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Flat elastic sheets tend to display wrinkles and folds. From pieces of clothing down to two-dimensional crystals, these corrugations appear in response to strain generated by sheet compression or stretching, thermal or mechanical mismatch with other elastic layers, or surface tension. Extensively studied in metals, polymers and, more recently, in van der Waals exfoliated layers, with the advent of thin single crystal freestanding films of complex oxides, researchers are now paying attention to novel microstructural effects induced by bending ferroelectric-ferroelastics, where polarization is strongly coupled to lattice deformation. Here we show that wrinkle undulations in BaTiO3 sheets bonded to a viscoelastic substrate transform into a buckle delamination geometry when transferred onto a rigid substrate. Using spatially resolved techniques at different scales (Raman, scanning probe and electron microscopy), we show how these delaminations in the free BaTiO3 sheets display a self-organization of ferroelastic domains along the buckle profile that strongly differs from the more studied sinusoidal wrinkle geometry. Moreover, we disclose the hierarchical distribution of a secondary set of domains induced by the misalignment of these folding structures from the preferred in-plane crystallographic orientations. Our results disclose the relevance of the morphology and orientation of buckling instabilities in ferroelectric free sheets, for the stabilization of different domain structures, pointing to new routes for domain engineering of ferroelectrics in flexible oxide sheets.

Whereas ferroelectricity may vanish in ultra-thin ferroelectric films, it is expected to emerge in ultra-thin anti-ferroelectric films, sparking people's interest in using antiferroelectric materials as an alternative to ferroelectric ones for high-density data storage applications. Lead Zirconate (PbZrO3) is considered the prototype material for antiferroelectricity, and indeed previous studies indicated that nanoscale PbZrO3 films exhibit ferroelectricity. The understanding of such phenomena from the microstructure aspect is crucial but still lacking. In this study, we fabricated a PbZrO3 film with thicknesses varying from 5 nm to 80 nm. Using Piezoresponse Force Microscopy, we discovered the film displayed a transition from antiferroelectric behaviour in the thicker areas to ferroelectric behaviour in the thinner ones, with a critical thickness between 10 and 15 nm. In this critical thickness range, a 12 nm PZO thin film was chosen for further study using aberration-corrected scanning transmission electron microscopy. The investigation showed that the film comprises both ferroelectric and ferrielectric phases. The ferroelectric phase is characterized by polarisation along the pseudocubic [011] projection direction. The positions of Pb, Zr, and O were determined using the integrated differential phase contrast method. This allowed us to ascertain that the ferroelectric PbZrO3 unit cell is half the size of that in the antiferroelectric phase on the ab plane. The observed unit cell is different from the electric field-induced ferroelectric rhombohedral phases. Additionally, we identified a ferrielectric phase with a unique up-up-zero-zero dipole configuration. The finding is crucial for understanding the performance of ultrathin antiferroelectric thin films and the subsequent design and development of antiferroelectric devices.

We report the switching dynamics of antiferroelectric Lead Zirconate (PbZrO3) free standing capacitors compared to their epitaxial counterparts. Frequency dependence of hysteresis indicates that freestanding capacitors exhibit a lower dispersion of switching fields, lower residual polarization, and faster switching response as compared to epitaxially-clamped capacitors. As a consequence, freestanding capacitor membranes exhibit better energy storage density and efficiency., Comment: 27 pages, 7 Figures, Supplementary material

Extraordinary physical properties arise at polar interfaces in oxide materials, including the emergence of two-dimensional electron gases, sheet-superconductivity, and multiferroicity. A special type of polar interface are ferroelectric domain walls, where electronic reconstruction phenomena can be driven by bound charges. Great progress has been achieved in the characterization of such domain walls and, over the last decade, their potential for next-generation nanotechnology has become clear. Established tomography techniques, however, are either destructive or offer insufficient spatial resolution, creating a pressing demand for 3D imaging compatible with future fabrication processes. Here, we demonstrate non-destructive tomographic imaging of ferroelectric domain walls using secondary electrons. Utilizing conventional scanning electron microscopy (SEM), we reconstruct the position, orientation, and charge state of hidden domain walls at distances up to several hundreds of nanometers away from the surface. A mathematical model is derived that links the SEM intensity variations at the surface to the local domain wall properties, enabling non-destructive tomography with good noise tolerance on the timescale of seconds. Our SEM-based approach facilitates high-throughput screening of materials with functional domain walls and domain-wall-based devices, which is essential for monitoring during the production of device architectures and quality control in real-time.

