Ferroelastic Domain Walls Research Articles

Symmetry and strain analysis of combined electronic and structural instabilities in tungsten trioxide, WO3

Lattice parameter data from the literature have been used to provide a complete description of spontaneous strain variations across each of the six known phase transitions of WO3 in the temperature interval 5–1273 K. Analysis of strain/order parameter coupling reveals the character of each phase transition, a unified description of strain across the full temperature range, the relationship between strain and electronic effects, and new insights into the strain gradients likely to be present in each of the different domain walls that develop in four different ferroelastic phases. Tetragonal and orthorhombic shear strains have values of 4%–6% and 2%–3%, respectively, and are dominated by coupling with the order parameter for antiferroelectric-type displacements. Conversely, shear strains, e4, e5, and e6, of up to 2% are controlled by octahedral tilting. Changes in electronic structure and properties have been related back to the susceptibility of W6+ to develop cooperative second-order-Jahn–Teller distortions. Proximity to tilt instabilities along with group–subgroup relationships in the P4/nmm parent structure results in two overlapping sequences of structural phase transitions, which differ in the form of their electronic structure. The possibility of a ground state structure in space group P21/c can be rationalized in terms of the efficiency by which different combinations of shearing and tilting of the WO6 octahedra can reduce the unit cell volume and would imply that WO3 has a re-entrant phase transition. Gradients in up to three order parameters coupled with gradients in strain of up to 12% across ferroelastic domain walls indicate that the different ferroelastic phases of WO3 should have domain walls with varied and potentially exotic electronic properties for device applications such as in nanoelectronics and neuromorphic computing.

Elastic moduli of potassium sodium niobate ceramics: Impact of spark plasma texturing

An alternative sintering methodology, Spark Plasma Texturing (SPT), allowed us to prepare 98.0% dense lead-free piezoelectric (K1-xNax)NbO3 (KNN) ceramics with a homogenous microstructure of small grains. In this work, Resonant Ultrasound Spectroscopy (RUS) was used to measure bulk, K, and shear, G, moduli of SPT KNN for comparison with conventionally sintered (CS) KNN. SPT fabrication resulted in the highest elastic moduli K = 120.3 GPa (127.7 GPa for 100% density) and G = 45.47 GPa (47.2 GPa for 100% density) ever reported for KNN ceramics. Moreover, by collecting RUS data in situ as a function of temperature, phase transitions at temperatures of 464 and 688 K for CS KNN, and 443 and 643 K for SPT KNN ceramics were determined. Low acoustic loss in the stability field of the cubic phase indicated that the ceramics were mechanically robust, while high loss in the stability fields of the tetragonal and orthorhombic structures demonstrated high mobility of ferroelastic domain walls.

Flexo-phototronic effect in centro-symmetric BiVO4 epitaxial films

With exciting functionality, topological defects in ferroic system have attracted significant attention. Under proper design, the emergence of polar domain walls in non-polar ferroelastics enables a flexo-phototronic effect. In this study, we revealed ferroelastic twin texture with localized flexoelectric effect in centrosymmetric epitaxial BiVO4 film. Supported by photodeposition and localized photocurrent analysis, we found the flexoelectric effect confined at domain wall area facilitates the photocarrier transport and the flexo-phototronic mechanism was further supported by dye-degradation and generation of reactive radicals. This work not only provides new insights into the introduction of flexo-phototronic effects in non-polar materials, but also sheds light on the use of material inhomogeneity for acquiring multifunctionality.

Flexoelectric Domain Walls Originated from Structural Phase Transition in Epitaxial BiVO4 Films.

Polar domain walls in centrosymmetric ferroelastics induce inhomogeneity that is the origin of advantageous multifunctionality. In particular, polar domain walls promote charge-carrier separation and hence are promising for energy conversion applications that overcome the hurdles of the rate-limiting step in the traditional photoelectrochemical water splitting processes. Yet, while macroscopic studies investigate the materials at the device scale, the origin of this phenomenon in general and the emergence of polar domain walls during the structural phase transition in particular has remained elusive, encumbering the development of this attractive system. Here, it is demonstrated that twin domain walls arise in centrosymmetric BiVO4 films and they exhibit localized piezoelectricity. It is also shown that during the structural phase transition from the tetragonal to monoclinic, the symmetry reduction is accompanied by an emergence of strain gradient, giving rise to flexoelectric effect and the polar domain walls. These results not only expose the emergence of polar domain walls at centrosymmetric systems by means of direct observation, but they also expand the realm of potential application of ferroelastics, especially in photoelectrochemistry and local piezoelectricity.

