In ferroelectric thin films, the complex interplay between mechanical and electrostatic boundary conditions in reduced dimensionality allows for the formation of a wide variety of domain configurations with fascinating properties. Domains are regions of uniformly oriented polarization, separated by interfaces termed domain walls (DWs). These domain walls can be as thin as a few atomic layers and exhibit physical properties and symmetry different from the parent phase—indeed, when polar, they can themselves be considered as individually switchable nanoscale ferroelectric entities. At larger length scales, domains can self-organize into superdomains—mesoscopic, spatially correlated assemblies of domains that behave as higher-order switching units. Superdomains differ from loosely arranged domain collections because their constituent domains exhibit cooperative dynamics, giving rise to collective polarization states, hierarchical organization, and emergent functional properties. Their characteristic length scales range from hundreds of nanometers to several micrometers, and their order parameter is the collective polarization. The interfaces between superdomains—superdomain walls—are distinct from conventional domain walls. They separate regions with different collective polarization arrangements and may host novel interfacial phenomena, offering opportunities for unique functionalities in devices such as non-volatile memories or for emergent effects like effective negative capacitance. Domains and superdomains can be found in different materials, in the form of bulk crystals, epitaxial, and free-standing thin films; their features, including size and density, can be tuned and/or controlled by changing, for instance, the strain state, the electrostatic boundary conditions of the system and, for thin films, the thickness, the deposition temperature, and other growth parameters, as shown in Fig. 1. In this experimentally driven review, we will explore the formation, structure, and properties of domains, superdomains, and superdomain walls in ferroelectric thin films. We will, in particular, focus on tetragonal perovskite ferroelectrics, which present the salient features we wish to address (the presence of both purely ferroelectric domains and ferroelectric/ferroelastic twins, as well as a broad range of complex polarization textures), while restraining the number of possible configurations with respect to, for example, orthorhombic or rhombohedral symmetry ferroelectrics. While this review is, thus, not intended to be exhaustive, we hope that it sparks interest in what we see as a dynamic and promising area—ferroelectric functional materials—with strong potential for future development and possible applications. It is worth mentioning that the philosophy followed for the figures is to illustrate our discussion with examples from the literature and from our own work, relatively briefly discussed in the main text. More details are found in the caption with references for the interested reader.

A polar oxide on the brink displays enhanced electromechanical response, classically from a combination of phase competition and domain wall motion. In epitaxial thin films, however, such enhancement is widely suppressed by substrate clamping, which immobilizes structural interfaces. Here, we show that by using a substrate that imposes directionally asymmetric strain, one can fundamentally engineer this constraint to stabilize a special class of glissile interfaces that amplify electromechanical response through their mobility. In BiFeO3 films grown on LaAlO3 (103), strain asymmetry stabilizes elastically compatible low-symmetry variants separated by dislocation-free, glissile interphase boundaries. These interfaces translate reversibly under weak electrical or mechanical perturbations, mediating collective nanoscale phase transformations that are forbidden under conventional biaxial strain. The resulting dynamics exhibit scale-free avalanche behavior characteristic of systems poised near an elastic instability. Our findings establish glissile interphase boundaries as an emergent interfacial state in anisotropically-strained oxides and provide a general framework for engineering phase competition and collective switching phenomena in epitaxial materials.

Nanoscale control of electromechanical coupling transforms frictional information into a direct probe of ferroelectric polarization. Here, we show that an asymmetric friction response induced by high contact forces applied with a scanning probe microscopy tip enables spatially resolved visualization of ferroelectric polarization in thin films and single crystals. In agreement with multifield coupled continuum mechanical simulations, our results reveal that this friction asymmetry results from flexoelectrically induced polarization either competing with or enhancing the ferroelectric polarization, thus giving mechanical information on its orientation. This technique, which we term polarization-derived friction microscopy, allows rapid, low-cost, and voltage-free imaging of ferroelectric domains, thereby minimizing electrostatic measurement artifacts and achieving high scan rates beyond 14 frames per second. Our work opens broad opportunities for high-throughput functional imaging of surfaces with extensive potential applications such as voltage-free data acquisition and studies of polarization dynamics in complex environments.

