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Cylindrical magnetic nanowires with large transversal magnetocrystalline anisotropy have been shown to sustain non-trivial magnetic configurations resulting from the interplay of spatial confinement, exchange, and anisotropies. Exploiting these peculiar 3D spin configurations and their solitonic inhomogeneities are prospected to improve magnetization switching in future spintronics, such as power-saving magnetic memory and logic applications. Here we employ holographic vector field electron tomography to reconstruct the remanent magnetic states in CoNi nanowires with 10 nm resolution in 3D, with a particular focus on domain walls between remanent states and ubiquitous real-structure effects stemming from irregular morphology and anisotropy variations. By tuning the applied magnetic field direction, both longitudinal and transverse multi-vortex states of different chiralities and peculiar 3D features such as shifted vortex cores are stabilized. The chiral domain wall between the longitudinal vortices of opposite chiralities exhibits a complex 3D shape characterized by a push out of the central vortex line and a gain in exchange and anisotropy energy. A similar complex 3D texture, including bent vortex lines, forms at the domain boundary between transverse-vortex states and longitudinal configurations. Micromagnetic simulations allow an understanding of the origin of the observed complex magnetic states., 22 pages, 5 figures, preprent of original paper

The authors study, as a promising candidate for photovoltaic applications, the Mott insulator LaVO${}_{3}$, epitaxially grown as a thin film on SrTiO${}_{3}$. They elucidate the electronic properties by electrical transport and photoemission measurements. The origin of the conducting interface is identified to be electronic reconstruction due to the polar discontinuity between film and substrate. The authors find a potential gradient in the film and a downward band bending in the substrate, with the electrons residing in interfacial Ti states.

In this study, faceted mesocrystals have been assembled from the dispersion of truncated cubic-shaped iron oxide nanoparticles stabilized by oleic acid (OA) molecules using the non-solvent “gas phase diffusion technique” into an organic solvent. The effects of synthesis conditions as well as of the nanoparticle size and shape on the structure and morphogenesis of mesocrystals were examined. The interactions of OA capped iron oxide nanoparticles with solvent molecules were probed by analytical ultracentrifugation and double difference pair distribution function analysis. It was shown that the structure of the organic shell significantly depends on the nature and polarity of solvent molecules.

Mesocrystals are nanostructured materials consisting of individual nanocrystals having a preferred crystallographic orientation. On mesoscopic length scales, the properties of mesocrystals are strongly affected by structural heterogeneity. Here, we report the detailed structural characterization of a faceted mesocrystal grain self-assembled from 60 nm sized gold nanocubes. Using coherent X-ray diffraction imaging, we determined the structure of the mesocrystal with the resolution sufficient to resolve each gold nanoparticle. The reconstructed electron density of the gold mesocrystal reveals its intrinsic structural heterogeneity, including local deviations of lattice parameters, and the presence of internal defects. The strain distribution shows that the average superlattice obtained by angular X-ray cross-correlation analysis and the real, “multidomain” structure of a mesocrystal are very close to each other, with a deviation less than 10%. These results will provide an important impact to understanding the fundamental principles of structuring and self-assembly including ensuing properties of mesocrystals.

Hybrid metallic nanoparticles encapsulated in oxide shells are currently intensely studied for plasmonic applications in sensing, medicine, catalysis, and photovoltaics. Here, we introduce a method for the synthesis of Au@Ag@SiO$_2$ cubes with a uniform silica shell of variable and adjustable thickness in the nanometer range; and we demonstrate their excellent, highly reproducible, and tunable optical response. Varying the silica shell thickness, we could tune the excitation energies of the single nanoparticle plasmon modes in a broad spectral range between 2.55 and 3.25\,eV. Most importantly, we reveal a strong coherent coupling of the surface plasmons at the silver-silica interface with the whispering gallery resonance at the silica-vacuum interface leading to a significant field enhancement at the encapsulated nanoparticle surface in the range of 100\,\% at shell thicknesses $t\,$$\simeq\,$20\,nm. Consequently, the synthesis method and the field enhancement open pathways to a widespread use of silver nanoparticles in plasmonic applications including photonic crystals and may be transferred to other non-precious metals.

