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For over three decades, scanning probe microscopy (SPM) has been a key method for exploring material structures and functionalities at nanometer and often atomic scales in ambient, liquid, and vacuum environments. Historically, SPM applications have predominantly been downstream, with images and spectra serving as a qualitative source of data on the microstructure and properties of materials, and in rare cases of fundamental physical knowledge. However, the fast growing developments in accelerated material synthesis via self-driving labs and established applications such as combinatorial spread libraries are poised to change this paradigm. Rapid synthesis demands matching capabilities to probe structure and functionalities of materials on small scales and with high throughput, which are characteristically inherent to SPM. Here, we overview SPM methods applicable to these emerging applications and emphasize their quantitativeness, focusing on piezoresponse force microscopy, electrochemical strain microscopy, conductive, and surface photovoltage measurements. We discuss the challenges and opportunities ahead, asserting that SPM will play a crucial role in closing the loop from material prediction and synthesis to characterization., Comment: 64 pages, 15 figures

Combinatorial libraries are a powerful approach for exploring the evolution of physical properties across binary and ternary cross-sections in multicomponent phase diagrams. Although the synthesis of these libraries has been developed since the 1960s and expedited with advanced laboratory automation, the broader application of combinatorial libraries relies on fast, reliable measurements of concentration-dependent structures and functionalities. Scanning Probe Microscopies (SPM), including piezoresponse force microscopy (PFM), offer significant potential for quantitative, functionally relevant combi-library readouts. Here we demonstrate the implementation of fully automated SPM to explore the evolution of ferroelectric properties in combinatorial libraries, focusing on Sm-doped BiFeO3 and ZnxMg1-xO systems. We also present and compare Gaussian Process-based Bayesian Optimization models for fully automated exploration, emphasizing local reproducibility (effective noise) as an essential factor in optimal experiment workflows. Automated SPM, when coupled with upstream synthesis controls, plays a pivotal role in bridging materials synthesis and characterization., Comment: 19 pages, 8 figures

Rapid progress in aberration corrected electron microscopy necessitates development of robust methods for the identification of phases, ferroic variants, and other pertinent aspects of materials structure from imaging data. While unsupervised methods for clustering and classification are widely used for these tasks, their performance can be sensitive to hyperparameter selection in the analysis workflow. In this study, we explore the effects of descriptors and hyperparameters on the capability of unsupervised ML methods to distill local structural information, exemplified by discovery of polarization and lattice distortion in Sm doped BiFeO3 (BFO) thin films. We demonstrate that a reward-driven approach can be used to optimize these key hyperparameters across the full workflow, where rewards were designed to reflect domain wall continuity and straightness, ensuring that the analysis aligns with the material's physical behavior. This approach allows us to discover local descriptors that are best aligned with the specific physical behavior, providing insight into the fundamental physics of materials. We further extend the reward driven workflows to disentangle structural factors of variation via optimized variational autoencoder (VAE). Finally, the importance of well-defined rewards was explored as a quantifiable measure of success of the workflow., Comment: 19 pages, 6 figures

Dynamic spectroscopies in Scanning Probe Microscopy (SPM) are critical for probing material properties, such as force interactions, mechanical properties, polarization switching, and electrochemical reactions and ionic dynamics. However, the practical implementation of these measurements is constrained by the need to balance imaging time and data quality. Signal to noise requirements favor long acquisition times and high frequencies to improve signal fidelity. However, these are limited on the low end by contact resonant frequency and photodiode sensitivity, and on the high end by the time needed to acquire high-resolution spectra, or the propensity for samples degradation under high field excitation over long times. The interdependence of key parameters such as instrument settings, acquisition times, and sampling rates makes manual tuning labor-intensive and highly dependent on user expertise, often yielding operator-dependent results. These limitations are prominent in techniques like Dual Amplitude Resonance Tracking (DART) in Piezoresponse Force Microscopy (PFM) that utilize multiple concurrent feedback loops for topography and resonance frequency tracking. Here, a reward-driven workflow is proposed that automates the tuning process, adapting experimental conditions in real time to optimize data quality. This approach significantly reduces the complexity and time required for manual adjustments and can be extended to other SPM spectroscopic methods, enhancing overall efficiency and reproducibility., Comment: 15 pages, 5 figures

Lithium-ion batteries are a key energy storage technology driving revolutions in mobile electronics, electric vehicles and renewable energy storage. Capacity retention is a vital performance measure that is frequently utilized to assess whether these batteries have approached their end-of-life. Machine learning (ML) offers a powerful tool for predicting capacity degradation based on past data, and, potentially, prior physical knowledge, but the degree to which an ML prediction can be trusted is of significant practical importance in situations where consequential decisions must be made based on battery state of health. This study explores the efficacy of fully Bayesian machine learning in forecasting battery health with the quantification of uncertainty in its predictions. Specifically, we implemented three probabilistic ML approaches and evaluated the accuracy of their predictions and uncertainty estimates: a standard Gaussian process (GP), a structured Gaussian process (sGP), and a fully Bayesian neural network (BNN). In typical applications of GP and sGP, their hyperparameters are learned from a single sample while, in contrast, BNNs are typically pre-trained on an existing dataset to learn the weight distributions before being used for inference. This difference in methodology gives the BNN an advantage in learning global trends in a dataset and makes BNNs a good choice when training data is available. However, we show that pre-training can also be leveraged for GP and sGP approaches to learn the prior distributions of the hyperparameters and that in the case of the pre-trained sGP, similar accuracy and improved uncertainty estimation compared to the BNN can be achieved. This approach offers a framework for a broad range of probabilistic machine learning scenarios where past data is available and can be used to learn priors for (hyper)parameters of probabilistic ML models.