Domain Wall Dynamics in a Ferroelastic Spin Crossover Complex with Giant Magnetoelectric Coupling.

Pinned and mobile ferroelastic domain walls are detected in response to mechanical stress in a Mn3+ complex with two-step thermal switching between the spin triplet and spin quintet forms. Single-crystal X-ray diffraction and resonant ultrasound spectroscopy on [MnIII(3,5-diCl-sal2(323))]BPh4 reveal three distinct symmetry-breaking phase transitions in the polar space group series Cc → Pc → P1 → P1(1/2). The transition mechanisms involve coupling between structural and spin state order parameters, and the three transitions are Landau tricritical, first order, and first order, respectively. The two first-order phase transitions also show changes in magnetic properties and spin state ordering in the Jahn–Teller-active Mn3+ complex. On the basis of the change in symmetry from that of the parent structure, Cc, the triclinic phases are also ferroelastic, which has been confirmed by resonant ultrasound spectroscopy. Measurements of magnetoelectric coupling revealed significant changes in electric polarization at both the Pc → P1 and P1 → P1(1/2) transitions, with opposite signs. All these phases are polar, while P1 is also chiral. Remanent electric polarization was detected when applying a pulsed magnetic field of 60 T in the P1→ P1(1/2) region of bistability at 90 K. Thus, we showcase here a rare example of multifunctionality in a spin crossover material where the strain and polarization tensors and structural and spin state order parameters are strongly coupled.

Static and dynamic strain relaxation associated with the paraelectric-antiferroelectric phase transition in PbZrO3

Order parameter coupling associated with the first order, improper ferroelastic (Pm3̅m - Pbam) transition at ~510 K in PbZrO3 has been analysed from the perspective of strain and elasticity. Formal treatment of spontaneous strains using lattice parameter data from the literature reveals typical coupling with the order parameter for octahedral tilting, Q R, and stronger coupling with the order parameter for antiferroelectric displacements,Q Σ. These indicate that coupling between the two order parameters via common strains is not only biquadratic, λQ 2RQ 2Σ, but may also have contributions from a higher order term, λQ 2RQ 4Σ. Variations of elastic and anelastic properties obtained by resonant ultrasound spectroscopy (RUS) at frequencies in the vicinity of 1 MHz show softening as the transition point is approached from above, discontinuous stiffening at the transition point and a pattern of further stiffening in the stability field of the orthorhombic structure. Below the transition point, the pattern of stiffening resembles the evolution of Q 2R and Q 2Σ, as is typical of coupling dominated by terms with the form λe2Q 2, where e is a spontaneous shear strain. The absence of softening due to terms of the form λeQ 2 implies that the relaxation time for changes in the order parameters in response to an induced shear strain is slower than ~10-6 s. Also in contrast with measurements from the literature made at lower frequencies, no evidence for mobility of ferroelastic domain walls was observed at RUS frequencies. A peak in acoustic loss observed at the transition point and precursor softening in the stability field of the cubic phase are consistent with evidence for local dynamical polar clusters. Apart from some differences in relaxation times, the antiferroelectric transition in PbZrO3 does not appear to be overtly different from ferroelectric transitions such as occur in BaTiO3.

Individual Barkhausen Pulses of Ferroelastic Nanodomains.

Ferroelectric materials, upon electric field biasing, display polarization discontinuities known as Barkhausen jumps, a subclass of a more general phenomenon known as crackling noise. Herein, we follow and visualize in real time the motion of single 90° needle domains induced by an electric field applied in the polarization direction of the prototypical ferroelectric BaTiO_{3}, inside a transmission electron microscope. The nature of motion and periodicity of the Barkhausen pulses leads to distinctive interactions between domains forming a herringbone pattern. Remarkably, the tips of the domains do not come into contact with the body of the perpendicular domain, suggesting the presence of strong electromechanical fields around the tips of the needle domains. Additionally, interactions of the domains with the lattice result in relatively free movement of the domain walls through the dielectric medium, indicating that their motion-related activation energy depends only on weak Peierls-like potentials. Control over the kinetics of ferroelastic domain wall motion can lead to novel nanoelectronic devices pertinent to computing and data storage applications.

Disentangling Ferroelectric Wall Dynamics and Identification of Pinning Mechanisms via Deep Learning.