This article addresses extraction of physically meaningful information from STEM EELS and EDX spectrum-images using methods of Multivariate Statistical Analysis. The problem is interpreted in terms of data distribution in a multi-dimensional factor space, which allows for a straightforward and intuitively clear comparison of various approaches. A new computationally efficient and robust method for finding physically meaningful endmembers in spectrum-image datasets is presented. The method combines the geometrical approach of Vertex Component Analysis with the statistical approach of Bayesian inference. The algorithm is described in detail at an example of EELS spectrum-imaging of a multi-compound CMOS transistor.

In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to any of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded green Dyadic, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam., Re-Submission to SciPost. Updated version: minor revisions, SciPost template

An often-overlooked property of transition metal oxide thin films is their microscopic surface structure and its effect on the electronic properties in the ultrathin limit. Contrary to the expected conservation of the perovskite stacking order in the (001) direction, heteroepitaxially grown SrIrO3 films on TiO2-terminated SrTiO3 are found to exhibit a terminating SrO surface layer. The proposed mechanism for the self-organized conversion involves the adsorption of excess oxygen ions at the apical sites of the IrO2-terminated surface and the subsequent decomposition of the IrO6 octahedra into gaseous molecular IrO3 and the remaining SrO-terminated surface. Whereas the ab initio calculated electronic structure of SrO-terminated SrIrO3 in the monolayer limit exhibits a striking similarity to bulk Sr2IrO4, the broken octahedral symmetry at the IrO2-terminated surface would mix the otherwise crystal field split e(g) and t(2g) states, resulting in distinctly different low-energy electronic states. Published under license by AIP Publishing.

The 2D layered honeycomb magnet α-ruthenium(III) chloride (α-RuCl3) is a promising candidate to realize a Kitaev spin model. As alteration of physical properties on the nanoscale is additionally intended, new synthesis approaches to obtain phase pure α-RuCl3 nanocrystals have been audited. Thermodynamic simulations of occurring gas phase equilibria were performed and optimization of synthesis conditions was achieved based on calculation results. Crystal growth succeeded via chemical vapor transport (CVT) in a temperature gradient of 973 K to 773 K on YSZ substrates. Single crystal sheets of high crystallinity with heights ≤30 nm were obtained via pure CVT. The crystal properties were characterized by means of optical and electron microscopy, AFM, SAED, micro-Raman and XPS proving their composition, morphology, crystallinity and phase-purity. A highlight of our study is the successful individualization of nanocrystals and the delamination of nanosheets on YSZ substrates down to the monolayer limit (≤1 nm) which was realized by means of substrate exfoliation and ultrasonication in a very reproducible way.

The nondestructive characterization of nanoscale devices, such as those based on semiconductor nanowires, in terms of functional potentials is crucial for correlating device properties with their morphological/materials features, as well as for precisely tuning and optimizing their growth process. Electron holographic tomography (EHT) has been used in the past to reconstruct the total potential distribution in three-dimension but hitherto lacked a quantitative approach to separate potential variations due to chemical composition changes (mean inner potential, MIP) and space charges. In this Letter, we combine and correlate EHT and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) tomography on an individual ⟨111⟩ oriented GaAs-AlGaAs core-multishell nanowire (NW). We obtain excellent agreement between both methods in terms of the determined Al concentration within the AlGaAs shell, as well as thickness variations of the few nanometer thin GaAs shell acting as quantum well tube. Subtracting the MIP determined from the STEM tomogram, enables us to observe functional potentials at the NW surfaces and at the Au-NW interface, both ascribed to surface/interface pinning of the semiconductor Fermi level.

PtBi$_2$ is a polymorphic system with interesting electronic properties. Here we report optimized crystal growth and structural characterization of pyrite-type and trigonal modification of PtBi$_2$. Selected area electron diffraction, X-ray powder diffraction and further Rietveld refinement confirms that trigonal PtBi$_2$ crystallizes in non-centrosymmetric $P31m$ space group, pyrite-type PtBi$_2$ in $Pa\bar{3}$ space group. Series of Pt$_{1-x}$Rh$_x$Bi$_2$ samples was obtained for $x=0, 0.03, 0.35$ in the trigonal PtBi$_2$ structure. These Pt$_{1-x}$Rh$_x$Bi$_2$ compounds become superconducting where critical temperature increases from $T_c=600$ mK for $x=0$ up to $T_c=2.7$ K for $x=0.35$. Furthermore we calculate the electronic band structure, using the structure parameters obtained. The calculated density of states (DOS) shows a minimum for the stochiometric compound at the Fermi level. These findings warrant further research by broader array of experimental techniques, as well as the effect of the substitution on the non-trivial band structure.