Unique polar properties of nanoscale hafnia-zirconia oxides (Hf$_x$Zr$_{1-x}$O$_2$) are of great interest for condensed matter physics, nanophysics and advanced applications. These properties are connected (at least partially) to the ionic-electronic and electrochemical phenomena at the hafnia surface, interfaces and/or internal grain boundaries. Here we calculated the phase diagrams, dielectric permittivity, spontaneous polar and antipolar ordering, and domain structure morphology in Hf$_x$Zr$_{1-x}$O$_2$ nanoparticles covered by ionic-electronic charge, originated from the surface electrochemical adsorption. We revealed that the ferro-ionic coupling supports the polar long-range order in the nanoscale Hf$_x$Zr$_{1-x}$O$_2$, induces and/or enlarges the stability region of the labyrinthine domains towards smaller sizes and smaller environmental dielectric constant at low concentrations of the surface ions, and causes the transition to the single-domain ferro-ionic state at high concentrations of the surface ions. We predict that the labyrinthine domain states, being multiple-degenerated, may significantly affect the emergence of the negative differential capacitance state in the nanograined/nanocrystalline Hf$_x$Zr$_{1-x}$O$_2$ films., Comment: 28 pages, 7 figures and Appendixes, Invited by the Journal of Applied Physics to the "Special Topic on Ferroic Materials, Domains, and Domain Walls: Bridging Fundamentals with Next-Generation Technology"

Exploration of complex high-dimensional spaces presents significant challenges in fields such as molecular discovery, process optimization, and supply chain management. Genetic Algorithms (GAs), while offering significant power for creating new candidate spaces, often entail high computational demands due to the need for evaluation of each new proposed solution. On the other hand, Deep Kernel Learning (DKL) efficiently navigates the spaces of preselected candidate structures but lacks generative capabilities. This study introduces an approach that amalgamates the generative power of GAs to create new candidates with the efficiency of DKL-based surrogate models to rapidly ascertain the behavior of new candidate spaces. This DKL-GA framework can be further used to build Bayesian Optimization (BO) workflows. We demonstrate the effectiveness of this approach through the optimization of the FerroSIM model, showcasing its broad applicability to diverse challenges, including molecular discovery and battery charging optimization., Comment: 17 pages, 5 figures

We have developed a Bayesian optimization (BO) workflow that integrates intra-step noise optimization into automated experimental cycles. Traditional BO approaches in automated experiments focus on optimizing experimental trajectories but often overlook the impact of measurement noise on data quality and cost. Our proposed framework simultaneously optimizes both the target property and the associated measurement noise by introducing time as an additional input parameter, thereby balancing the signal-to-noise ratio and experimental duration. Two approaches are explored: a reward-driven noise optimization and a double-optimization acquisition function, both enhancing the efficiency of automated workflows by considering noise and cost within the optimization process. We validate our method through simulations and real-world experiments using Piezoresponse Force Microscopy (PFM), demonstrating the successful optimization of measurement duration and property exploration. Our approach offers a scalable solution for optimizing multiple variables in automated experimental workflows, improving data quality, and reducing resource expenditure in materials science and beyond., Comment: 22 pages, 9 figures

Automated experiments in scanning transmission electron microscopy (STEM) require rapid image segmentation to optimize data representation for human interpretation, decision-making, site-selective spectroscopies, and atomic manipulation. Currently, segmentation tasks are typically performed using supervised machine learning methods, which require human-labeled data and are sensitive to out-of-distribution drift effects caused by changes in resolution, sampling, or beam shape. Here, we operationalize and benchmark a recently proposed reward-driven optimization workflow for on-the fly image analysis in STEM. This unsupervised approach is much more robust, as it does not rely on human labels and is fully explainable. The explanatory feedback can help the human to verify the decision making and potentially tune the model by selecting the position along the Pareto frontier of reward functions. We establish the timing and effectiveness of this method, demonstrating its capability for real-time performance in high-throughput and dynamic automated STEM experiments. The reward driven approach allows to construct explainable robust analysis workflows and can be generalized to a broad range of image analysis tasks in electron and scanning probe microscopy and chemical imaging., Comment: 17 pages, 6 images

The fundamental aspect of physics of ferroelectric materials is the screening of uncompensated bound charges by the dissociative adsorption of ionic charges from the environment. The adsorption of ions can be especially strong when the ferroelectric undergoes the temperature-induced transition from the paraelectric phase to the ferroelectric state. Here we demonstrate that the adsorption of ions and free radicals by the polar surface of ferroelectric nanoparticles can be very efficient in aqueous solutions due to the strong ferro-ionic coupling in the nanoparticles. Obtained results can be useful for the elaboration of alternative methods and tools for adsorption of the cations (Li+, K+, Na+, etc.), anions (Cl-, Br-, J-), and/or free radicals (CO-, NH4+, etc.) from aqueous solutions by the lead-free uniaxial ferroelectric nanoparticles. The results may become an alternative way for the environment-friendly laboratory-scale purification of different aqueous solutions from ionic contamination using controllable cyclic temperature variations., Comment: Accepted to Physical Review Applied, 23 pages, including 4 figures and Supplement

Using the model of four sublattices, the Landau-Ginzburg-Devonshire-Kittel phenomenological approach and the Stephenson-Highland ionic adsorption model for the description of coupled polar and antipolar long-range orders in ferroics, we calculated analytically the phase diagrams and polar properties of Bi$_{1-x}$Sm$_x$FeO$_3$ nanoparticles covered by surface ions in dependence on their size, surface ions density, samarium content "x" and temperature. The size effects and ferro-ionic coupling govern the appearance and stability conditions of the long-range ordered ferroelectric, reentrant ferrielectric and antiferroelectric phases in the Bi1-xSmxFeO3 nanoparticles. Calculated phase diagrams are in a qualitative agreement with the X-ray diffraction phase analysis, electron paramagnetic resonance, infra-red spectroscopy and electrophysical measurements of the Bi$_{1-x}$Sm$_x$FeO$_3$ nanopowders sintered by the solution combustion method. The combined theoretical-experimental approach allows to establish the influence of the ferro-ionic coupling and size effects in Bi$_{1-x}$Sm$_x$FeO$_3$ nanoparticles on their polar properties., Comment: 53 pages, including 13 figures and 2 Appendixes, Revised version, Resubmitted to Physical Review B