Field-induced domain-wall dynamics in ferroelectric materials underpins multiple applications ranging from actuators to information technology devices and necessitates a quantitative description of the associated mechanisms including giant electromechanical couplings, controlled nonlinearities, or low coercive voltages. While the advances in dynamic piezoresponse force microscopy measurements over the last two decades have rendered visualization of polarization dynamics relatively straightforward, the associated insights into the local mechanisms have been elusive. This work explores the domain dynamics in model polycrystalline materials using a workflow combining deep-learning-based segmentation of the domain structures with nonlinear dimensionality reduction using multilayer rotationally invariant autoencoders (rVAE). The former allows unambiguous identification and classification of the ferroelectric and ferroelastic domain walls. The rVAE discovers the latent representations of the domain wall geometries and their dynamics, thus providing insight into the intrinsic mechanisms of polarization switching, that can further be compared to simple physical models. The rVAE disentangles the factors affecting the pinning efficiency of ferroelectric walls, offering insights into the correlation of ferroelastic wall distribution and ferroelectric wall pinning.

Signatures of polarity in ferroelastic domain walls and antiphase boundaries of SrTiO3 and other perovskites

In the present work we study the polar properties of domain walls using a recently developed method of combining layer group analysis with order parameter symmetry [Schranz et al. PRB 100 (2019) 184105]. Using this method we obtain a detailed overview on the microscopic and macroscopic properties of domain walls which we can quantify with results from Landau-Ginzburg-Devonshire theory. Recently, we have applied [Schranz et al. PRB 102 (2020) 184101] the method to analyse the symmetry and polar properties of ferroelastic twin walls and antiphase boundaries in SrTiO3. Here we discuss the elastic anomalies observed in SrTiO3 at various temperatures in the light of these findings.

Low temperature ferroelectricity in Strontium Titanate domain walls detected by depolarization pyrocurrents

The low temperature phenomenology of Strontium Titanate is rich and intriguing, with anomalies producing signals of small intensity. We show that depolarization pyrocurrents are a suitable technique to greatly enhance these features, otherwise rather elusive when observed with other methods. Depolarization currents have been measured on a single phase sintered SrTiO3 pellet, prepared by solid state reaction. They increase with increasing poling voltage and switch to symmetric negative values by inversion of the poling sign, which is a property commonly considered as a clue of ferroelectricity. Moreover, three intensity maxima are revealed at T=16, 24 and 45 K respectively. In particular, the anomaly at T ≃ 45 K can be associated with the emerging of ferroelectricity in walls between antiphase ferroelastic domain walls, whose nanoscale polar character is already known from literature.We demonstrate and estimate such ferroelectricity reconstructing a static polarization hysteresis loop by applying suitable poling patterns.

Effect of Methylene Chain Length on the Thermodynamic Properties, Ferroelastic Properties, and Molecular Dynamics of the Perovskite-type Layer Crystal [NH3(CH2) n NH3]MnCl4 (n = 2, 3, and 4).

The structures and phase transitions of [NH3(CH2)nNH3]MnCl4 (n = 2, 3, and 4) crystals were confirmed through X-ray diffraction and differential scanning calorimetry (DSC) experiments. Thermodynamic properties, ferroelastic properties, and molecular dynamics of three crystals were studied as a function of the number (n) of CH2 groups in the alkylene chains. The loss in molecular weight due to a decrease in n marked the onset of the partial thermal decomposition. The thermal decomposition temperature, Td, increased with increasing length of the CH2 chain. While the ferroelastic twin domain walls for n = 2 and 4 were in the same direction at all temperatures, the domain walls for n = 3 were rotated by 45°, and the direction of extinction in phase II was rotated by 45° with respect to phases I and III. The 1H and 13C MAS NMR spectra of the three crystals were recorded as a function of temperature. With increasing length of the CH2 chain, the 1H spin relaxation time decreased, indicating that molecular motions were activated. These results provide insights into the thermodynamic properties and structural dynamics of the [NH3(CH2)nNH3]MnCl4 crystals and are expected to facilitate their potential applications.

Optical second-harmonic generation microscopy as a tool for ferroelastic domain wall exploration

Domain walls (DWs) of four typical ferroelastics, CaTiO3 (CTO), LaAlO3 (LAO), Pb3(PO4)2 (PPO), and BiVO4 (BVO), were observed by the second harmonic generation (SHG) microscopy, and the results were compared. The DWs of the examined ferroelastics are all polar. This fact does not depend on whether the crystal is an insulator (CTO, LAO, and PPO) or a semiconductor (BVO), on whether it has ferroelectric instability (CTO) or not (LAO, PPO, and BVO), or on the DW state, namely, whether the DW is crystallographically prominent or non-prominent. The symmetry of these DWs was determined from the SHG anisotropy, and it was clarified that they are a subgroup of the high temperature phase. In the cases of CTO and PPO, stress was applied to move the DW, and its polarity and symmetry were examined. The main characteristics did not change even when stress was applied. In all samples, uniform SHG was observed for each DW. This indicates that the DWs of the examined ferroelastics seem to be in a ferroelectric single domain state.