We have investigated the effect of potassium (K) intercalation on $2H$-MoS$_2$ using transmission electron energy-loss spectroscopy. For K concentrations up to approximately 0.4, the crystals appear to be inhomogeneous with a mix of structural phases and irregular potassium distribution. Above this intercalation level, MoS$_2$ exhibits a $2a \times 2a$ superstructure in the $ab$ plane and unit cell parameters of a = 3.20 $\unicode{x212B}$ and c = 8.23 $\unicode{x212B}$ indicating a conversion from the $2H$ to the $1T'$ or $1T''$ polytypes. The diffraction patterns also show a $\sqrt{3}a \times \sqrt{3}a$ and a much weaker $2\sqrt{3}a \times 2\sqrt{3}a$ superstructure that is very likely associated with the ordering of the potassium ions. A semiconductor-to-metal transition occurs signified by the disappearance of the excitonic features from the electron energy-loss spectra and the emergence of a charge carrier plasmon with an unscreened plasmon frequency of 2.78 eV. The plasmon has a positive, quadratic dispersion and appears to be superimposed with an excitation arising from interband transitions. The behavior of the plasmon peak energy positions as a function of potassium concentration shows that potassium stoichiometries of less than $\sim 0.3$ are thermodynamically unstable while higher stoichiometries up to $\sim 0.5$ are thermodynamically stable. Potassium concentrations greater than $\sim 0.5$ lead to the decomposition of MoS$_2$ and the formation of K$_2$S. The real part of the dielectric function and the optical conductivity of K$_{0.41}$MoS$_2$ were derived from the loss spectra via Kramers-Kronig analysis., Comment: 7 Figures, 2 Tables

We report an optimized chemical vapor transport method that enables the growth of FeP single crystals up to 500 mg in mass and $80\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{3}$ in volume. The high quality of the crystals obtained by this method was confirmed by means of energy-dispersive x-ray spectroscopy, high-resolution transmission electron microscopy, low-temperature single-crystal x-ray diffraction, and neutron diffraction experiments. We investigated the transport and magnetic properties of the single crystals, and we calculated the electronic structure of FeP. We show both theoretically and experimentally that the ground state of FeP is metallic. The examination of the magnetic data reveals antiferromagnetic order below ${T}_{\mathrm{N}}=119\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ while transport remains metallic in both the paramagnetic and the antiferromagnetic phase. The analysis of the neutron diffraction data shows an incommensurate magnetic structure with the propagation vector $\mathbf{Q}=(0,0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})$, where \ensuremath{\delta} is close to 0.2. For a full understanding of the magnetic state, further experiments are needed. The successful growth of large high-quality single crystals paves the way for further investigations of itinerant magnets with incommensurate spin structures using a wide range of experimental tools.

The reduced dimensionality in two-dimensional materials leads to a wealth of unusual properties, which are currently explored for both fundamental and applied sciences. In order to study the crystal structure, edge states, the formation of defects and grain boundaries, or the impact of adsorbates, high-resolution microscopy techniques are indispensable. Here we report on the development of an electron holography (EH) transmission electron microscopy (TEM) technique, which facilitates high spatial resolution by an automatic correction of geometric aberrations. Distinguished features of EH beyond conventional TEM imaging are gap-free spatial information signal transfer and higher dose efficiency for certain spatial frequency bands as well as direct access to the projected electrostatic potential of the two-dimensional material. We demonstrate these features with the example of h-BN, for which we measure the electrostatic potential as a function of layer number down to the monolayer limit and obtain evidence for a systematic increase of the potential at the zig-zag edges.