Since the dawn of scanning probe microscopy (SPM), tapping or intermittent contact mode has been one of the most widely used imaging modes. Manual optimization of tapping mode not only takes a lot of instrument and operator time, but also often leads to frequent probe and sample damage, poor image quality and reproducibility issues for new types of samples or inexperienced users. Despite wide use, optimization of tapping mode imaging is an extremely hard problem, ill-suited to either classical control methods or machine learning. Here we introduce a reward-driven workflow to automate the optimization of SPM in the tapping mode. The reward function is defined based on multiple channels with physical and empirical knowledge of good scans encoded, representing a sample-agnostic measure of image quality and imitating the decision-making logic employed by human operators. This automated workflow gives optimal scanning parameters for different probes and samples and gives high-quality SPM images consistently in the attractive mode. This study broadens the application and accessibility of SPM and opens the door for fully automated SPM., Comment: 20 pages, 6 figures

Microscopy techniques have played vital roles in materials science, biology, and nanotechnology, offering high-resolution imaging and detailed insights into properties at nanoscale and atomic level. The automation of microscopy experiments, in combination with machine learning approaches, is a transformative advancement, offering increased efficiency, reproducibility, and the capability to perform complex experiments. Our previous work on autonomous experimentation with scanning probe microscopy (SPM) demonstrated an active learning framework using deep kernel learning (DKL) for structure-property relationship discovery. This approach has demonstrated broad applications in various microscopy techniques. Here, to address limitations of workflows based on DKL, we developed methods to incorporate prior knowledge and human interest into DKL-based workflows and implemented these workflows in SPM. By integrating expected rewards from structure libraries or spectroscopic features, we enhanced the exploration efficiency of autonomous microscopy, demonstrating more efficient and targeted exploration in autonomous microscopy. We demonstrated the application of these methods in SPM, but we suggest that these methods can be seamlessly applied to other microscopy and imaging techniques. Furthermore, the concept can be adapted for general Bayesian optimization in material discovery across a broad range of autonomous experimental fields.

Analytical calculations corroborated by the finite element modelling show that thin films of Van der Waals ferrielectrics covered by a 2D-semiconductor are promising candidates for the controllable reduction of the dielectric layer capacitance due to the negative capacitance (NC) effect emerging in the ferrielectric film. The NC state is conditioned by energy-degenerated poly-domain states of the ferrielectric polarization induced in the films under incomplete screening conditions in the presence of a dielectric layer. Calculations performed for the FET-type heterostructure "ferrielectric CuInP2S6 film - 2D-MoS2 single-layer - SiO2 dielectric layer" reveal the pronounced size effect of the multilayer capacitance. Derived analytical expressions for the electric polarization and multilayer capacitance allow to predict the thickness range of the dielectric layer and ferrielectric film for which the NC effect is the most pronounced in various Van der Waals ferrielectrics, and the corresponding subthreshold swing becomes much less than the Boltzmann's limit. Obtained results can be useful for the size and temperature control of the NC effect in the steep-slope ferrielectric FETs., Comment: 40 pages, 6 figures, 4 Appendices

Scanning Transmission Electron Microscopy (STEM) coupled with Electron Energy Loss Spectroscopy (EELS) presents a powerful platform for detailed material characterization via rich imaging and spectroscopic data. Modern electron microscopes can access multiple length scales and sampling rates far beyond human perception and reaction time. Recent advancements in machine learning (ML) offer a promising avenue to enhance these capabilities by integrating ML algorithms into the STEM-EELS framework, fostering an environment of active learning. This work enables the seamless integration of STEM with High-Performance Computing (HPC) systems. We present several implemented workflows that exemplify this integration. These workflows include sophisticated techniques such as object finding and Deep Kernel Learning (DKL). Through these developments, we demonstrate how the fusion of STEM-EELS with ML and HPC enhances the efficiency and scope of material characterization for 70% STEM available globally. The codes are available at GitHub link.

We consider nanoflakes of van der Waals ferrielectric CuInP$_2$S$_6$ covered by an ionic surface charge and reveal the appearance of polar states with relatively high polarization ~5 microC/cm$^2$ and stored free charge ~10 microC/cm$%2$, which can mimic "mid-gap" states associated with a surface field-induced transfer of Cu and/or In ions in the van der Waals gap. The change in the ionic screening degree and mismatch strains induce a broad range of the transitions between paraelectric phase, antiferroelectric, ferrielectric, and ferri-ionic states in CuInP$_2$S$_6$ nanoflakes. The states' stability and/or metastability is determined by the minimum of the system free energy consisting of electrostatic energy, elastic energy, and a Landau-type four-well potential of the ferrielectric dipole polarization. The possibility to govern the transitions by strain and ionic screening can be useful for controlling the tunneling barrier in thin film devices based on CuInP$_2$S$_6$ nanoflakes. Also, we predict that the CuInP$_2$S$_6$ nanoflakes reveal features of the controllable negative capacitance effect, which make them attractive for advanced electronic devices, such as nano-capacitors and gate oxide nanomaterials with reduced heat dissipation., Comment: 46 pages, including 5 figures and Appendix with 6 figures. Revised version

The rapid development of computation power and machine learning algorithms has paved the way for automating scientific discovery with a scanning probe microscope (SPM). The key elements towards operationalization of automated SPM are the interface to enable SPM control from Python codes, availability of high computing power, and development of workflows for scientific discovery. Here we build a Python interface library that enables controlling an SPM from either a local computer or a remote high-performance computer (HPC), which satisfies the high computation power need of machine learning algorithms in autonomous workflows. We further introduce a general platform to abstract the operations of SPM in scientific discovery into fixed-policy or reward-driven workflows. Our work provides a full infrastructure to build automated SPM workflows for both routine operations and autonomous scientific discovery with machine learning., Comment: 16 pages, 7 figures

