electrode effects unexplored. Here, Peters et al. show that the polarisation curling and formation of vortex and flux-closure structures is a generic effect appearing in ultrathin ferroelectric films.

Single-domain multiferroic BiFeO3 films

The strong coupling between antiferromagnetism and ferroelectricity at room temperature found in BiFeO₃ generates high expectations for the design and development of technological devices with novel functionalities. However, the multi-domain nature of the material tends to nullify the properties of interest and complicates the thorough understanding of the mechanisms that are responsible for those properties. Here we report the realization of a BiFeO₃ material in thin film form with single-domain behaviour in both its magnetism and ferroelectricity: the entire film shows its antiferromagnetic axis aligned along the crystallographic b axis and its ferroelectric polarization along the c axis. With this we are able to reveal that the canted ferromagnetic moment due to the Dzyaloshinskii–Moriya interaction is parallel to the a axis. Furthermore, by fabricating a Co/BiFeO₃ heterostructure, we demonstrate that the ferromagnetic moment of the Co film does couple directly to the canted moment of BiFeO₃.

The coupling of ferroelectric and antiferromagnetic order in BiFeO₃ makes it appealing for applications however the presence of domain structure acts to undermine this potential. Here, the authors demonstrate BiFeO₃ thin films with a single domain of electrical polarization and canted antiferromagnetic order.

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.

Polar-Graded Multiferroic SrMnO3 Thin Films

Engineering defects and strains in oxides provides a promising route for the quest of thin film materials with coexisting ferroic orders, multiferroics, with efficient magnetoelectric coupling at room temperature. Precise control of the strain gradient would enable custom tailoring of the multiferroic properties but presently remains challenging. Here we explore the existence of a polar-graded state in epitaxially strained antiferromagnetic SrMnO3 thin films, whose polar nature was predicted theoretically and recently demonstrated experimentally. By means of aberration-corrected scanning transmission electron microscopy we map the polar rotation of the ferroelectric polarization with atomic resolution, both far from and near the domain walls, and find flexoelectricity resulting from vertical strain gradients. The origin of this particular strain state is a gradual distribution of oxygen vacancies across the film thickness, according to electron energy loss spectroscopy. Herein we present a chemistry-mediated route to induce polar rotations in oxygen-deficient multiferroic films, resulting in flexoelectric polar rotations and with potentially enhanced piezoelectricity.

Humidity effect of domain wall roughening behavior in ferroelectric copolymer thin films

We have demonstrated that domain switching in ferroelectric copolymer films can be significantly affected by humidity. With increasing relative humidity (RH), we observed larger domains with highly irregular boundaries as a result of lateral spreading of the tip-induced electric field that originates from water adsorption. Fractal dimension study of irregular domains reveals that the fractal dimension is higher in cases where the RH is higher. The results show that the RH is one of the major switching parameters in ferroelectric copolymers, and therefore could allow clear understanding with regard to domain switching behavior in the ferroelectric copolymer films under ambient conditions.

Tuning of the depolarization field and nanodomain structure in ferroelectric thin films

The screening efficiency of a metal-ferroelectric interface plays a critical role in determining the polarization stability and hence the functional properties of ferroelectric thin films. Imperfect screening leads to strong depolarization fields that reduce the spontaneous polarization or drive the formation of ferroelectric domains. We demonstrate that by modifying the screening at the metal-ferroelectric interface through insertion of ultrathin dielectric spacers, the strength of the depolarization field can be tuned and thus used to control the formation of nanoscale domains. Using piezoresponse force microscopy, we follow the evolution of the domain configurations as well as polarization stability as a function of depolarization field strength.

Effects of Interfaces on the Structure and Novel Physical Properties in Epitaxial Multiferroic BiFeO₃ Ultrathin Films

