Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform.

Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task. All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.

Ultrafast current imaging by Bayesian inversion.

Spectroscopic measurements of current-voltage curves in scanning probe microscopy is the earliest and one of the most common methods for characterizing local energy-dependent electronic properties, providing insight into superconductive, semiconductor, and memristive behaviors. However, the quasistatic nature of these measurements renders them extremely slow. Here, we demonstrate a fundamentally new approach for dynamic spectroscopic current imaging via full information capture and Bayesian inference. This general-mode I-V method allows three orders of magnitude faster measurement rates than presently possible. The technique is demonstrated by acquiring I-V curves in ferroelectric nanocapacitors, yielding >100,000 I-V curves in <20 min. This allows detection of switching currents in the nanoscale capacitors, as well as determination of the dielectric constant. These experiments show the potential for the use of full information capture and Bayesian inference toward extracting physics from rapid I-V measurements, and can be used for transport measurements in both atomic force and scanning tunneling microscopy.

Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling.

Flexoelectricity refers to electric polarization generated by heterogeneous mechanical strains, namely strain gradients, in materials of arbitrary crystal symmetries. Despite more than 50 years of work on this effect, an accurate identification of its coupling strength remains an experimental challenge for most materials, which impedes its wide recognition. Here, we show the presence of flexoelectricity in the recently discovered polar vortices in PbTiO3/SrTiO3 superlattices based on a combination of machine-learning analysis of the atomic-scale electron microscopy imaging data and phenomenological phase-field modeling. By scrutinizing the influence of flexocoupling on the global vortex structure, we match theory and experiment using computer vision methodologies to determine the flexoelectric coefficients for PbTiO3 and SrTiO3. Our findings highlight the inherent, nontrivial role of flexoelectricity in the generation of emergent complex polarization morphologies and demonstrate a viable approach to delineating this effect, conducive to the deeper exploration of both topics.

Atomic-scale observation of structural and electronic orders in the layered compound α-RuCl3.

A pseudospin-1/2 Mott phase on a honeycomb lattice is proposed to host the celebrated two-dimensional Kitaev model which has an elusive quantum spin liquid ground state, and fascinating physics relevant to the development of future templates towards topological quantum bits. Here we report a comprehensive, atomically resolved real-space study by scanning transmission electron and scanning tunnelling microscopies on a novel layered material displaying Kitaev physics, α-RuCl3. Our local crystallography analysis reveals considerable variations in the geometry of the ligand sublattice in thin films of α-RuCl3 that opens a way to realization of a spatially inhomogeneous magnetic ground state at the nanometre length scale. Using scanning tunnelling techniques, we observe the electronic energy gap of ≈0.25 eV and intra-unit cell symmetry breaking of charge distribution in individual α-RuCl3 surface layer. The corresponding charge-ordered pattern has a fine structure associated with two different types of charge disproportionation at Cl-terminated surface.

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.

Electrochemical reactivity and proton transport mechanisms in nanostructured ceria.

Electrochemical reactivity and ionic transport at the nanoscale are essential in many energy applications. In this study, time-resolved Kelvin probe force microscopy (tr-KPFM) is utilized for surface potential mapping of nanostructured ceria, in both space and time domains. The fundamental mechanisms of proton injection and transport are studied as a function of environmental conditions and the presence or absence of triple phase boundaries. Finite element modeling is used to extract physical parameters from the experimental data, allowing not only quantification of the observed processes, but also decoupling of their contributions to the measured signal. The constructed phase diagrams of the parameters demonstrate a thermally activated proton injection reaction at the triple phase boundary, and two transport processes that are responsible for the low-temperature proton conductivity of nanostructured ceria.

Big Data Analytics for Scanning Transmission Electron Microscopy Ptychography.

Electron microscopy is undergoing a transition; from the model of producing only a few micrographs, through the current state where many images and spectra can be digitally recorded, to a new mode where very large volumes of data (movies, ptychographic and multi-dimensional series) can be rapidly obtained. Here, we discuss the application of so-called "big-data" methods to high dimensional microscopy data, using unsupervised multivariate statistical techniques, in order to explore salient image features in a specific example of BiFeO3 domains. Remarkably, k-means clustering reveals domain differentiation despite the fact that the algorithm is purely statistical in nature and does not require any prior information regarding the material, any coexisting phases, or any differentiating structures. While this is a somewhat trivial case, this example signifies the extraction of useful physical and structural information without any prior bias regarding the sample or the instrumental modality. Further interpretation of these types of results may still require human intervention. However, the open nature of this algorithm and its wide availability, enable broad collaborations and exploratory work necessary to enable efficient data analysis in electron microscopy.