Combinatorial spread libraries offer a unique approach to explore evolution of materials properties over the broad concentration, temperature, and growth parameter spaces. However, the traditional limitation of this approach is the requirement for the read-out of functional properties across the library. Here we demonstrate the application of automated Piezoresponse Force Microscopy (PFM) for the exploration of the physics in the SmxBi1-xFeO3 system with the ferroelectric-antiferroelectric morphotropic phase boundary. This approach relies on the synergy of the quantitative nature of PFM and the implementation of automated experiments that allows PFM-based gird sampling over macroscopic samples. The concentration dependence of pertinent ferroelectric parameters has been determined and used to develop the mathematical framework based on Ginzburg-Landau theory describing the evolution of these properties across the concentration space. We pose that combination of automated scanning probe microscope and combinatorial spread library approach will emerge as an efficient research paradigm to close the characterization gap in the high-throughput materials discovery. We make the data sets open to the community and hope that will stimulate other efforts to interpret and understand the physics of these systems., Comment: 19 pages; 5 figures

The rise of electron microscopy has expanded our ability to acquire nanometer and atomically resolved images of complex materials. The resulting vast datasets are typically analyzed by human operators, an intrinsically challenging process due to the multiple possible analysis steps and the corresponding need to build and optimize complex analysis workflows. We present a methodology based on the concept of a Reward Function coupled with Bayesian Optimization, to optimize image analysis workflows dynamically. The Reward Function is engineered to closely align with the experimental objectives and broader context and is quantifiable upon completion of the analysis. Here, cross-section, high-angle annular dark field (HAADF) images of ion-irradiated $(Y, Dy)Ba_2Cu_3O_{7-\delta}$ thin-films were used as a model system. The reward functions were formed based on the expected materials density and atomic spacings and used to drive multi-objective optimization of the classical Laplacian-of-Gaussian (LoG) method. These results can be benchmarked against the DCNN segmentation. This optimized LoG* compares favorably against DCNN in the presence of the additional noise. We further extend the reward function approach towards the identification of partially-disordered regions, creating a physics-driven reward function and action space of high-dimensional clustering. We pose that with correct definition, the reward function approach allows real-time optimization of complex analysis workflows at much higher speeds and lower computational costs than classical DCNN-based inference, ensuring the attainment of results that are both precise and aligned with the human-defined objectives., Comment: 12 pages, 4 figures

Scientific advancement is universally based on the dynamic interplay between theoretical insights, modelling, and experimental discoveries. However, this feedback loop is often slow, including delayed community interactions and the gradual integration of experimental data into theoretical frameworks. This challenge is particularly exacerbated in domains dealing with high-dimensional object spaces, such as molecules and complex microstructures. Hence, the integration of theory within automated and autonomous experimental setups, or theory in the loop automated experiment, is emerging as a crucial objective for accelerating scientific research. The critical aspect is not only to use theory but also on-the-fly theory updates during the experiment. Here, we introduce a method for integrating theory into the loop through Bayesian co-navigation of theoretical model space and experimentation. Our approach leverages the concurrent development of surrogate models for both simulation and experimental domains at the rates determined by latencies and costs of experiments and computation, alongside the adjustment of control parameters within theoretical models to minimize epistemic uncertainty over the experimental object spaces. This methodology facilitates the creation of digital twins of material structures, encompassing both the surrogate model of behavior that includes the correlative part and the theoretical model itself. While demonstrated here within the context of functional responses in ferroelectric materials, our approach holds promise for broader applications, the exploration of optical properties in nanoclusters, microstructure-dependent properties in complex materials, and properties of molecular systems. The analysis code that supports the funding is publicly available at https://github.com/Slautin/2024_Co-navigation/tree/main, Comment: 23 pages, 10 figures

Exploring the structural, chemical, and physical properties of matter on the nano- and atomic scales has become possible with the recent advances in aberration-corrected electron energy-loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM). However, the current paradigm of STEM-EELS relies on the classical rectangular grid sampling, in which all surface regions are assumed to be of equal a priori interest. This is typically not the case for real-world scenarios, where phenomena of interest are concentrated in a small number of spatial locations. One of foundational problems is the discovery of nanometer- or atomic scale structures having specific signatures in EELS spectra. Here we systematically explore the hyperparameters controlling deep kernel learning (DKL) discovery workflows for STEM-EELS and identify the role of the local structural descriptors and acquisition functions on the experiment progression. In agreement with actual experiment, we observe that for certain parameter combinations the experiment path can be trapped in the local minima. We demonstrate the approaches for monitoring automated experiment in the real and feature space of the system and monitor knowledge acquisition of the DKL model. Based on these, we construct intervention strategies, thus defining human-in the loop automated experiment (hAE). This approach can be further extended to other techniques including 4D STEM and other forms of spectroscopic imaging.

Exploring molecular spaces is crucial for advancing our understanding of chemical properties and reactions, leading to groundbreaking innovations in materials science, medicine, and energy. This paper explores an approach for active learning in molecular discovery using Deep Kernel Learning (DKL), a novel approach surpassing the limits of classical Variational Autoencoders (VAEs). Employing the QM9 dataset, we contrast DKL with traditional VAEs, which analyze molecular structures based on similarity, revealing limitations due to sparse regularities in latent spaces. DKL, however, offers a more holistic perspective by correlating structure with properties, creating latent spaces that prioritize molecular functionality. This is achieved by recalculating embedding vectors iteratively, aligning with the experimental availability of target properties. The resulting latent spaces are not only better organized but also exhibit unique characteristics such as concentrated maxima representing molecular functionalities and a correlation between predictive uncertainty and error. Additionally, the formation of exclusion regions around certain compounds indicates unexplored areas with potential for groundbreaking functionalities. This study underscores DKL's potential in molecular research, offering new avenues for understanding and discovering molecular functionalities beyond classical VAE limitations.

