Coupling Charge and Topological Reconstructions at Polar Oxide Interfaces.

In oxide heterostructures, different materials are integrated into a single artificial crystal, resulting in a breaking of inversion symmetry across the heterointerfaces. A notable example is the interface between polar and nonpolar materials, where valence discontinuities lead to otherwise inaccessible charge and spin states. This approach paved the way for the discovery of numerous unconventional properties absent in the bulk constituents. However, control of the geometric structure of the electronic wave functions in correlated oxides remains an open challenge. Here, we create heterostructures consisting of ultrathin SrRuO_{3}, an itinerant ferromagnet hosting momentum-space sources of Berry curvature, and LaAlO_{3}, a polar wide-band-gap insulator. Transmission electron microscopy reveals an atomically sharp LaO/RuO_{2}/SrO interface configuration, leading to excess charge being pinned near the LaAlO_{3}/SrRuO_{3} interface. We demonstrate through magneto-optical characterization, theoretical calculations and transport measurements that the real-space charge reconstruction drives a reorganization of the topological charges in the band structure, thereby modifying the momentum-space Berry curvature in SrRuO_{3}. Our results illustrate how the topological and magnetic features of oxides can be manipulated by engineering charge discontinuities at oxide interfaces.

Single Atom Detection from Low Contrast-to-Noise Ratio Electron Microscopy Images.

Single atom detection is of key importance to solving a wide range of scientific and technological problems. The strong interaction of electrons with matter makes transmission electron microscopy one of the most promising techniques. In particular, aberration correction using scanning transmission electron microscopy has made a significant step forward toward detecting single atoms. However, to overcome radiation damage, related to the use of high-energy electrons, the incoming electron dose should be kept low enough. This results in images exhibiting a low signal-to-noise ratio and extremely weak contrast, especially for light-element nanomaterials. To overcome this problem, a combination of physics-based model fitting and the use of a model-order selection method is proposed, enabling one to detect single atoms with high reliability.

Controlled lateral anisotropy in correlated manganite heterostructures by interface-engineered oxygen octahedral coupling.

Controlled in-plane rotation of the magnetic easy axis in manganite heterostructures by tailoring the interface oxygen network could allow the development of correlated oxide-based magnetic tunnelling junctions with non-collinear magnetization, with possible practical applications as miniaturized high-switching-speed magnetic random access memory (MRAM) devices. Here, we demonstrate how to manipulate magnetic and electronic anisotropic properties in manganite heterostructures by engineering the oxygen network on the unit-cell level. The strong oxygen octahedral coupling is found to transfer the octahedral rotation, present in the NdGaO3 (NGO) substrate, to the La2/3Sr1/3MnO3 (LSMO) film in the interface region. This causes an unexpected realignment of the magnetic easy axis along the short axis of the LSMO unit cell as well as the presence of a giant anisotropic transport in these ultrathin LSMO films. As a result we possess control of the lateral magnetic and electronic anisotropies by atomic-scale design of the oxygen octahedral rotation.

Element specific atom counting for heterogeneous nanostructures: Combining multiple ADF STEM images for simultaneous thickness and composition determination.

In this paper, a methodology is presented to count the number of atoms in heterogeneous nanoparticles based on the combination of multiple annular dark field scanning transmission electron microscopy (ADF STEM) images. The different non-overlapping annular detector collection regions are selected based on the principles of optimal statistical experiment design for the atom-counting problem. To count the number of atoms, the total intensities of scattered electrons for each atomic column, the so-called scattering cross-sections, are simultaneously compared with simulated library values for the different detector regions by minimising the squared differences. The performance of the method is evaluated for simulated Ni@Pt and Au@Ag core-shell nanoparticles. Our approach turns out to be a dose efficient alternative for the investigation of beam-sensitive heterogeneous materials as compared to the combination of ADF STEM and energy dispersive X-ray spectroscopy.

Advanced three-dimensional electron microscopy techniques in the quest for better structural and functional materials.

After a short review of electron tomography techniques for materials science, this overview will cover some recent results on different shape memory and nanostructured metallic systems obtained by various three-dimensional (3D) electron imaging techniques. In binary Ni-Ti, the 3D morphology and distribution of Ni4Ti3 precipitates are investigated by using FIB/SEM slice-and-view yielding 3D data stacks. Different quantification techniques will be presented including the principal ellipsoid for a given precipitate, shape classification following a Zingg scheme, particle distribution function, distance transform and water penetration. The latter is a novel approach to quantifying the expected matrix transformation in between the precipitates. The different samples investigated include a single crystal annealed with and without compression yielding layered and autocatalytic precipitation, respectively, and a polycrystal revealing different densities and sizes of the precipitates resulting in a multistage transformation process. Electron tomography was used to understand the interaction between focused ion beam-induced Frank loops and long dislocation structures in nanobeams of Al exhibiting special mechanical behaviour measured by on-chip deposition. Atomic resolution electron tomography is demonstrated on Ag nanoparticles in an Al matrix.