Localized interlayer excitons in semiconducting transition-metal dichalcogenide heterobilayers are quantum emitters with a static electric dipole moment, making them excellent nanoscale charge sensors to probe correlated quantum phases in a proximal layer. These emitters are electrically tunable and inherit spin-valley selection rules, yet their deterministic spatial control remains challenging due to subwavelength confinement. Here, we present a platform that combines cryogenic optical spectroscopy with scanning probe microscopy to investigate trapped interlayer excitons in WSe_2/MoSe_2 bilayers. By exploiting AFM-based local Stark shift, we achieve super-resolution localization of emitters separated by only a few tens of nanometers and demonstrate deterministic control of individual charge states, including trion formation, opening a path towards coherent inter-dot coupling. Time-resolved measurements reveal tip-induced modification of the electromagnetic vacuum around individual emitters, thus controlling their radiative emission. Our multi-point charge sensing platform with optical readout is particularly well-suited to study fractionalization and anyon dynamics in semiconducting FCIs.

In this study, we explore the ferroelectric domain structure and mechanical properties of PbTiO_3-based membranes, which develops a well-ordered and crystallographic-oriented ripple pattern upon release from their growth substrate. The ferrolectric domain structure of the PbTiO_3 layer was examined at various length scales using optical second harmonic generation, piezoresponse force microscopy, and scanning transmission electron microscopy. These methods reveal the presence of purely in-plane domains organized into superdomains at the crest of the ripples, while an in-plane/out-of-plane domain structure was observed in the flat regions separating the ripples, in agreement with phase-field simulations. The mechanical properties of the membrane were assessed using contact resonance force microscopy, which identified distinct mechanical behaviors at the ripples compared to the flat regions. This study shows that the physical properties of the ferroelectric layer in membranes can be locally controlled within an ordered array of ripples, with well-defined geometric characteristics.

Piezoresponse force microscopy (PFM) has emerged as a tool of choice to probe ferroelectric materials through electrochemomechanical coupling at the nanoscale. However, this technique is not without its challenges, with artefacts related to electrostatic and topographical features presenting a significant obstacle to the accurate interpretation of PFM data. Here, we investigate the bias-dependent off-surface electrostatic response of soda lime glass, a material not traditionally associated with electromechanical activity. Unexpectedly, we observe a distinctive ferroelectric-like hysteresis behavior that is highly dependent on both the tip-sample separation and relative humidity. We also show the dynamic nature of these interactions, through a temporal analysis of the relaxation of this electrochemomechanical response. While the presence of an electrostatic force is expected, we can infer that this hysteretic effect is not inherent to the pure electrostatics of the voltage application and residual surface charges in an air-water capacitor, but is probably due to the incomplete charge and discharge dynamics of the soda lime glass. The choice of tip and the control of environmental conditions are thus essential for the measurement of true electromechanical responses of ferroelectrics.

Nanoscale electrostatic control of oxide interfaces enables physical phenomena and exotic functionalities beyond the realm of the bulk material. In technologically-relevant ferroelectric thin films, the interface-mediated polarization control is usually exerted by engineering the depolarizing field. Here, in contrast, we introduce polarizing surfaces and lattice chemistry engineering as an alternative strategy. Specifically, we engineer the electric-dipole ordering in ferroelectric oxide heterostructures by exploiting the charged sheets of the layered Aurivillius model system. By tracking in-situ the formation of the Aurivillius charged Bi_2O_2 sheets, we reveal their polarizing effect leading to the characteristic Aurivillius out-of-plane antipolar ordering. Next, we use the polarizing Bi_2O_2 stacking as a versatile electrostatic environment to create new electric dipole configurations. We insert multiferroic BiFeO_3 into the Aurivillius framework to stabilize a ferrielectric-like non-collinear electric-dipole order in the final heterostructure while maintaining the antiferromagnetic order of BiFeO_3. We thus demonstrate that engineering the lattice chemistry stabilizes unconventional ferroic orderings at the nanoscale, a strategy that may be expanded beyond the realm of electrically ordered materials.