To describe the polar properties of the nanosized HfxZr1-xO2-y, we evolve the "effective" Landau-Ginzburg-Devonshire (LGD) model based on the parametrization of the Landau expansion coefficients for the polar and antipolar orderings. We have shown that the effective LGD model can predict the influence of screening conditions and size effects on phase diagrams, polarization reversal and structural properties of the nanosized HfxZr1-xO2-y of various shape and sizes. To verify the model, we use available experimental results for HfxZr1-xO2 thin films and oxygen-deficient HfO2-y nanoparticles prepared at different annealing conditions. X-ray diffraction, which was used to determine the phase composition of the HfO2-y nanoparticles, revealed the formation of the ferroelectric orthorhombic phase in them. Micro-Raman spectroscopy was used to explore the correlation of lattice dynamics and structural changes appearing in dependence on the oxygen vacancies concentration in the HfO2-y nanoparticles. Since our approach allows to determine the conditions (shape, sizes, Zr content and/or oxygen vacancies amount) for which the nanosized HfxZr1-xO2-y are ferroelectrics or antiferroelectrics, we hope that obtained results are useful for creation of next generation of Si-compatible ferroelectric gate oxide nanomaterials., Comment: 24 pages, 7 figures, 1 Appendix

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often non-differentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time-consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest towards active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge on the system in form of partially known physics laws and often varies exploration policies during the experiment. Here, we explore interactive workflows building on multi-fidelity BO (MFBO), starting with classical (data-driven) MFBO, then structured (physics-driven) sMFBO, and extending it to allow human in the loop interactive iMFBO workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly non-smooth multi-fidelity simulation data generated from an Ising model, considering spin-spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and on-the-fly human decisions for improved exploration, current challenges, and potential opportunities for algorithm development with combining data, physics and real time human decisions., Comment: Main text includes 29 pages and 10 figures, Supplementary mat. includes 4 pages and 4 figures

Ferroelectric materials promise exceptional attributes including low power dissipation, fast operational speeds, enhanced endurance, and superior retention to revolutionize information technology. However, the practical application of ferroelectric-semiconductor memory devices has been significantly challenged by the incompatibility of traditional perovskite oxide ferroelectrics with metal-oxide-semiconductor technology. Recent discoveries of ferroelectricity in binary oxides such as Zn1-xMgxO and Hf1-xZrxO have been a focal point of research in ferroelectric information technology. This work investigates the ferroelectric properties of Zn1-xMgxO utilizing automated band excitation piezoresponse force microscopy. Our findings reveal the coexistence of two ferroelectric subsystems within Zn1-xMgxO. We propose a "fringing-ridge mechanism" of polarization switching that is characterized by initial lateral expansion of nucleation without significant propagation in depth, contradicting the conventional domain growth process observed in ferroelectrics. This unique polarization dynamics in Zn1-xMgxO suggests a new understanding of ferroelectric behavior, contributing to both the fundamental science of ferroelectrics and their application in information technology., Comment: 23 pages; 7 figures

The rapid growth of automated and autonomous instrumentations brings forth an opportunity for the co-orchestration of multimodal tools, equipped with multiple sequential detection methods, or several characterization tools to explore identical samples. This can be exemplified by the combinatorial libraries that can be explored in multiple locations by multiple tools simultaneously, or downstream characterization in automated synthesis systems. In the co-orchestration approaches, information gained in one modality should accelerate the discovery of other modalities. Correspondingly, the orchestrating agent should select the measurement modality based on the anticipated knowledge gain and measurement cost. Here, we propose and implement a co-orchestration approach for conducting measurements with complex observables such as spectra or images. The method relies on combining dimensionality reduction by variational autoencoders with representation learning for control over the latent space structure, and integrated into iterative workflow via multi-task Gaussian Processes (GP). This approach further allows for the native incorporation of the system's physics via a probabilistic model as a mean function of the GP. We illustrated this method for different modalities of piezoresponse force microscopy and micro-Raman on combinatorial $Sm-BiFeO_3$ library. However, the proposed framework is general and can be extended to multiple measurement modalities and arbitrary dimensionality of measured signals. The analysis code that supports the funding is publicly available at https://github.com/Slautin/2024_Co-orchestration., Comment: 22 pages, 9 figures

The current focus in Autonomous Experimentation (AE) is on developing robust workflows to conduct the AE effectively. This entails the need for well-defined approaches to guide the AE process, including strategies for hyperparameter tuning and high-level human interventions within the workflow loop. This paper presents a comprehensive analysis of the influence of initial experimental conditions and in-loop interventions on the learning dynamics of Deep Kernel Learning (DKL) within the realm of AE in Scanning Probe Microscopy. We explore the concept of 'seed effect', where the initial experiment setup has a substantial impact on the subsequent learning trajectory. Additionally, we introduce an approach of the seed point interventions in AE allowing the operator to influence the exploration process. Using a dataset from Piezoresponse Force Microscopy (PFM) on PbTiO3 thin films, we illustrate the impact of the 'seed effect' and in-loop seed interventions on the effectiveness of DKL in predicting material properties. The study highlights the importance of initial choices and adaptive interventions in optimizing learning rates and enhancing the efficiency of automated material characterization. This work offers valuable insights into designing more robust and effective AE workflows in microscopy with potential applications across various characterization techniques. The analysis code that supports the funding is publicly available at https://github.com/Slautin/2024_Seed_effect_DKL_BO., Comment: 24 pages, 11 figures

On- and off-axis electron energy loss spectroscopy (EELS) is a powerful method for probing local electronic structure on single atom level. However, many materials undergo electron-beam induced transformation during the scanning transmission electron microscopy (STEM) and spectroscopy, the problem particularly acute for off-axis EELS signals. Here, we propose and operationalize the rapid object detection and action system (RODAS) for dynamic exploration of the structure-property relationships in STEM-EELS. In this approach, the electron beam is used to induce dynamic transformations creating new defect types at sufficiently small rates and avoiding complete material destruction. The deep convolutional neural networks trained via the ensemble learning iterative training (ELIT) approach are used to identify the defects as they form and perform EELS measurements only at specific defect types. Overall, in this case the EEL spectra are collected only at predefined objects of interest, avoiding measurements on the ideal regions or holes. We note that this approach can be extended to identify new defect classes as they appear, allowing for efficient collection of structure-property relationship data via balanced sampling over defect types.