Unveiling Temperature-Induced Structural Domains and Movement of Oxygen Vacancies in SrTiO3 with Graphene.

Heterointerfaces coupling complex oxides exhibit coexisting functional properties such as magnetism, superconductivity, and ferroelectricity, often absent in their individual constituent. SrTiO3 (STO), a canonical band insulator, is an active constituent of such heterointerfaces. Temperature-, strain-, or mechanical stress-induced ferroelastic transition leads to the formation of narrow domains and domain walls in STO. Such ferroelastic domain walls have been studied using imaging or transport techniques and, often, the findings are influenced by the choice and interaction of the electrodes with STO. In this work, we use graphene as a unique platform to unveil the movement of oxygen vacancies and ferroelastic domain walls near the STO surface by studying the temperature and gate bias dependence of charge transport in graphene. By sweeping the back gate voltage, we observe antihysteresis in graphene typically observed in conventional ferroelectric oxides. Interestingly, we find features in antihysteresis that are related to the movement of domain walls and of oxygen vacancies in STO. We ascertain this by analyzing the time dependence of the graphene square resistance at different temperatures and gate bias. Density functional calculations estimate the surface polarization and formation energies of layer-dependent oxygen vacancies in STO. This corroborates quantitatively with the activation energies determined from the temperature dependence of the graphene square resistance. Introduction of a hexagonal boron nitride (hBN) layer, of varying thicknesses, between graphene and STO leads to a gradual disappearance of the observed features, implying the influence of the domain walls onto the potential landscape in graphene.

Polarization of domain boundaries in SrTiO3 studied by layer group and order-parameter symmetry

Based on a recently developed combination of layer group analysis with order-parameter symmetry, we study the polarity of antiphase domain boundaries (APBs) and ferroelastic twin boundaries (TBs) in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$. In addition to the celebrated layer group analysis of domain twins, the present method allows us to investigate tensor properties of domain walls also for the case where order-parameter variables other than the spontaneous ones are active. We find that antiphase boundaries in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ can carry a polarization if in addition to the spontaneous order parameter $(0,0,{\ensuremath{\phi}}_{s})$ a second component, i.e., $({\ensuremath{\phi}}_{1},0,{\ensuremath{\phi}}_{s})$, develops within the domain wall. This result, which is solely based on symmetry arguments, strongly suggests that polarization in APBs is possible if a phase transition from an Ising-type wall to a N\'eel- or Bloch-like wall occurs. This is in very good agreement with previous calculations based on Landau-Ginzburg free energy expansions including biquadratic ($\ensuremath{\propto}{P}_{i}{P}_{j}{\ensuremath{\phi}}_{k}{\ensuremath{\phi}}_{l}$) [A. K. Tagantsev et al. Phys. Rev. B 64, 224107 (2001)] and flexoelectric ($\ensuremath{\propto}{P}_{k}\frac{\ensuremath{\partial}{u}_{ij}}{\ensuremath{\partial}\ensuremath{\xi}}$) coupling terms [A. N. Morozovska et al. Phys. Rev. B. 85, 094107 (2012)]. The present results also unveil a close connection between the recently discovered macroscopic polarization in antiferrodistortive cycloids of ferroelastic domain walls of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ and a mechanism for explaining polarization of APBs.

Ferroelastic domain walls as templates for multiferroic devices

Ferroelastic domain walls are typically twin interfaces. They contain a multitude of emerging properties, including (super-)conductivity, polarity, optically activity, and photovoltaic properties and may contain a number of magnetic properties even when there is no magnetic element in the ferroelastic matrix. Current progress to determine these properties is reviewed. Local wall properties change a little if the domain walls are deformed, but external fields can shift the location of the wall. Mobile domain boundaries carry with them the locus of any emerging property. The double flexibility of functional domain walls and the possibility to move domain boundaries provide a new design concept for device manufacturing. Some potential avenues for device designs are discussed.