In functional oxide films, different electrical/mechanical boundaries near film surfaces induce rich phase diagrams and exotic phenomena. In this paper, we review some key points which underpin structure, phase transition and related properties in BiFeO₃ ultrathin films. Compared with the bulk counterparts, we survey the recent results of epitaxial BiFeO₃ ultrathin films to illustrate how the atomic structure and phase are markedly influenced by the interface between the film and the substrate, and to emphasize the roles of misfit strain and depolarization field on determining the domain patterns, phase transformation and associated physical properties of BiFeO₃ ultrathin films, such as polarization, piezoelectricity, and magnetism. One of the obvious consequences of the misfit strain on BiFeO₃ ultrathin films is the emergence of a sequence of phase transition from tetragonal to mixed tetragonal & rhombohedral, the rhombohedral, mixed rhombohedral & orthorhombic, and finally orthorhombic phases. Other striking features of this system are the stable domain patterns and the crossover of 71° and 109° domains with different electrical boundary conditions on the film surface, which can be controlled and manipulated through the depolarization field. The external field-sensitive enhancements of properties for BiFeO₃ ultrathin films, including the polarization, magnetism and morphotropic phase boundary-relevant piezoelectric response, offer us deeper insights into the investigations of the emergent properties and phenomena of epitaxial ultrathin films under various mechanical/electrical constraints. Finally, we briefly summarize the recent progress and list open questions for future study on BiFeO₃ ultrathin films.

Large magnetoelectric coupling in magnetically short-range ordered Bi₅Ti₃FeO₁₅ film

Multiferroic materials, which offer the possibility of manipulating the magnetic state by an electric field or vice versa, are of great current interest. However, single-phase materials with such cross-coupling properties at room temperature exist rarely in nature; new design of nano-engineered thin films with a strong magneto-electric coupling is a fundamental challenge. Here we demonstrate a robust room-temperature magneto-electric coupling in a bismuth-layer-structured ferroelectric Bi₅Ti₃FeO₁₅ with high ferroelectric Curie temperature of ~1000 K. Bi₅Ti₃FeO₁₅ thin films grown by pulsed laser deposition are single-phase layered perovskit with nearly (00l)-orientation. Room-temperature multiferroic behavior is demonstrated by a large modulation in magneto-polarization and magneto-dielectric responses. Local structural characterizations by transmission electron microscopy and Mössbauer spectroscopy reveal the existence of Fe-rich nanodomains, which cause a short-range magnetic ordering at ~620 K. In Bi₅Ti₃FeO₁₅ with a stable ferroelectric order, the spin canting of magnetic-ion-based nanodomains via the Dzyaloshinskii-Moriya interaction might yield a robust magneto-electric coupling of ~400 mV/Oe·cm even at room temperature.

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.

Domain wall roughness in stripe phase BiFeO3 thin films

Using the model system of ferroelectric domain walls, we explore the effects of long-range dipolar interactions and periodic ordering on the behavior of pinned elastic interfaces. In piezoresponse force microscopy studies of the characteristic roughening of intrinsic 71° stripe domains in BiFeO3 thin films, we find unexpectedly high values of the roughness exponent ζ=0.74±0.10, significantly different from those obtained for artificially written domain walls in this and other ferroelectric materials. The large value of the exponent suggests that a random field-dominated pinning, combined with stronger disorder and strain effects due to the step-bunching morphology of the samples, could be the dominant source of pinning in the system.

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.

Thickness-dependent polarization of strained BiFeO3 films with constant tetragonality

We measure the ferroelectric polarization of BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultrathin films, the energetics of near open circuit electrical boundary conditions, i.e., an unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to nanoscale stripe domains. It gives rise to an average polarization close to zero as measured by the electron microscopy while maintaining the relatively large tetragonal distortion imposed by the nonzero polarization state of each individual domain.

Multiscaling analysis of ferroelectric domain wall roughness

Using multiscaling analysis, we compare the characteristic roughening of ferroelectric domain walls in Pb(Zr0.2Ti0.8)O3 thin films with numerical simulations of weakly pinned one-dimensional interfaces. Although at length scales up to L(MA)≥5  μm the ferroelectric domain walls behave similarly to the numerical interfaces, showing a simple monoaffine scaling (with a well-defined roughness exponent ζ), we demonstrate more complex scaling at higher length scales, making the walls globally multiaffine (varying ζ at different observation length scales). The dominant contributions to this multiaffine scaling appear to be very localized variations in the disorder potential, possibly related to dislocation defects present in the substrate.