Highly mobile ferroelastic domain walls in compositionally graded ferroelectric thin films.

Domains and domain walls are critical in determining the response of ferroelectrics, and the ability to controllably create, annihilate, or move domains is essential to enable a range of next-generation devices. Whereas electric-field control has been demonstrated for ferroelectric 180° domain walls, similar control of ferroelastic domains has not been achieved. Here, using controlled composition and strain gradients, we demonstrate deterministic control of ferroelastic domains that are rendered highly mobile in a controlled and reversible manner. Through a combination of thin-film growth, transmission-electron-microscopy-based nanobeam diffraction and nanoscale band-excitation switching spectroscopy, we show that strain gradients in compositionally graded PbZr1-xTixO3 heterostructures stabilize needle-like ferroelastic domains that terminate inside the film. These needle-like domains are highly labile in the out-of-plane direction under applied electric fields, producing a locally enhanced piezoresponse. This work demonstrates the efficacy of novel modes of epitaxy in providing new modalities of domain engineering and potential for as-yet-unrealized nanoscale functional devices.

Nanoscale mapping of heterogeneity of the polarization reversal in lead-free relaxor-ferroelectric ceramic composites.

Relaxor/ferroelectric ceramic/ceramic composites have shown to be promising in generating large electromechanical strain at moderate electric fields. Nonetheless, the mechanisms of polarization and strain coupling between grains of different nature in the composites remain unclear. To rationalize the coupling mechanisms we performed advanced piezoresponse force microscopy (PFM) studies of 0.92BNT-0.06BT-0.02KNN/0.93BNT-0.07BT (ergodic/non-ergodic relaxor) composites. PFM is able to distinguish grains of different phases by characteristic domain patterns. Polarization switching has been probed locally, on a sub-grain scale. k-Means clustering analysis applied to arrays of local hysteresis loops reveals variations of polarization switching characteristics between the ergodic and non-ergodic relaxor grains. We report a different set of switching parameters for grains in the composites as opposed to the pure phase samples. Our results confirm ceramic/ceramic composites to be a viable approach to tailor the piezoelectric properties and optimize the macroscopic electromechanical characteristics.

Electrocatalysis-induced elasticity modulation in a superionic proton conductor probed by band-excitation atomic force microscopy.

Variable temperature band-excitation atomic force microscopy in conjunction with I-V spectroscopy was used to investigate the crystalline superionic proton conductor CsHSO4 during proton exchange induced by a Pt-coated conductive scanning probe. At a sample temperature of 150 °C and under an applied bias <1 V, reduction currents of up to 1 nA were observed. Simultaneously, we show that the electrochemical reactions are accompanied by a reversible decrease in the elastic modulus of CsHSO4, as seen by a contact resonance shift, and find evidence for superplasticity during scanning. These effects were not observed in the room-temperature phase of CsHSO4 or in the case of catalytically inactive conductive probes, proving the utility of this technique for monitoring electrochemical processes on the nanoscale, as well as the use of local contact stiffness as a sensitive indicator of electrochemical reactions.

Giant elastic tunability in strained BiFeO3 near an electrically induced phase transition.

Elastic anomalies are signatures of phase transitions in condensed matters and have traditionally been studied using various techniques spanning from neutron scattering to static mechanical testing. Here, using band-excitation elastic/piezoresponse spectroscopy, we probed sub-MHz elastic dynamics of a tip bias-induced rhombohedral-tetragonal phase transition of strained (001)-BiFeO3 (rhombohedral) ferroelectric thin films from ∼10(3) nm(3) sample volumes. Near this transition, we observed that the Young's modulus intrinsically softens by over 30% coinciding with two- to three-fold enhancement of local piezoresponse. Coupled with phase-field modelling, we also addressed the influence of polarization switching and mesoscopic structural heterogeneities (for example, domain walls) on the kinetics of this phase transition, thereby providing fresh insights into the morphotropic phase boundary in ferroelectrics. Furthermore, the giant electrically tunable elastic stiffness and corresponding electromechanical properties observed here suggest potential applications of BiFeO3 in next-generation frequency-agile electroacoustic devices, based on the utilization of the soft modes underlying successive ferroelectric phase transitions.

CuInP2S6 Room Temperature Layered Ferroelectric.