Understanding the mechanisms underlying a stable polarization at the surface of ferroelectric thin films is of particular importance both from a fundamental point of view and to achieve control of the surface polarization itself. In this study, it is demonstrated that the X-ray standing wave technique allows the polarization near the surface of a ferroelectric thin film to be probed directly. The X-ray standing wave technique is employed to determine, with picometer accuracy, Ti and Ba atomic positions near the surface of three differently strained $\mathrm{BaTiO_3}$ thin films grown on scandate substrates, with a $\mathrm{SrRuO_3}$ film as bottom electrode. This technique gives direct access to atomic positions, and thus to the local ferroelectric polarization, within the first 3 unit cells below the surface. By employing X-ray photoelectron spectroscopy, a detailed overview of the oxygen-containing species adsorbed on the surface, upon exposure to ambient conditions, is obtained. The combination of structural and spectroscopic information allows us to conclude on the most plausible mechanisms that stabilize the surface polarization in the three samples under study. The different amplitude and orientation of the local ferroelectric polarizations are associated with surface charges attributed to the type, amount and spatial distribution of the oxygen-containing adsorbates.

Complex oxides offer a wide range of functional properties, and recent advances in fabrication of freestanding membranes of these oxides are adding new mechanical degrees of freedom to this already rich functional ecosystem. Here, we demonstrate photoactuation in freestanding thin film resonators of ferroelectric Barium Titanate (BaTiO3) and paraelectric Strontium Titanate (SrTiO3). The free-standing films, transferred onto perforated supports, act as nano-drums, oscillating at their natural resonance frequency when illuminated by a frequency-modulated laser. The light-induced deflections in the ferroelectric BaTiO3 membranes are two orders of magnitude larger than in the paraelectric SrTiO3 ones. Time-resolved X-ray micro-diffraction under illumination and temperature-dependent and holographic interferometry provide combined evidence for the photostrictive strain in BaTiO3 originating from partial screening of ferroelectric polarization by photo-excited carriers, which decreases the tetragonality of the unit cell. These findings showcase the potential of photostrictive freestanding ferroelectric films as wireless actuators operated by light.

The phase diagram of ice is complex and contains many phases, but the most common (frozen water at ambient pressure, also known as Ih ice) is a non-polar material despite individual water molecules being polar. Consequently, ice is not piezoelectric and cannot generate electricity under pressure. On the other hand, the coupling between polarization and strain gradient (flexoelectricity) is universal, so ice may in theory generate electricity under bending. Here we report the experimental demonstration that ice is flexoelectric, finding a coefficient comparable to that of ceramics such as SrTiO3 or TiO2. Additionally, and unexpectedly, the sensitivity of flexoelectric measurements to surface boundary conditions has also revealed a ferroelectric phase transition around 163 confined in the near-surface region of the ice slabs. The electromechanical properties of ice may find applications for low-cost transducers made in-situ in cold and remote locations, but perhaps more important are the consequences for natural phenomena involving ice electrification. In particular, we have calculated the flexoelectric polarization generated in collisions between ice and graupel particles, which reproduces the experimentally reported results for contact electrification in such events, known to cause electrification in storm clouds.

In the archetypal antiferroelectric PbZrO3, antiparallel electric dipoles cancel each other, resulting in zero spontaneous polarisation at the macroscopic level. Yet in actual hysteresis loops, the cancellation is rarely perfect and some remnant polarization is often observed, suggesting the metastability of polar phases in this material. In this work, using aberration-corrected scanning transmission electron microscopy methods on a PbZrO3 single crystal, we uncover the coexistence of the common antiferroelectric phase and a ferrielectric phase featuring an electric dipole pattern of "up down up". This dipole arrangement, predicted by Aramberri et al. (2021) to be the ground state of PbZrO3 at 0K, appears at room temperature in the form of translational boundaries that aggregate to form wider stripe domains of the polar phase embedded within the antiferroelectric matrix.