A decade of atom-counting in STEM: From the first results toward reliable 3D atomic models from a single projection.

Quantitative structure determination is needed in order to study and understand nanomaterials at the atomic scale. Materials characterisation resulting in precise structural information is a crucial point to understand the structure-property relation of materials. Counting the number of atoms and retrieving the 3D atomic structure of nanoparticles plays an important role here. In this paper, an overview will be given of the atom-counting methodology and its applications over the past decade. The procedure to count the number of atoms will be discussed in detail and it will be shown how the performance of the method can be further improved. Furthermore, advances toward mixed element nanostructures, 3D atomic modelling based on the atom-counting results, and quantifying the nanoparticle dynamics will be highlighted.

Real-time simulations of ADF STEM probe position-integrated scattering cross-sections for single element fcc crystals in zone axis orientation using a densely connected neural network.

Quantification of annular dark field (ADF) scanning transmission electron microscopy (STEM) images in terms of composition or thickness often relies on probe-position integrated scattering cross sections (PPISCS). In order to compare experimental PPISCS with theoretically predicted ones, expensive simulations are needed for a given specimen, zone axis orientation, and a variety of microscope settings. The computation time of such simulations can be in the order of hours using a single GPU card. ADF STEM simulations can be efficiently parallelized using multiple GPUs, as the calculation of each pixel is independent of other pixels. However, most research groups do not have the necessary hardware, and, in the best-case scenario, the simulation time will only be reduced proportionally to the number of GPUs used. In this manuscript, we use a learning approach and present a densely connected neural network that is able to perform real-time ADF STEM PPISCS predictions as a function of atomic column thickness for most common face-centered cubic (fcc) crystals (i.e., Al, Cu, Pd, Ag, Pt, Au and Pb) along [100] and [111] zone axis orientations, root-mean-square displacements, and microscope parameters. The proposed architecture is parameter efficient and yields accurate predictions for the PPISCS values for a wide range of input parameters that are commonly used for aberration-corrected transmission electron microscopes.

Optimal experiment design for element specific atom counting using multiple annular dark field scanning transmission electron microscopy detectors.

This paper investigates the possible benefits for counting atoms of different chemical nature when analysing multiple 2D scanning transmission electron microscopy (STEM) images resulting from independent annular dark field (ADF) detector regimes. To reach this goal, the principles of statistical detection theory are used to quantify the probability of error when determining the number of atoms in atomic columns consisting of multiple types of elements. In order to apply this theory, atom-counting is formulated as a statistical hypothesis test, where each hypothesis corresponds to a specific number of atoms of each atom type in an atomic column. The probability of error, which is limited by the unavoidable presence of electron counting noise, can then be computed from scattering-cross sections extracted from multiple ADF STEM images. Minimisation of the probability of error as a function of the inner and outer angles of a specified number of independent ADF collection regimes results in optimal experimental designs. Based on simulations of spherical Au@Ag and Au@Pt core-shell nanoparticles, we investigate how the combination of two non-overlapping detector regimes helps to improve the probability of error when unscrambling two types of atoms. In particular, the combination of a narrow low angle ADF detector with a detector formed by the remaining annular collection regime is found to be optimal. The benefit is more significant if the atomic number Z difference becomes larger. In addition, we show the benefit of subdividing the detector regime into three collection areas for heterogeneous nanostructures based on a structure consisting of three types of elements, e.g., a mixture of Au, Ag and Al atoms. Finally, these results are compared with the probability of error resulting when one would ultimately use a pixelated 4D STEM detector and how this could help to further reduce the incident electron dose.

Dynamical diffraction of high-energy electrons investigated by focal series momentum-resolved scanning transmission electron microscopy at atomic resolution.

We report a study of scattering dynamics in crystals employing momentum-resolved scanning transmission electron microscopy under varying illumination conditions. As we perform successive changes of the probe focus, multiple real-space signals are obtained in dependence of the shape of the incident electron wave. With support from extensive simulations, each signal is shown to be characterised by an optimum focus for which the contrast is maximum and which differs among different signals. For instance, a systematic focus mismatch is found between images formed by high-angle scattering, being sensitive to thickness and chemical composition, and the first moment in diffraction space, being sensitive to electric fields. It follows that a single recording at one specific probe focus is usually insufficient to characterise materials comprehensively. Most importantly, we demonstrate in experiment and simulation that the second moment µ20+µ02=〈p2〉 of the diffracted intensity exhibits a contrast maximum when the electron probe is focused at the top and bottom faces of the specimen, making the presented concept attractive for measuring local topography. Given the versatility of 〈p2〉, we furthermore present a detailed study of its large-angle convergence both analytically using the Mott scattering approach, and by dynamical simulations using the multislice algorithm including thermal diffuse scattering. Both approaches are in very good agreement and yield logarithmic divergence with increasing scattering angle.