Directed atomic fabrication using an aberration-corrected scanning transmission electron microscope (STEM) opens new pathways for atomic engineering of functional materials. In this approach, the electron beam is used to actively alter the atomic structure through electron beam induced irradiation processes. One of the impediments that has limited widespread use thus far has been the ability to understand the fundamental mechanisms of atomic transformation pathways at high spatiotemporal resolution. Here, we develop a workflow for obtaining and analyzing high-speed spiral scan STEM data, up to 100 fps, to track the atomic fabrication process during nanopore milling in monolayer MoS2. An automated feedback-controlled electron beam positioning system combined with deep convolution neural network (DCNN) was used to decipher fast but low signal-to-noise datasets and classify time-resolved atom positions and nature of their evolving atomic defect configurations. Through this automated decoding, the initial atomic disordering and reordering processes leading to nanopore formation was able to be studied across various timescales. Using these experimental workflows a greater degree of speed and information can be extracted from small datasets without compromising spatial resolution. This approach can be adapted to other 2D materials systems to gain further insights into the defect formation necessary to inform future automated fabrication techniques utilizing the STEM electron beam.

The unique aspect of the hybrid perovskites is their tunability, allowing to engineer the bandgap via substitution. From application viewpoint, this allows creation of the tandem cells between perovskites and silicon, or two or more perovskites, with associated increase of efficiency beyond single-junction Schokley-Queisser limit. However, the concentration dependence of optical bandgap in the hybrid perovskite solid solutions can be non-linear and even non-monotonic, as determined by the band alignments between endmembers, presence of the defect states and Urbach tails, and phase separation. Exploring new compositions brings forth the joint problem of the discovery of the composition with the desired band gap, and establishing the physical model of the band gap concentration dependence. Here we report the development of the experimental workflow based on structured Gaussian Process (sGP) models and custom sGP (c-sGP) that allow the joint discovery of the experimental behavior and the underpinning physical model. This approach is verified with simulated data sets with known ground truth, and was found to accelerate the discovery of experimental behavior and the underlying physical model. The d/c-sGP approach utilizes a few calculated thin film bandgap data points to guide targeted explorations, minimizing the number of thin film preparations. Through iterative exploration, we demonstrate that the c-sGP algorithm that combined 5 bandgap models converges rapidly, revealing a relationship in the bandgap diagram of MA1-xGAxPb(I1-xBrx)3. This approach offers a promising method for efficiently understanding the physical model of band gap concentration dependence in the binary systems, this method can also be extended to ternary or higher dimensional systems.

Machine learning methods are progressively gaining acceptance in the electron microscopy community for de-noising, semantic segmentation, and dimensionality reduction of data post-acquisition. The introduction of the APIs by major instrument manufacturers now allows the deployment of ML workflows in microscopes, not only for data analytics but also for real-time decision-making and feedback for microscope operation. However, the number of use cases for real-time ML remains remarkably small. Here, we discuss some considerations in designing ML-based active experiments and pose that the likely strategy for the next several years will be human-in-the-loop automated experiments (hAE). In this paradigm, the ML learning agent directly controls beam position and image and spectroscopy acquisition functions, and human operator monitors experiment progression in real- and feature space of the system and tunes the policies of the ML agent to steer the experiment towards specific objectives.

Ferroelectricity in van der Waals (vdW) layered material has attracted a great deal of interest recently. CuInP$_2$S$_6$ (CIPS), the only vdW layered material whose ferroelectricity in the bulk was demonstrated by direct polarization measurements, was shown to remain ferroelectric down to a thickness of a few nanometers. However, its ferroelectric properties have just started to be explored in the context of potential device applications. We report here the preparation and measurements of metal-ferroelectric semiconductor-metal heterostructures using nanosheets of CIPS obtained by mechanical exfoliation. Four bias voltage and polarization dependent resistive states were observed in the current-voltage characteristics, which we attribute to the formation of ferroelectric Schottky diode, along with switching behavior., Comment: 19 pages, 8 figures

The low-dimensional ferroelectrics, ferrielectrics and antiferroelectrics are of urgent scientific interest due to their unusual polar, piezoelectric, electrocaloric and pyroelectric properties. The strain engineering and strain control of the ferroelectric properties of layered 2D Van der Waals materials, such as CuInP$_2$(S,Se)$_6$ monolayers, thin films and nanoflakes, are of fundamental interest and especially promising for their advanced applications in nanoscale nonvolatile memories, energy conversion and storage, nano-coolers and sensors. Here, we study the polar, piezoelectric, electrocaloric and pyroelectric properties of thin strained films of a ferrielectric CuInP$_2$S$_6$ covered by semiconducting electrodes and reveal an unusually strong effect of a mismatch strain on these properties. In particular, the sign of the mismatch strain and its magnitude determine the complicated behavior of piezoelectric, electrocaloric and pyroelectric responses. The strain effect on these properties is opposite, i.e., "anomalous", in comparison with many other ferroelectric films, for which the out-of-plane remanent polarization, piezoelectric, electrocaloric and pyroelectric responses increase strongly for tensile strains and decrease or vanish for compressive strains., Comment: 16 pages, 5 figures, to be presented at the VI Lithuanian-Polish Meeting on Physics of Ferroelectrics. arXiv admin note: text overlap with arXiv:2304.04097

Despite fascinating experimental results, the influence of defects and elastic strains on the physical state of nanosized ferroelectrics is still poorly explored theoretically. One of unresolved theoretical problems is the analytical description of the strongly enhanced spontaneous polarization, piezoelectric response, and dielectric properties of ferroelectric oxide thin films and core-shell nanoparticles induced by elastic strains and stresses. In particular, the 10-nm quasi-spherical BaTiO3 core-shell nanoparticles reveal a giant spontaneous polarization up to 130 mu_C/cm2, where the physical origin is a large Ti off-centering. The available theoretical description cannot explain the giant spontaneous polarization observed in these spherical nanoparticles. This work analyzes polar properties of BaTiO3 core-shell spherical nanoparticles using the Landau-Ginzburg-Devonshire approach, which considers the nonlinear electrostriction coupling and large Vegard strains in the shell. We reveal that a spontaneous polarization greater than 50 mu_C/cm2 can be stable in a (10-100) nm BaTiO3 core at room temperature, where a 5 nm paraelectric shell is stretched by (3-6)% due to Vegard strains, which contribute to the elastic mismatch at the core-shell interface. The polarization value 50 mu_C/cm2 corresponds to high tetragonality ratios (1.02 - 1.04), which is further increased up to 100 mu_C/cm2 by higher Vegard strains and/or intrinsic surface stresses leading to unphysically high tetragonality ratios (1.08 - 1.16). The nonlinear electrostriction coupling and the elastic mismatch at the core-shell interface are key physical factors of the spontaneous polarization enhancement in the core. Doping with the highly-polarized core-shell nanoparticles can be useful in optoelectronics and nonlinear optics, electric field enhancement, reduced switching voltages, catalysis, and electrocaloric nanocoolers., Comment: 34 pages, including 5 figures and 1 Appendix