Halide perovskites have outstanding photovoltaic properties which have been optimized through interfacial engineering. However, as these materials approach the limits imposed by the physics of semiconductor junctions, it is urgent to explore alternatives, such as the bulk photovoltaic effect, whose physical origin is different and not bound by the same limits. In this context, we focus on the flexo-photovoltaic effect, a type of bulk photovoltaic effect that was recently observed in oxides under strain gradients. We have measured the flexo-photovoltaic effect of MAPbBr3 and MAPbI3 crystals under bending and found it to be orders of magnitude larger than for SrTiO3, the benchmark flexo-photovoltaic oxide. For sufficiently large strain gradients, photovoltages bigger than the bandgap can be produced. Bulk photovoltaic effects are additive and, for MAPbI3, the flexo-photovoltage exists on top of a native bulk photovoltage that is hysteretic, consistent with the electrically switchable macroscopic polarization of this material. The results suggest that harnessing the flexo-photovoltaic effect through strain gradient engineering can provide a functional leap forward for halide perovskites., Comment: 20 pages, 11 figures

Artificially induced asymmetric tribological properties of ferroelectrics offer an alternative route to visualize and control ferroelectric domains. Here, we observe the switchable friction and wear behavior of ferroelectrics using a nanoscale scanning probe where down domains having lower friction coefficient than up domains can be used as smart masks as they show slower wear rate than up domains. This asymmetry is enabled by flexoelectrically coupled polarization in the up and down domains under a sufficiently high contact force. Moreover, we determine that this polarization-sensitive tribological asymmetry is universal across ferroelectrics with different chemical composition and crystalline symmetry. Finally, using this switchable tribology and multi-pass patterning with a domain-based dynamic smart mask, we demonstrate three-dimensional nanostructuring exploiting the asymmetric wear rates of up and down domains, which can, furthermore, be scaled up to technologically relevant (mm-cm) size. These findings establish that ferroelectrics are electrically tunable tribological materials at the nanoscale for versatile applications., Comment: 72 pages, 33 figures

Compound phases often display properties that are symmetry-forbidden relative to their nominal, average crystallographic symmetry, even if extrinsic reasons (defects, strain, imperfections) are not apparent. Here, we investigate macroscopic inversion symmetry breaking in nominally centrosymmetric materials and measure Resonant Piezoelectric Spectroscopy (RPS) and Resonant Ultrasound Spectroscopy (RUS) in 15 compounds, 18 samples, and 21 different phases, including unpoled ferroelectrics, paraelectrics, relaxors, ferroelastics, incipient ferroelectrics, and isotropic materials with low defect concentrations, i.e. NaCl,cfused silica, and CaF2. We exclude the flexoelectric effect as a source of the observed piezoelectricity yetcobserve piezoelectricity in all nominally cubic phases of these samples. By scaling the RPS intensities with those of RUS, we calibrate the effective piezoelectric coefficients using single crystal quartz as standard. Using this scaling we determine the effective piezoelectric modulus in nominally non-piezoelectric phases, finding that the "symmetry-forbidden" piezoelectric effect ranges from 1 pm/V to 10E-5 pm/V. The values for unpoled ferroelectric phases are only slightly higher than those in the paraelectric phase of the same material. The lowest coefficients are well below the detection limit of conventional piezoelectric measurements and demonstrate RPS as an ultra-highly sensitive method to measure piezoelectricity. We suggestt hat symmetry-breaking piezoelectricity in nominally centrosymmetric materials and disordered, unpoled ferroelectrics is ubiquitous.

We present a detailed analysis of the temperature dependence of the thermal conductivity of a ferroelectric PbTiO3 thin film deposited in a composition-spread geometry enabling a continuous range of compositions from ~25% titanium-deficient to ~20% titanium-rich to be studied. By fitting the experimental results to the Debye model we deconvolve and quantify the two main phonon scattering sources in the system: ferroelectric domain walls (DWs) and point defects. Our results prove that ferroelectric DWs are the main agent limiting the thermal conductivity in this system, not only in the stoichiometric region of the thin film ([Pb]/[Ti]~1), but also when the concentration of cation point defects is significant (up to ~15%). Hence, DWs in ferroelectric materials are a source of phonon scattering at least as effective as point defects. Our results demonstrate the viability and effectiveness of using reconfigurable DWs to control the thermal conductivity in solid-state devices.