Atom column detection from simultaneously acquired ABF and ADF STEM images.

In electron microscopy, the maximum a posteriori (MAP) probability rule has been introduced as a tool to determine the most probable atomic structure from high-resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM) images exhibiting low contrast-to-noise ratio (CNR). Besides ADF imaging, STEM can also be applied in the annular bright-field (ABF) regime. The ABF STEM mode allows to directly visualize light-element atomic columns in the presence of heavy columns. Typically, light-element nanomaterials are sensitive to the electron beam, limiting the incoming electron dose in order to avoid beam damage and leading to images exhibiting low CNR. Therefore, it is of interest to apply the MAP probability rule not only to ADF STEM images, but to ABF STEM images as well. In this work, the methodology of the MAP rule, which combines statistical parameter estimation theory and model-order selection, is extended to be applied to simultaneously acquired ABF and ADF STEM images. For this, an extension of the commonly used parametric models in STEM is proposed. Hereby, the effect of specimen tilt has been taken into account, since small tilts from the crystal zone axis affect, especially, ABF STEM intensities. Using simulations as well as experimental data, it is shown that the proposed methodology can be successfully used to detect light elements in the presence of heavy elements.

Effect of amorphous layers on the interpretation of restored exit waves.

The effects of amorphous layers on the quality of exit wave restorations have been investigated. Two independently developed software implementations for exit wave restoration have been used to simulated focal series of images of <001> SrTiO3 with amorphous carbon layers incorporated. The restored exit waves have been compared both qualitatively and quantitatively. We have shown that amorphous layers have a strong impact on the quantitative measurements of atomic column positions, however, the error in the position measurements is still in the picometer range.

The maximum a posteriori probability rule for atom column detection from HAADF STEM images.

Recently, the maximum a posteriori (MAP) probability rule has been proposed as an objective and quantitative method to detect atom columns and even single atoms from high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images. The method combines statistical parameter estimation and model-order selection using a Bayesian framework and has been shown to be especially useful for the analysis of the structure of beam-sensitive nanomaterials. In order to avoid beam damage, images of such materials are usually acquired using a limited incoming electron dose resulting in a low contrast-to-noise ratio (CNR) which makes visual inspection unreliable. This creates a need for an objective and quantitative approach. The present paper describes the methodology of the MAP probability rule, gives its step-by-step derivation and discusses its algorithmic implementation for atom column detection. In addition, simulation results are presented showing that the performance of the MAP probability rule to detect the correct number of atomic columns from HAADF STEM images is superior to that of other model-order selection criteria, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Moreover, the MAP probability rule is used as a tool to evaluate the relation between STEM image quality measures and atom detectability resulting in the introduction of the so-called integrated CNR (ICNR) as a new image quality measure that better correlates with atom detectability than conventional measures such as signal-to-noise ratio (SNR) and CNR.

The atomic lensing model: New opportunities for atom-by-atom metrology of heterogeneous nanomaterials.

The atomic lensing model has been proposed as a promising method facilitating atom-counting in heterogeneous nanocrystals [1]. Here, image simulations will validate the model, which describes dynamical diffraction as a superposition of individual atoms focussing the incident electrons. It will be demonstrated that the model is reliable in the annular dark field regime for crystals having columns containing dozens of atoms. By using the principles of statistical detection theory, it will be shown that this model gives new opportunities for detecting compositional differences.

Frozen lattice and absorptive model for high angle annular dark field scanning transmission electron microscopy: A comparison study in terms of integrated intensity and atomic column position measurement.

In this paper, both the frozen lattice (FL) and the absorptive potential (AP) approximation models are compared in terms of the integrated intensity and the precision with which atomic columns can be located from an image acquired using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM). The comparison is made for atoms of Cu, Ag, and Au. The integrated intensity is computed for both an isolated atomic column and an atomic column inside an FCC structure. The precision has been computed using the so-called Cramér-Rao Lower Bound (CRLB), which provides a theoretical lower bound on the variance with which parameters can be estimated. It is shown that the AP model results into accurate measurements for the integrated intensity only for small detector ranges under relatively low angles and for small thicknesses. In terms of the attainable precision, both methods show similar results indicating picometer range precision under realistic experimental conditions.