Switchable 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—down domains have lower friction coefficients and show slower wear rates than up domains and can be used as smart masks. 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 widely applicable across various ferroelectrics with different chemical compositions 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 demonstrate that ferroelectrics are electrically tunable tribological materials at the nanoscale for versatile applications.

Defects have a significant influence on the polarization and electromechanical properties of ferroelectric materials. Statistically, they can be seen as random pinning centers acting on an elastic manifold, slowing domain-wall propagation and raising the energy required to switch polarization. Here we show that the "dressing" of defects can lead to unprecedented control of domain-wall dynamics. We engineer defects of two different dimensionalities in ferroelectric oxide thin films-point defects externally induced via He^{2+} bombardment, and extended quasi-one-dimensional a domains formed in response to internal strains. The a domains act as extended strong pinning sites (as expected) imposing highly localized directional constraints. Surprisingly, the induced point defects in the He^{2+} bombarded samples orient and align to impose further directional pinning, screening the effect of a domains. This defect interplay produces more uniform and predictable domain-wall dynamics. Such engineered interactions between defects are crucial for advancements in ferroelectric devices.

Power-law distributions provide a general description of diverse natural phenomena in which events with a logarithmically increasing size occur with logarithmically decreasing probability. However, experimentally derived correlated two-dimensional information is often difficult to cleanly interpret as discrete events of defined size. Moreover, physical limitation of techniques such as those based on scanning probe microscopy, which can ideally be used to observe power-law behavior, reduce event number and thus render straightforward power-law fits even more challenging. Here we develop and compare different techniques to analyze event distributions from two-dimensional images. We show that tracking interface position allows the associated scaling parameters to be accurately extracted from both experimental and synthetic image-based datasets. We also show how these techniques can differentiate between power-law and non-power-law behavior by comparison of Hill, moments, and kernel estimators of this scaling parameter. We thus present computational tools to analyze power-law fits in two-dimensional datasets and identify the scaling parameters that best describe these distributions.

The recent observation of correlated phases in transition metal dichalcogenide moiré systems at integer and fractional filling promises new insight into metal-insulator transitions and the unusual states of matter that can emerge near such transitions. Here, we combine real- and momentum-space mapping techniques to study moiré superlattice effects in 57.4° twisted WSe_{2} (tWSe_{2}). Our data reveal a split-off flat band that derives from the monolayer Γ states. Using advanced data analysis, we directly quantify the moiré potential from our data. We further demonstrate that the global valence band maximum in tWSe_{2} is close in energy to this flat band but derives from the monolayer K states which show weaker superlattice effects. These results constrain theoretical models and open the perspective that Γ-valley flat bands might be involved in the correlated physics of twisted WSe_{2}.

Second‐harmonic generation (SHG) is a nonlinear optical method allowing the study of the local structure, symmetry, and ferroic order in noncentrosymmetric materials such as ferroelectrics. The combination of SHG microscopy with local polarization analysis is particularly efficient for deriving the local polarization orientation. This, however, entails the use of tedious and time‐consuming modeling methods of nonlinear optical emission. Moreover, extracting the complex domain structures often observed in thin films requires a pixel‐by‐pixel analysis and the fitting of numerous polar plots to ascribe a polarization angle to each pixel. Here, the domain structure of GeTe films is studied using SHG polarimetry assisted by machine learning. The method is applied to two film thicknesses: A thick film containing large domains visible in SHG images, and a thin film in which the domains' size is below the SHG resolution limit. Machine learning‐assisted methods show that both samples exhibit four domain variants of the same type. This result is confirmed in the case of the thick film, both by the manual pixel‐by‐pixel analysis and by using piezoresponse force microscopy. The proposed approach foreshows new prospects for optical studies by enabling enhanced sensitivity and high throughput analysis.