Polarization dynamics and domain structure evolution in ferroelectric Al$_{0.93}$B$_{0.07}$N are studied using piezoresponse force microscopy and spectroscopies in ambient and controlled atmosphere environments. The application of negative unipolar, and bipolar first-order reverse curve (FORC) waveforms leads to a protrusion-like feature on the Al$_{0.93}$B$_{0.07}$N surface and reduction of electromechanical response due to electrochemical reactivity. A surface change is also observed on the application of fast alternating current bias. At the same time, the application of positive biases does not lead to surface changes. Comparatively in a controlled glove box atmosphere, stable polarization patterns can be observed, with minuscule changes in surface morphology. This surface morphology change is not isolated to applying biases to free surface, a similar topographical change is also observed at the electrode edges when cycling a capacitor in ambient environment. The study suggests that surface electrochemical reactivity may have a significant impact on the functionality of this material in the ambient environment. However, even in the controlled atmosphere, the participation of the surface ions in polarization switching phenomena and ionic compensation is possible., Comment: 16 pages; 5 figures

To describe the charge-polarization coupling in the nanostructure formed by a thin Hf$_x$Zr$_{1-x}$O$_2$ film with a single-layer graphene as a top electrode, we develop the "effective" Landau-Ginzburg-Devonshire model. This approach is based on the parametrization of the Landau expansion coefficients for the polar (FE) and antipolar (AFE) orderings in thin Hf$_x$Zr$_{1-x}$O$_2$ films from a limited number of polarization-field curves and hysteresis loops. The Landau expansion coefficients are nonlinearly dependent on the film thickness h and Zr/[Hf+Zr] ratio x, in contrast to h-independent and linearly x-dependent expansion coefficients of a classical Landau energy. We explain the dependence of the Landau expansion coefficients by the strong nonmonotonic dependence of the polar properties on the Hf$_x$Zr$_{1-x}$O$_2$ film thickness, grain size and surface energy. The proposed Landau free energy with five "effective" expansion coefficients, which are interpolation functions of x and h, describes the continuous transformation of polarization dependences on applied electric field and hysteresis loop shapes induced by the changes of x and h in the range 0 < x < 1 and 5 nm < h < 35 nm. Using the effective free energy, we demonstrated that the polarization of Hf$_x$Zr$_{1-x}$O$_2$ films influences strongly on the graphene conductivity, and the full correlation between the distribution of polarization and charge carriers in graphene is revealed. In accordance with our modeling, the polarization of the (5 - 25) nm thick Hf$_x$Zr$_{1-x}$O$_2$ films, which are in the ferroelectric-like or antiferroelectric-like states for the chemical compositions 0.35 < x < 0.95, determine the concentration of carriers in graphene and can control its field dependence. The result can be promising for creation of next generation Si-compatible nonvolatile memories and graphene-ferroelectric FETs., Comment: 38 pages including 8 figures and 1 Appendix with 2 figures

Using Landau-Ginzburg-Devonshire (LGD) phenomenological approach we analyze the bending-induced re-distribution of electric polarization and field, elastic stresses and strains inside ultrathin layers of van der Waals ferrielectrics. We consider a CuInP2S6 (CIPS) thin layer with fixed edges and suspended central part, the bending of which is induced by external forces. The unique aspect of CIPS is the existence of two ferrielectric states, FI1 and FI2, corresponding to big and small polarization values, which arise due to the specific four-well potential of the eighth-order LGD functional. When the CIPS layer is flat, the single-domain FI1 state is stable in the central part of the layer, and the FI2 states are stable near the fixed edges. With an increase of the layer bending below the critical value, the sizes of the FI2 states near the fixed edges decreases, and the size of the FI1 region increases. When the bending exceeds the critical value, the edge FI2 states disappear being substituted by the FI1 state, but they appear abruptly near the inflection regions and expand as the bending increases. The bending-induced isostructural FI1-FI2 transition is specific for the bended van der Waals ferrielectrics described by the eighth (or higher) order LGD functional with consideration of linear and nonlinear electrostriction couplings. The isostructural transition, which is revealed in the vicinity of room temperature, can significantly reduce the coercive voltage of ferroelectric polarization reversal in CIPS nanoflakes, allowing for the curvature-engineering control of various flexible nanodevices., Comment: 26 pages, 7 figures and Appendices A-C

Nanoscale ferroelectric 2D materials offer unique opportunity to investigate curvature and strain effects on materials functionalities. Among these, CuInP2S6 (CIPS) has attracted tremendous research interest in recent years due to combination of room temperature ferroelectricity, scalability to a few layers thickness, and unique ferrielectric properties due to coexistence of 2 polar sublattices. Here, we explore the local curvature and strain effect on the polarization in CIPS via piezoresponse force microscopy and spectroscopy. To explain the observed behaviors and decouple the curvature and strain effects in 2D CIPS, we introduce finite element Landau-Ginzburg-Devonshire model. The results show that bending induces ferrielectric domains in CIPS, and the polarization-voltage hysteresis loops differ in bending and non-bending regions. Our simulation indicates that the flexoelectric effect can affect local polarization hysteresis. These studies open a novel pathway for the fabrication of curvature-engineered nanoelectronic devices., Comment: 20 pages; 7 figures