We explore ferroelectric properties of cleaved 2-D flakes of copper indium thiophosphate, CuInP2S6 (CITP), and probe size effects along with limits of ferroelectric phase stability, by ambient and ultra high vacuum scanning probe microscopy. CITP belongs to the only material family known to display ferroelectric polarization in a van der Waals, layered crystal at room temperature and above. Our measurements directly reveal stable, ferroelectric polarization as evidenced by domain structures, switchable polarization, and hysteresis loops. We found that at room temperature the domain structure of flakes thicker than 100 nm is similar to the cleaved bulk surfaces, whereas below 50 nm polarization disappears. We ascribe this behavior to a well-known instability of polarization due to depolarization field. Furthermore, polarization switching at high bias is also associated with ionic mobility, as evidenced both by macroscopic measurements and by formation of surface damage under the tip at a bias of 4 V-likely due to copper reduction. Mobile Cu ions may therefore also contribute to internal screening mechanisms. The existence of stable polarization in a van-der-Waals crystal naturally points toward new strategies for ultimate scaling of polar materials, quasi-2D, and single-layer materials with advanced and nonlinear dielectric properties that are presently not found in any members of the growing "graphene family".

Quantitative 3D-KPFM imaging with simultaneous electrostatic force and force gradient detection.

Kelvin probe force microscopy (KPFM) is a powerful characterization technique for imaging local electrochemical and electrostatic potential distributions and has been applied across a broad range of materials and devices. Proper interpretation of the local KPFM data can be complicated, however, by convolution of the true surface potential under the tip with additional contributions due to long range capacitive coupling between the probe (e.g. cantilever, cone, tip apex) and the sample under test. In this work, band excitation (BE)-KPFM is used to negate such effects. In contrast to traditional single frequency KPFM, multifrequency BE-KPFM is shown to afford dual sensitivity to both the electrostatic force and the force gradient detection, analogous to simultaneous amplitude modulated and frequency modulated KPFM imaging. BE-KPFM is demonstrated on a Pt/Au/SiO(x) test structure and electrostatic force gradient detection is found to lead to an improved lateral resolution compared to electrostatic force detection. Finally, a 3D-KPFM imaging technique is developed. Force volume (FV) BE-KPFM allows the tip-sample distance dependence of the electrostatic interactions (force and force gradient) to be recorded at each point across the sample surface. As such, FVBE-KPFM provides a much needed pathway towards complete tip-sample capacitive de-convolution in KPFM measurements and will enable quantitative surface potential measurements with nanoscale resolution.

Breaking the limits of structural and mechanical imaging of the heterogeneous structure of coal macerals.

The correlation between local mechanical (elasto-plastic) and structural (composition) properties of coal presents significant fundamental and practical interest for coal processing and for the development of rheological models of coal to coke transformations. Here, we explore the relationship between the local structural, chemical composition, and mechanical properties of coal using a combination of confocal micro-Raman imaging and band excitation atomic force acoustic microscopy for a bituminous coal. This allows high resolution imaging (10s of nm) of mechanical properties of the heterogeneous (banded) architecture of coal and correlating them to the optical gap, average crystallite size, the bond-bending disorder of sp(2) aromatic double bonds, and the defect density. This methodology allows the structural and mechanical properties of coal components (lithotypes, microlithotypes, and macerals) to be understood, and related to local chemical structure, potentially allowing for knowledge-based modeling and optimization of coal utilization processes.

Deterministic arbitrary switching of polarization in a ferroelectric thin film.

Ferroelectrics have been used as memory storage devices, with an upper bound on the total possible memory levels generally dictated by the number of degenerate states allowed by the symmetry of the ferroelectric phase. Here, we introduce a new concept for storage wherein the polarization can be rotated arbitrarily, effectively decoupling it from the crystallographic symmetry of the ferroelectric phase on the mesoscale. By using a Bi5Ti3FeO15-CoFe2O4 film and via Band-Excitation Piezoresponse Force Microscopy, we show the ability to arbitrarily rotate polarization, create a spectrum of switched states, and suggest the reason for polarization rotation is an abundance of sub-50 nm nanodomains. Transmission electron microscopy-based strain mapping confirms significant local strain undulations imparted on the matrix by the CoFe2O4 inclusions, which causes significant local disorder. These experiments point to controlled tuning of polarization rotation in a standard ferroelectric, and hence the potential to greatly extend the attainable densities for ferroelectric memories.

Band excitation in scanning probe microscopy: recognition and functional imaging.