The large electrocaloric coupling in PbZrO3 allows using high-speed infrared imaging to visualize antiferroelectric switching dynamics via the associated temperature change. We find that in ceramic samples of homogeneous temperature and thickness, switching is nucleation-limited and fast, with devices responding in the milisecond range. By introducing gradients of thickness, however, it is possible to change the dynamics from nucleation-limited to propagation-limited, whereby a single phase boundary sweeps across the sample like a cold front, at a speed of c.a. 20 cm/s. Additionally, introducing thermostatic temperature differences between two sides of the sample enables the simultaneous generation of a negative electrocaloric effect on one side and a positive one on the other, yielding a Janus-like electrocaloric response.

We have studied the electrocaloric response of the archetypal antiferroelectric PbZrO3 as a function of voltage and temperature in the vicinity of its antiferroelectric-paraelectric phase transition. Large electrocaloric effects of opposite signs, ranging from an electro-cooling of -3.5 K to an electro-heating of +5.5 K, were directly measured with an infrared camera. We show by calorimetric and electromechanical measurements that the large negative electrocaloric effect comes from an endothermic antiferroelectric-ferroelectric switching, in contrast to dipole destabilization of the antiparallel lattice, previously proposed as an explanation for the negative electrocaloric effect of antiferroelectrics., Comment: Article (17 pages) and supplemental material (12 pages) present in .pdf file

The observation of electronic phase separation textures in vanadium dioxide (VO2), a prototypical electron-correlated oxide, has recently added new perspectives on the long standing debate about its metal-insulator transition and its applications. Yet, the lack of atomically-resolved information on phases accompanying such complex patterns still hinders a comprehensive understanding of the transition and its implementation in practical devices. In this work, atomic resolution imaging and spectroscopy unveils the existence of ferroelastic tweed structures on ~5 nm length scales, well below the resolution limit of currently employed spectroscopic imaging techniques. Moreover, density functional theory calculations show that such fine tweeds are formed by a metallic structure, formed by partially dimerized V-chains, that appears tetragonal (rutile) on average, but is locally monoclinic. These observations suggest that the metal/insulator coexistence among low-symmetry forms of VO2 is driven by lattice degrees of freedom, and provide a multiscale perspective for the interpretation of existing data, whereby phase coexistence and structural intermixing can occur all the way down to the atomic scale., Comment: Main text: 24 pages, 4 figures. Supplemental information: 9 pages, 1 table, 4 figures

Domain walls are functionally different from the domains they separate, but little is known about their mechanical properties. Using scanning probe microscopy, we have measured the mechanical response of ferroelectric 180o domain walls and observed that, despite separating domains that are mechanically identical (non-ferroelastic), the walls are mechanically distinct -- softer -- compared to the domains. This effect has been observed in different ferroelectric materials (LiNbO3, BaTiO3, PbTiO3) and with different morphologies (from single crystals to thin films) so it appears to be universal. We propose a theoretical framework that explains the domain wall softening and justifies that the effect should be common to all ferroelectrics., Comment: 17 pages, 5 color figures

The recent discovery of bone flexoelectricity (electrical polarization induced by strain gradient) suggests that flexoelectricity could have physiological effects in bones, and specifically near bone fractures, where flexoelectricity is theoretically highest. Here, we report a cytological study of the interaction between crack stress and bone cells. We have cultured MC3T3-E1 mouse osteoblastic cells in biomimetic microcracked hydroxyapatite substrates, differentiated into osteocytes and applied a strain gradient to the samples. The results show a strong apoptotic cellular response, whereby mechanical stimulation causes those cells near the crack to die, as indicated by live-dead and caspase staining. In addition, analysis two weeks after stimulation shows increased cell attachment and mineralization around microcracks and a higher expression of osteocalcin, an osteogenic protein known to be promoted by physical exercise. The results are consistent with flexoelectricity playing at least two different roles in bone remodelling: apoptotic trigger of the repair protocol, and electrostimulant of the bone-building activity of osteoblasts.