We investigate nanoscale domain engineering via epitaxial coupling in a set of SrRuO_3/PbTiO_3/SrRuO_3 heterostructures epitaxially grown on (110)_o-oriented DyScO_3 substrates. The SrRuO_3 layer thickness is kept at 55 unit cells, whereas the PbTiO_3 layer is grown to thicknesses of 23, 45 and 90 unit cells. Through a combination of atomic force microscopy, x-ray diffraction and high resolution scanning transmission electron microscopy studies, we find that above a certain critical thickness of the ferroelectric layer, the large structural distortions associated with the ferroelastic domains propagate through the top SrRuO_3 layer, locally modifying the orientation of the orthorhombic SrRuO_3 and creating a modulated structure that extends beyond the ferroelectric layer boundaries.

Ferroelectrics, due to their polar nature and reversible switching, can be used to dynamically control surface chemistry for catalysis, chemical switching, and other applications such as water splitting. However, this is a complex phenomenon where ferroelectric domain orientation and switching are intimately linked to surface charges. In this work, the temperature-induced domain behavior of ferroelectric-ferroelastic domains in free-standing BaTiO3 films under different gas environments, including vacuum and oxygen-rich, is studied by in situ scanning transmission electron microscopy (STEM). An automated pathway to statistically disentangle and detect domain structure transformations using deep autoencoders, providing a pathway towards real-time analysis is also established. These results show a clear difference in the temperature at which phase transition occurs and the domain behavior between various environments, with a peculiar domain reconfiguration at low temperatures, from a-c to a-a at ≈60 °C. The vacuum environment exhibits a rich domain structure, while under the oxidizing environment, the domain structure is largely suppressed. The direct visualization provided by in situ gas and heating STEM allows to investigate the influence of external variables such as gas, pressure, and temperature, on oxide surfaces in a dynamic manner, providing invaluable insights into the intricate surface-screening mechanisms in ferroelectrics.

We study the complex ferroelastic/ferroelectric domain structure in the prototypical ferroelectric PbTiO3 epitaxially strained on (110)o-oriented DyScO3 substrates, using a combination of atomic force microscopy, laboratory and synchrotron x-ray diffraction and high resolution scanning transmission electron microscopy. We observe that the anisotropic strain imposed by the orthorhombic substrate creates a large asymmetry in the domain configuration, with domain walls macroscopically aligned along one of the two in-plane directions. We show that the periodicity as a function of film thickness deviates from the Kittel law. As the ferroelectric film thickness increases, we find that the domain configuration evolves from flux-closure to a/c-phase, with a larger scale arrangement of domains into superdomains.

The wealth of properties in functional materials at the nanoscale has attracted tremendous interest over the last decades, spurring the development of ever more precise and ingenious characterization techniques. In ferroelectrics, for instance, scanning probe microscopy based techniques have been used in conjunction with advanced optical methods to probe the structure and properties of nanoscale domain walls, revealing complex behaviours such as chirality, electronic conduction or localised modulation of mechanical response. However, due to the different nature of the characterization methods, only limited and indirect correlation has been achieved between them, even when the same spatial areas were probed. Here, we propose a fast and unbiased analysis method for heterogeneous spatial data sets, enabling quantitative correlative multi-technique studies of functional materials. The method, based on a combination of data stacking, distortion correction, and machine learning, enables a precise mesoscale analysis. When applied to a data set containing scanning probe microscopy piezoresponse and second harmonic generation polarimetry measurements, our workflow reveals behaviours that could not be seen by usual manual analysis, and the origin of which is only explainable by using the quantitative correlation between the two data sets.