A ferroelectric memristor

Memristors are continuously tunable resistors that emulate biological synapses. Conceptualized in the 1970s, they traditionally operate by voltage-induced displacements of matter, although the details of the mechanism remain under debate. Purely electronic memristors based on well-established physical phenomena with albeit modest resistance changes have also emerged. Here we demonstrate that voltage-controlled domain configurations in ferroelectric tunnel barriers yield memristive behaviour with resistance variations exceeding two orders of magnitude and a 10 ns operation speed. Using models of ferroelectric-domain nucleation and growth, we explain the quasi-continuous resistance variations and derive a simple analytical expression for the memristive effect. Our results suggest new opportunities for ferroelectrics as the hardware basis of future neuromorphic computational architectures.

Room temperature electrical manipulation of giant magnetoresistance in spin valves exchange-biased with BiFeO3

Magnetoelectric multiferroics are attractive materials for the development of low-power electrically controlled spintronic devices. Here we report the optimization of the exchange bias as well as the giant magnetoresistance effect (GMR) of spin valves deposited on top of BiFeO(3)-based heterostructures. We show that the exchange bias can be electrically controlled through a change in the relative proportion of 109° domain walls and propose solutions toward a reversible process.

Spatially resolved photodetection in leaky ferroelectric BiFeO(3)

Potential gradients due to the spontaneous polarization of BiFeO(3) yield asymmetric and nonlinear photocarrier dynamics. Photocurrent direction is determined by local ferroelectric domain orientation, whereas magnitude is spectrally centered around charged domain walls that are associated with oxygen vacancy migration. Photodetection can be electrically controlled by manipulating ferroelectric domain configurations.

Critical behavior of the Ising model on random fractals

We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d(f) is approximately equal to 1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.

High-resolution studies of domain switching behavior in nanostructured ferroelectric polymers

We have demonstrated an effective electrical control of polarization in the individual crystalline nanomesas of the ferroelectric polymer, poly(vinylidene fluoride)-trifluoroethylene (PVDF-TrFE) and its relation to the polymer structure. The mechanism of polarization reversal has been investigated via sub-10 nm real space imaging of domain pattern evolution under an applied electric field. The domain switching behavior revealed in PVDF-TrFE nanomesas is drastically different from that observed in inorganic solid-state crystalline ferroelectrics. The nanoscale features of the switching process include remote domain nucleation and spatially nonuniform wall velocity. Local switching spectroscopy and domain dynamics studies relate the observed switching features to a random-bond type disorder associated with defects in conformation and molecular packing.

Nanoscale polarization switching mechanisms in multiferroic BiFeO₃ thin films

Ferroelectric switching in BiFeO₃ multiferroic thin films was studied by piezoresponse force microscopy, as a function of the tip voltage and sweep direction, for samples with two different intrinsic domain structures. In all films, the switched polarization direction follows the in-plane and out-of-plane components of the highly inhomogeneous electric field applied by the microscope tip. In films with 'bubble-like' intrinsic domains, we observed in-plane switching assisted by out-of-plane switching for lower voltage values, and independent in-plane and out-of-plane switching for higher voltages, in both cases allowing full control of the ferroelectric polarization depending on the tip voltage polarity and sweep direction. In films with 'stripe-like' intrinsic domains, independent in-plane and out-of-plane switching was observed, but unswitched stripe domains prevented full control of the ferroelectric polarization over large areas. We correlate the observed switching behavior with the field-driven onset of a highly distorted tetragonal phase predicted by ab initio calculations, which leads to a very high in-plane susceptibility during the return to the non-distorted monoclinic phase when the field is decreased. Depending on the specific strain and disorder present in the sample, the transition towards the highly distorted phase may be asymmetrized, and easier to reach when an electric field opposite to the out-of-plane polarization direction is applied.

Origin and tailoring of the antiferromagnetic domain structure in α-Fe2O3 thin films unraveled by statistical analysis of dichroic spectromicroscopy (x-ray photoemission electron microscopy) images

The magnetic microstructure and domain wall distribution of antiferromagnetic α-Fe2O3 epitaxial layers is determined by statistical image analyses. Using dichroic spectromicroscopy images, we demonstrate that the domain structure is statistically invariant with thickness and that the antiferromagnetic domain structure of the thin films is inherited from the ferrimagnetic precursor layer one, even after complete transformation into antiferromagnetic α-Fe2O3. We show that modifying the magnetic domain structure of the precursor layer is a genuine way to tune the magnetic domain structure and domain walls of the antiferromagnetic layers.