Very sensitive responses to external forces are found near phase transitions. However, phase transition dynamics and pre-equilibrium phenomena are difficult to detect and control. We have directly observed that the equilibrium domain structure following a phase transition in BaTiO3, a ferroelectric and ferroelastic material, is attained by halving of the domain periodicity, sequentially and multiple times. The process is reversible, displaying periodicity doubling as temperature is increased. This observation is backed theoretically and can explain the fingerprints of domain period multiplicity observed in other systems, strongly suggesting this as a general model for pattern formation during phase transitions in ferroelastic materials.

The propagation front of a crack generates large strain gradients and it is therefore a strong source of gradient-induced polarization (flexoelectricity). Herein, we demonstrate that, in piezoelectric materials, a consequence of flexoelectricity is that crack propagation will be helped or hindered depending on whether it is parallel or antiparallel to the piezoelectric polar axis. This means that the theory of fracture physics can no longer assume mechanical symmetry in polar materials. The discovery of fracture asymmetry also has practical repercussions for the electromechanical fatigue of ferroelectrics and piezoelectric transducers, as well enabling a new degree of freedom for crack-based nanopatterning., Comment: 15 pages, 4 figures

The origin of "giant" flexoelectricity, orders of magnitude larger than theoretically predicted, yet frequently observed, is under intense scrutiny. There is mounting evidence correlating giant flexoelectric-like effects with parasitic piezoelectricity, but it is not clear how piezoelectricity (polarization generated by strain) manages to imitate flexoelectricity (polarization generated by strain gradient) in typical beam-bending experiments, since in a bent beam the net strain is zero. In addition, and contrary to flexoelectricity, piezoelectricity changes sign under space inversion, and this criterion should be able to distinguish the two effects and yet "giant" flexoelectricity is insensitive to space inversion, seemingly contradicting a piezoelectric origin. Here we show that, if a piezoelectric material has its piezoelectric coefficient be asymmetrically distributed across the sample, it will generate a bending-induced polarization impossible to distinguish from true flexoelectricity even by inverting the sample. The effective flexoelectric coefficient caused by piezoelectricity is functionally identical to, and often larger than, intrinsic flexoelectricity: the calculations show that, for standard perovskite ferroelectrics, even a tiny gradient of piezoelectricity (1% variation of piezoelectric coefficient across 1 mm) is sufficient to yield a giant effective flexoelectric coefficient of 1 $\mu$C/m, three orders of magnitude larger than the intrinsic expectation value.

Flexoelectricity (coupling between polarization and strain gradients) is a property of all dielectric materials that has been theoretically known for decades, but it is only relatively recently that it has begun to attract experimental attention. As a consequence, there are still entire families of materials whose flexoelectric performance is unknown. This is the case, for example, of antiferroelectrics: materials with an antipolar but switchable arrangement of dipoles. And yet, these materials could be flexoelectrically relevant because it has been hypothesised that the origin of their antiferroelectricity might be flexoelectric. In this work, we have measured the flexoelectricity of two different antiferroelectrics (PbZrO3 and AgNbO3) as a function of temperature, up to and beyond their Curie temperature. Neither flexoelectricity nor the flexocoupling coefficients are anomalously high, but the flexocoupling shows a sharp peak at the antiferroelectric phase transition., Comment: 12 pages, 3 figures

The instability of ferroelectric ordering in ultra-thin films is one of the most important fundamental issues pertaining realization of a number of electronic devices with enhanced functionality, such as ferroelectric and multiferroic tunnel junctions or ferroelectric field effect transistors. In this paper, we investigate the polarization state of archetypal ultrathin (several nanometres) ferroelectric heterostructures: epitaxial single-crystalline BaTiO$_3$ films sandwiched between the most habitual perovskite electrodes, SrRuO$_3$, on top of the most used perovskite substrate, SrTiO$_3$. We use a combination of piezoresponse force microscopy, dielectric measurements and structural characterization to provide conclusive evidence for the ferroelectric nature of the relaxed polarization state in ultrathin BaTiO$_3$ capacitors. We show that even the high screening efficiency of SrRuO$_3$ electrodes is still insufficient to stabilize polarization in SrRuO$_3$/BaTiO$_3$/SrRuO$_3$ heterostructures at room temperature. We identify the key role of domain wall motion in determining the macroscopic electrical properties of ultrathin capacitors and discuss their dielectric response in the light of the recent interest in negative capacitance behaviour., Comment: 13 pages, 4 figures