Evolution of ferroelastic domain walls during phase transitions in barium titanate nanoparticles

In this work, ferroelastic domain walls inside ${\mathrm{BaTiO}}_{3}$ (BTO) tetragonal nanocrystals are distinguished by Bragg peak position and studied with Bragg coherent x-ray diffraction imaging (BCDI). Convergence-related features of the BCDI method for strongly phased objects are reported. A ferroelastic domain wall inside a BTO crystal has been tracked and imaged across the tetragonal-cubic phase transition and proves to be reversible. The linear relationship of relative displacement between two twin domains with temperature is measured and shows a different slope for heating and cooling, while the tetragonality reproduces well over temperature changes in both directions. An edge dislocation is also observed and found to annihilate when heating the crystal close to the phase transition temperature.

Flexopiezoelectricity at ferroelastic domain walls in WO3 films

The emergence of a domain wall property that is forbidden by symmetry in bulk can offer unforeseen opportunities for nanoscale low-dimensional functionalities in ferroic materials. Here, we report that the piezoelectric response is greatly enhanced in the ferroelastic domain walls of centrosymmetric tungsten trioxide thin films due to a large strain gradient of 106 m−1, which exists over a rather wide width (~20 nm) of the wall. The interrelationship between the strain gradient, electric polarity, and the electromechanical property is scrutinized by detecting of the lattice distortion using atomic scale strain analysis, and also by detecting the depolarized electric field using differential phase contrast technique. We further demonstrate that the domain walls can be manipulated and aligned in specific directions deterministically using a scanning tip, which produces a surficial strain gradient. Our findings provide the comprehensive observation of a flexopiezoelectric phenomenon that is artificially controlled by externally induced strain gradients.

Stabilization of ferroelastic charged domain walls in self-assembled BiFeO3 nanoislands

Understanding the microscopic origin of exotic domain configurations and emergent properties in charged domain walls is essential for both fundamental physics and applications in next-generation nanoelectronics. In self-assembled BiFeO3 nanoislands, 71° ferroelastic charged domain walls were spontaneously formed, which were traditionally regarded as unstable architectures. Here, by combining scanning transmission electron microscopy, geometric phase analysis, and energy dispersion spectrum, we explored the microscopic mechanism of stabilizing the tail-to-tail charged domain walls with upward center-divergent quad-domain structures in BiFeO3 nanoislands. The comprehensive factors include the fully relaxed rhombohedral phase in nanoislands, negative surface screening charges, and upward built-in bias at the BiFeO3-(La,Sr)MnO3 interface, which are respectively induced by interfacial periodic dislocations, surface reconstructions, and interfacial terminations. Moreover, the unusual polarization state and domain-wall arrangement in the nanoislands were also proved to be stable even at an elevated temperature.

Current vortices and magnetic fields driven by moving polar twin boundaries in ferroelastic materials

Ferroelastic twin boundaries often have properties that do not exist in bulk, such as superconductivity, polarity etc. Designing and optimizing domain walls can hence functionalize ferroelastic materials. Using atomistic simulations, we report that moving domain walls have magnetic properties even when there is no magnetic element in the material. The origin of a robust magnetic signal lies in polar vortex structures induced by moving domain walls, e.g., near the tips of needle domains and near domain wall kinks. These vortices generate displacement currents, which are the origin of magnetic moments perpendicular to the vortex plane. This phenomenon is universal for ionic crystals and holds for all ferroelastic domain boundaries containing dipolar moments. The magnetic moment depends on the speed of the domain boundary, which can reach the speed of sound under strong mechanical forcing. We estimate that the magnetic moment can reach several tens of Bohr magnetons for a collective thin film of 1000 lattice planes and movements of the vortex by the speed of sound. The predicted magnetic fields in thin slabs are much larger than those observed experimentally in SrTiO3/LaAlO3 heterostructures, which may be due to weak (accidental) forcing and slow changes of the domain patterns during their experiments. The dynamical multiferroic properties of ferroelastic domain walls may have the potential to be used to construct localized magnetic memory devices in future.

Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials

Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level. When this spatial confinement is combined with observations of emergent functional properties, such as polarity in non-polar systems or electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent new and exciting objects in matter. In this Review, we discuss the exotic polarization profiles that can arise at domain walls with multiple order parameters and the different mechanisms that lead to domain-wall polarity in non-polar ferroelastic materials. The emergence of energetically degenerate variants of the domain walls themselves suggests the existence of interesting quasi-1D topological defects within such walls. We also provide an overview of the general notions that have been postulated as fundamental mechanisms responsible for domain-wall conduction in ferroelectrics. We then discuss the prospect of combining domain walls with transition regions observed at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects, enabling emergent properties beyond those available in today’s topological systems. Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level and emergent functional properties. This Review discusses the exotic polarization profiles that arise at domain walls and the fundamental mechanisms responsible for domain-wall conduction.