Ferroelectrics are technologically important, with wide application in micromechanical systems, nonlinear optics, and information storage. Re-cent discoveries of exotic polarisation textures in these materials, which can strongly influence their properties, have brought to the forefront ques-tions about the nature of their domain walls – long believed to be primarily Ising, with locally null polarisation. Here, combining three complementary techniques – second harmonic generation microscopy, piezoresponse force microscopy, and transmission electron microscopy - to cover all the relevant lengthscales, we reveal the Néel character (non-Ising polarisation oriented perpendicular to the wall) of 180 ° domain walls in c -phase tetragonal ferroelectric lead titanate epitaxial thin films, for both artificial and intrinsic domains at room temperature. Furthermore, we show that variations in the domain density – detected both optically and via local piezoresponse, then quantified by radial autocorrelation analysis – can give us insight into the underlying defect potential present in these materials. TEM Cross-sections for STEM were prepared via FIB milling at accelerat-ing voltages of 30, 16, 8, 5 and 2 kV on an FEI Scios DualBeam instrument. STEM measurements were performed on a probe-corrected FEI Titan Themis operated at 200 kV and with a probe convergence angle of 21.2 mrad. High angle annular dark field (HAADF) imaging was performed with inner/outer collection angles of 56.3 and 200 mrad, respectively. DPC imaging was performed with a 4 segment annular detector with inner/outer collection angles of 13.2 and 73.6 mrad, respectively. The specimen thickness was estimated from the t/λ (thickness/inelastic mean free path) from a zero loss electron energy loss (EEL) spectrum acquired using a Gatan Enfinium spectrometer. Atomic resolution images were acquired as series of 15 frames with pixel dwell time of 100 ns before being summed and corrected for drift in Velox by Thermo Fisher Scientific . Gaussian fitting was performed using Atomap [63] and Matlab.

Describing the spatial velocity of climate change is essential to assessing the challenge of natural and human systems to follow its pace by adapting or migrating sufficiently fast. We propose a fully-determined approach, "MATCH", to calculate a realistic and continuous velocity field of any climate parameter, without the need for ad hoc assumptions. We apply this approach to the displacement of isotherms predicted by global and regional climate models between 1950 and 2100 under the IPCC-AR5 RCP 8.5 emission scenario, and show that it provides detailed velocity patterns especially at the regional scale. This method thus favors comparisons between models as well as the analysis of regional or local features. Furthermore, the trajectories obtained using the MATCH approach are less sensitive to inter-annual fluctuations and therefore allow us to introduce a trajectory regularity index, offering a quantitative perspective on the discussion of climate sinks and sources.

Understanding and controlling the motion, stability, and equilibrium configuration of ferroelectric domain walls is key for their integration into potential nanoelectronics applications, such as ferroelectric racetrack memories. Using piezoresponse force microscopy we analyse the growth and roughness of ferroelectric domains in epitaxial thin film Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$, driven by the electric fields at straight edges of planar electrodes at two different temperatures. This device relevant geometry allows us to confirm that the domain walls are well described as 1-dimensional monoaffine elastic interfaces driven in random-bond disorder. However, we observe a progressive increase of roughness as initially flat domain walls move through the disorder landscape, which could prove a significant limiting factor for racetrack-type memories using ferroelectrics.

Research in materials science increasingly depends on the correlation of information from multiple characterisation techniques, acquired in ever larger datasets. Efficient methods of processing and storing these complex datasets are therefore crucial. Reliably keeping track of data processing is also essential to conform with the goals of open science. Here, we introduce Hystorian, a generic materials science data analysis Python package built at its core to improve the traceability, reproducibility, and archival ability of data processing. Proprietary data formats are converted into open hierarchical data format (HDF5) files, with both datasets and subsequent workflows automatically stored into a single location, thus allowing easy management of multiple data types. At present, Hystorian provides a basic scanning probe microscopy and x-ray diffraction analysis toolkit, and is readily extensible to suit user needs. It is also able to wrap over any existing processing functions, making it easy to append in an extant workflow.