Strain-induced transitions of polarization reversal in thin films of a ferrielectric CuInP$_2$S$_6$ (CIPS) with ideally-conductive electrodes is explored using the Landau-Ginzburg-Devonshire (LGD) approach with an eighth-order free energy expansion in polarization powers. Due to multiple potential wells, the height and position of which are temperature- and strain-dependent, the energy profiles of CIPS can flatten in the vicinity of the non-zero polarization states. This behavior differentiates these materials from classical ferroelectrics with the first or second order ferroelectric-paraelectric phase transition, for which potential energy profiles can be shallow or flat near the transition point only, corresponding to zero spontaneous polarization. Thereby we reveal an unusually strong effect of the mismatch strain on the out-of-plane polarization reversal, hysteresis loops shape, dielectric susceptibility, and piezoelectric response of CIPS films. In particular, by varying the sign of the mismatch strain and its magnitude in a narrow range, quasi-static hysteresis-less paraelectric curves can transform into double, triple, and other types of pinched and single hysteresis loops. The strain effect on the polarization reversal is opposite, i.e., "anomalous", in comparison with many other ferroelectric films in that the out-of-plane remanent polarization and coercive field increases strongly for tensile strains, meanwhile the polarization decreases or vanish for compressive strains. We explain the effect by "inverted" signs of linear and nonlinear electrostriction coupling coefficients of CIPS and their strong temperature dependence. For definite values of temperature and mismatch strain, the low-frequency hysteresis loops of polarization may exhibit negative slope in the relatively narrow range of external field amplitude and frequency., Comment: 26 pages, including 8 figures and 1 Appendix

Optimization of experimental materials synthesis and characterization through active learning methods has been growing over the last decade, with examples ranging from measurements of diffraction on combinatorial alloys at synchrotrons, to searches through chemical space with automated synthesis robots for perovskites. In virtually all cases, the target property of interest for optimization is defined apriori with limited human feedback during operation. In contrast, here we present the development of a new type of human in the loop experimental workflow, via a Bayesian optimized active recommender system (BOARS), to shape targets on the fly, employing human feedback. We showcase examples of this framework applied to pre-acquired piezoresponse force spectroscopy of a ferroelectric thin film, and then implement this in real time on an atomic force microscope, where the optimization proceeds to find symmetric piezoresponse amplitude hysteresis loops. It is found that such features appear more affected by subsurface defects than the local domain structure. This work shows the utility of human-augmented machine learning approaches for curiosity-driven exploration of systems across experimental domains. The analysis reported here is summarized in Colab Notebook for the purpose of tutorial and application to other data: https://github.com/arpanbiswas52/varTBO, Comment: 7 figures in main text, 3 figures in Supp Material

Machine learning (ML) has become critical for post-acquisition data analysis in (scanning) transmission electron microscopy, (S)TEM, imaging and spectroscopy. An emerging trend is the transition to real-time analysis and closed-loop microscope operation. The effective use of ML in electron microscopy now requires the development of strategies for microscopy-centered experiment workflow design and optimization. Here, we discuss the associated challenges with the transition to active ML, including sequential data analysis and out-of-distribution drift effects, the requirements for the edge operation, local and cloud data storage, and theory in the loop operations. Specifically, we discuss the relative contributions of human scientists and ML agents in the ideation, orchestration, and execution of experimental workflows and the need to develop universal hyper languages that can apply across multiple platforms. These considerations will collectively inform the operationalization of ML in next-generation experimentation., Comment: Review Article

The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards data set and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The jupyter notebooks that encapsulate the complete analysis accompany the article., Comment: 8 Figures, 26 pages

Reducing the dimensions of ferroelectric materials down to the nanoscale has strong implications on the ferroelectric polarization pattern and on the ability to switch the polarization. As the size of ferroelectric domains shrinks to nanometer scale, the heterogeneity of the polarization pattern becomes increasingly pronounced, enabling a large variety of possible polar textures in nanocrystalline and nanocomposite materials. Critical to the understanding of fundamental physics of such materials and hence their applications in electronic nanodevices, is the ability to investigate their ferroelectric polarization at the nanoscale in a non-destructive way. We show that contact Kelvin probe force microscopy (cKPFM) combined with a k-means response clustering algorithm enables to measure the ferroelectric response at a mapping resolution of 8 nm. In a BaTiO3 thin film on silicon composed of tetragonal and hexagonal nanocrystals, we determine a nanoscale lateral distribution of discrete ferroelectric response clusters, fully consistent with the nanostructure determined by transmission electron microscopy. Moreover, we apply this data clustering method to the cKPFM responses measured at different temperatures, which allows us to follow the corresponding change in polarization pattern as the Curie temperature is approached and across the phase transition. This work opens up perspectives for mapping complex ferroelectric polarization textures such as curled/swirled polar textures that can be stabilized in epitaxial heterostructures and more generally mapping the polar domain distribution of any spatially-highly-heterogeneous ferroelectric materials.

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Electronic states within superconducting vortices hold crucial information about paring mechanisms and topology. While scanning tunneling microscopy/spectroscopy(STM/S) can image the vortices, it is difficult to isolate the intrinsic electronic states from extrinsic effects like subsurface defects and disorders. We combine STM/S with unsupervised machine learning to develop a method for screening out the vortices pinned by embedded disorder in Fe-based superconductors. The approach provides an unbiased way to reveal intrinsic vortex-core states and may address puzzles on Majorana zero modes.

The broad adoption of machine learning (ML)-based automated and autonomous experiments (AE) in physical characterization and synthesis requires development of strategies for understanding and intervention in the experimental workflow. Here, we introduce and realize strategies for post-acquisition forensic analysis applied to the deep kernel learning based AE scanning probe microscopy. This approach yields real-time and post-acquisition indicators of the progression of an active learning process interacting with an experimental system. We further illustrate that this approach can be extended towards human-in-the-loop autonomous experiments, where human operators make high-level decisions at high latencies setting the policies for AE, and the ML algorithm performs low-level fast decisions. The proposed approach is universal and can be extended to other physical and chemical imaging techniques and applications such as combinatorial library analysis. The full forensic analysis notebook is publicly available on GitHub at https://github.com/yongtaoliu/Forensics-DKL-BEPS., Comment: 24 pages, 8 figures