Layered iridates have been the subject of intense scrutiny on account of their unusually strong spin-orbit coupling, which opens up a narrow gap in a material that would otherwise be a metal. This insulating state is very sensitive to external perturbations. Here, we show that vertical compression at the nanoscale, delivered using the tip of a standard scanning probe microscope, is capable of inducing a five orders of magnitude change in the room temperature resistivity of Sr2IrO4. The extreme sensitivity of the electronic structure to anisotropic deformations opens up a new angle of interest on this material, and the giant and fully reversible perpendicular piezoresistance makes iridates a promising material for room temperature piezotronic devices.

We have measured the bending-induced polarization of Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals with compositions at the relaxor-ferroelectric phase boundary. The crystals display very large flexoelectricity, with flexocoupling coefficients an order of magnitude bigger than the theoretical upper limit set by the theories of Kogan and Tagantsev. This enhancement persists in the paraphrase up to a temperature T* that coincides with the start of elastic softening in the crystals. Analysis of the temperature dependence and cross-correlation between flexoelectric, dielectric and elastic properties indicates that the large bendinginduced polarization of relaxor ferroelectrics is not caused by intrinsically giant flexoelectricity, but by the reorientation of polar nanotwins that become ferroelastically active below T*.

We analyze the hypothetical link between octahedral straightening and increased conductivity inside the domain walls of BiFeO3. Our calculations for 109 degree walls predict a lattice parameter expansion of c.a. 1 percent in the direction perpendicular to the wall, and an associated straightening of the octahedral rotation angle of 4 degrees, which is comparable to that observed in the high temperature metallic phase of BiFeO3. On the other hand, in the closely related family of rare-earth orthoferrites, straighter octahedra do not correlate with increased bandgap, which suggests that the correlation between octahedral straightening and bandgap reduction in BiFeO3 is perhaps fortuitous and not necessarily the cause of increased conductivity at the walls., Comment: Article published in a Ferroelectrics special issue conmemorating Prof. J. F. Scott's 70th birthday

We calculate the exact analytical solution to the domain wall properties in a multiferroic system with two order parameters that are coupled bi-quadratically. This is then adapted to the case of a magnetoelectric multiferroic material such as BiFeO3, with a view to examine critically whether the domain walls can account for the enhancement of magnetization reported for thin films fo this material, in view of the correlation between increasing magnetization and increasing volume fraction of domain walls as films become thinner. The present analysis can be generalized to describe a class of magnetoelectric devices based upon domain walls rather than bulk properties., Comment: 9 pages, 4 figures

High temperature powder neutron diffraction experiments have been conducted around the reported beta-gamma, insulator-metal phase transition (~ 930 C) in BiFeO3. The results demonstrate that while a small volume contraction is observed at the transition temperature, consistent with an insulator-metal transition, both the beta and gamma phase of BiFeO3 exhibit orthorhombic symmetry i.e. no further increase of symmetry occurs under the present experimental conditions, contrary to previous suggestions. Furthermore we observe the gamma orthorhombic phase to persist up to a temperature of approximately 950 C before complete decomposition into Bi2Fe4O9 (and liquid Bi2O3), which subsequently begins to decompose at approximately 960 C.

Comments on "Giant Dielectric Response in the One-Dimensional Charge-Ordered Semiconductor (NbSe_{4})_{3}I" (D. Staresinic et al., Phys. Rev. Lett. 96, 046402 (2006)) and "Colossal Magnetocapacitance and Colossal Magnetoresistance in HgCr_{2}S_{4}" (S. Weber et al., Phys. Rev. Lett. 96, 157202 (2006)), Comment: Comment submitted to Physical Review Letters; 1 figure (color online)