Field confinement at the junction between a biased scanning probe microscope's tip and solid surface enables local probing of various bias-induced transformations, such as polarization switching, ionic motion, and electrochemical reactions. The nanoscale size of the biased region, smaller or comparable to that of features such as grain boundaries and dislocations, potentially allows for the study of kinetics and thermodynamics at the level of a single defect. In contrast to classical statistically averaged approaches, this approach allows one to link structure to functionality and deterministically decipher associated mesoscopic and atomistic mechanisms. Furthermore, responses measured as a function of frequency and bias can serve as a fingerprint of local material functionality, allowing for local recognition imaging of inorganic and biological systems. This article reviews current progress in multidimensional scanning probe microscopy techniques based on band excitation time and voltage spectroscopies, including discussions on data acquisition, dimensionality reduction, and visualization, along with future challenges and opportunities for the field.

Open loop Kelvin probe force microscopy with single and multi-frequency excitation.

Conventional Kelvin probe force microscopy (KPFM) relies on closed loop (CL) bias feedback for the determination of surface potential (SP). However, SP measured by CL-KPFM has been shown to be strongly influenced by the choice of measurement parameters due to non-electrostatic contributions to the input signal of the bias feedback loop. This often leads to systematic errors of several hundred mV and can also result in topographical crosstalk. Here, open loop (OL)-KPFM modes are investigated as a means of obtaining a quantitative, crosstalk free measurement of the SP of graphene grown on Cu foil, and are directly contrasted with CL-KPFM. OL-KPFM operation is demonstrated in both single and multi-frequency excitation regimes, yielding quantitative SP measurements. The SP difference between single and multilayer graphene structures using OL-KPFM was found to be 63 ± 11 mV, consistent with values previously reported by CL-KPFM. Furthermore, the same relative potential difference between Al2O3-coated graphene and Al2O3-coated Cu was observed using both CL and OL techniques. We observed an offset of 55 mV between absolute SP values obtained by OL and CL techniques, which is attributed to the influence of non-electrostatic contributions to the input of the bias feedback used in CL-KPFM.

Higher order harmonic detection for exploring nonlinear interactions with nanoscale resolution.

Nonlinear dynamics underpin a vast array of physical phenomena ranging from interfacial motion to jamming transitions. In many cases, insight into the nonlinear behavior can be gleaned through exploration of higher order harmonics. Here, a method using band excitation scanning probe microscopy (SPM) to investigate higher order harmonics of the electromechanical response, with nanometer scale spatial resolution is presented. The technique is demonstrated by probing the first three harmonics of strain for a Pb(Zr(1-x)Ti(x))O3 (PZT) ferroelectric capacitor. It is shown that the second order harmonic response is correlated with the first harmonic response, whereas the third harmonic is not. Additionally, measurements of the second harmonic reveal significant deviations from Rayleigh-type models in the form of a much more complicated field dependence than is observed in the spatially averaged data. These results illustrate the versatility of n(th) order harmonic SPM detection methods in exploring nonlinear phenomena in nanoscale materials.

Exploring mesoscopic physics of vacancy-ordered systems through atomic scale observations of topological defects.

Vacancy-ordered transition metal oxides have multiple similarities to classical ferroic systems including ferroelectrics and ferroelastics. The expansion coefficients for corresponding Ginzburg-Landau-type free energies are readily accessible from bulk phase diagrams. Here, we demonstrate that the gradient and interfacial terms can quantitatively be determined from the atomically resolved scanning transmission electron microscopy data of the topological defects and interfaces in model lanthanum-strontium cobaltite. With this knowledge, the interplay between ordering, chemical composition, and mechanical effects at domain walls, interfaces and structural defects can be analyzed.

Domain wall geometry controls conduction in ferroelectrics.

A new paradigm of domain wall nanoelectronics has emerged recently, in which the domain wall in a ferroic is itself an active device element. The ability to spatially modulate the ferroic order parameter within a single domain wall allows the physical properties to be tailored at will and hence opens vastly unexplored device possibilities. Here, we demonstrate via ambient and ultrahigh-vacuum (UHV) scanning probe microscopy (SPM) measurements in bismuth ferrite that the conductivity of the domain walls can be modulated by up to 500% in the spatial dimension as a function of domain wall curvature. Landau-Ginzburg-Devonshire calculations reveal the conduction is a result of carriers or vacancies migrating to neutralize the charge at the formed interface. Phase-field modeling indicates that anisotropic potential distributions can occur even for initially uncharged walls, from polarization dynamics mediated by elastic effects. These results are the first proof of concept for modulation of charge as a function of domain wall geometry by a proximal probe, thereby expanding potential applications for oxide ferroics in future nanoscale electronics.