Thickness dependence of scattering cross-sections in quantitative scanning transmission electron microscopy.

In quantitative scanning transmission electron microscopy (STEM), scattering cross-sections have been shown to be very sensitive to the number of atoms in a column and its composition. They correspond to the integrated intensity over the atomic column and they outperform other measures. As compared to atomic column peak intensities, which saturate at a given thickness, scattering cross-sections increase monotonically. A study of the electron wave propagation is presented to explain the sensitivity of the scattering cross-sections. Based on the multislice algorithm, we analyse the wave propagation inside the crystal and its link to the scattered signal for the different probe positions contained in the scattering cross-section for detector collection in the low-, middle- and high-angle regimes. The influence to the signal from scattering of neighbouring columns is also discussed.

Electron channelling based crystallography.

Electron channelling occurs when the incident electron beam is parallel to the atom columns of an object, such as a crystal or a particular crystal defect. Then, the electrons are trapped in the electrostatic potential of an atom column in which they scatter dynamically. This picture provides physical insight and explains why a one-to-one correspondence is maintained between the exit wave and the projected structure, even in case of strong dynamical scattering. Moreover, the theory is very useful to invert the dynamical scattering, that is, to derive the projected structure from the exit wave. Finally, it can be used to determine the composition of an atom column with single atom sensitivity or to explain dynamical electron diffraction effects. In this paper, an overview of the channelling theory will be given together with some recent applications.

Locating light and heavy atomic column positions with picometer precision using ISTEM.

Recently, imaging scanning transmission electron microscopy (ISTEM) has been proposed as a promising new technique combining the advantages of conventional TEM (CTEM) and STEM (Rosenauer et al., 2014 [1]). The ability to visualize light and heavy elements together makes it a particularly interesting new, spatially incoherent imaging mode. Here, we evaluate this technique in term of precision with which atomic column locations can be measured. By using statistical parameter estimation theory, we will show that these locations can be accurately measured with a precision in the picometer range. Furthermore, a quantitative comparison is made with HAADF STEM imaging to investigate the advantages of ISTEM.

How precise can atoms of a nanocluster be located in 3D using a tilt series of scanning transmission electron microscopy images?

In this paper, we investigate how precise atoms of a small nanocluster can ultimately be located in three dimensions (3D) from a tilt series of images acquired using annular dark field (ADF) scanning transmission electron microscopy (STEM). Therefore, we derive an expression for the statistical precision with which the 3D atomic position coordinates can be estimated in a quantitative analysis. Evaluating this statistical precision as a function of the microscope settings also allows us to derive the optimal experimental design. In this manner, the optimal angular tilt range, required electron dose, optimal detector angles, and number of projection images can be determined.

Atom-counting in High Resolution Electron Microscopy:TEM or STEM - That's the question.

In this work, a recently developed quantitative approach based on the principles of detection theory is used in order to determine the possibilities and limitations of High Resolution Scanning Transmission Electron Microscopy (HR STEM) and HR TEM for atom-counting. So far, HR STEM has been shown to be an appropriate imaging mode to count the number of atoms in a projected atomic column. Recently, it has been demonstrated that HR TEM, when using negative spherical aberration imaging, is suitable for atom-counting as well. The capabilities of both imaging techniques are investigated and compared using the probability of error as a criterion. It is shown that for the same incoming electron dose, HR STEM outperforms HR TEM under common practice standards, i.e. when the decision is based on the probability function of the peak intensities in HR TEM and of the scattering cross-sections in HR STEM. If the atom-counting decision is based on the joint probability function of the image pixel values, the dependence of all image pixel intensities as a function of thickness should be known accurately. Under this assumption, the probability of error may decrease significantly for atom-counting in HR TEM and may, in theory, become lower as compared to HR STEM under the predicted optimal experimental settings. However, the commonly used standard for atom-counting in HR STEM leads to a high performance and has been shown to work in practice.

Depth sectioning combined with atom-counting in HAADF STEM to retrieve the 3D atomic structure.

Aberration correction in scanning transmission electron microscopy (STEM) has greatly improved the lateral and depth resolution. When using depth sectioning, a technique during which a series of images is recorded at different defocus values, single impurity atoms can be visualised in three dimensions. In this paper, we investigate new possibilities emerging when combining depth sectioning and precise atom-counting in order to reconstruct nanosized particles in three dimensions. Although the depth resolution does not allow one to precisely locate each atom within an atomic column, it will be shown that the depth location of an atomic column as a whole can be measured precisely. In this manner, the morphology of a nanoparticle can be reconstructed in three dimensions. This will be demonstrated using simulations and experimental data of a gold nanorod.