We introduce a three-step seed-mediated synthesis for single crystalline gold nanoparticles (Au NPs) stabilized by hexadecylpyridinium chloride (CPC) in variable sizes with an independently adjustable ratio of the cubic and octahedral facets. The effect of KBr and ascorbic acid (AA) on shape and growth kinetics is systematically investigated. The kinetic data were evaluated using the minimalistic Finke–Watzky autocatalytic two-step mechanism, which allows to estimate the rate constants of the “pseudoelementary” reactions. The proposed surface-mediated mechanism of reduction of gold ions and Au NP growth allows to explain the effect of gradual increase of bromide ion concentration on switching the Au NP morphology from cubic to octahedral. The plasmonic properties of single particles of different facetings and their assemblies are investigated.

Electron holographic tomography was used to obtain three-dimensional reconstructions of the morphology and electrostatic potential gradient of axial GaInP/InP nanowire tunnel diodes. Crystal growth was carried out in two opposite directions: GaInP-Zn/InP-S and InP-Sn/GaInP-Zn, using Zn as the p-type dopant in the GaInP but with changes to the n-type dopant (S or Sn) in the InP. Secondary electron and electron beam-induced current images obtained using scanning electron microscopy indicated the presence of p-n junctions in both cases and current-voltage characteristics measured via lithographic contacts showed the negative differential resistance, characteristic of band-to-band tunneling, for both diodes. Electron holographic tomography measurements confirmed a short depletion width in both cases (21 ± 3 nm) but different built-in potentials, Vbi, of 1.0 V for the p-type (Zn) to n-type (S) transition, and 0.4 V for both were lower than the expected 1.5 V for these junctions if degenerately doped. Charging induced by the electron beam was evident in phase images which showed nonlinearity in the surrounding vacuum, most severe in the case of the nanowire grounded at the p-type Au contact. We attribute their lower Vbi to asymmetric secondary electron emission, beam-induced current biasing, and poor grounding contacts.

Utilizing the Pauli equation based multislice method, introduced in Phys. Rev. Lett. 116, 127203 (2016), we study the atomic resolution differential phase contrast (DPC) imaging on an example of a hard magnet FePt with in-plane magnetization. Simulated center of mass pattern in a scanning transmission electron microscopy (STEM) experiment carries information about both electric and magnetic fields. The momentum transfer remains curl-free, which has consequences for interpretation of the integrated DPC technique. The extracted magnetic component of the pattern is compared to the expected projected microscopic magnetic field as obtained by density functional theory calculation. Qualitative agreement is obtained for low sample thicknesses and a suitable range of collection angles., 9 pages, 8 figures

Rubrene single crystal domains with hundreds of micrometers size fully covering different substrates are achieved by thermal annealing of evaporated amorphous thin films with the help of a thin glassy underlayer. The sufficiently large energy level offset of the underlayer material and rubrene enables high performance staggered bottom gate rubrene crystalline transistors with maximum field-effect linear mobility over 5 cm2V−1s−1 (μAvg = 4.35 ± 0.76 cm2V−1s−1) for short channel devices of 20 μm, comparable to high quality rubrene bulk single crystals. Moreover, since molecular dopants up to several mole percent can be incorporated into the single crystals with a minimal disturbance of the lattice, the contact resistance of the transistors is significantly reduced to around 1 kOhm.cm by contact doping via adlayer epitaxy of p-type doped rubrene. Our results pave the way for novel high-performance organic electronics using crystalline active materials with mass-production compatible deposition techniques.

Off-axis electron holography is a well-established transmission electron microscopy technique, typically employed to investigate electric and magnetic fields in and around nanoscale materials, which modify the phase of the reconstructed electron wave function. Here, we elaborate on a detailed analysis of the two characteristic intensity terms that are completing the electron hologram, the conventional image intensity and the interference fringe intensity. We show how both are related to elastic and inelastic scattering absorption at the sample and how they may be separated to analyze the chemical composition of the sample. Since scattering absorption is aperture dependent, a quantitative determination of the corresponding attenuation coefficients (reciprocal mean free path lengths) requires the use of holographic image modi with well-defined objective aperture stops in the back-focal plane of the objective lens. The proposed method extends quantitative electron holography to a correlated three-in-one characterization of electric and magnetic fields, Z-contrast and dielectric losses in materials.

Chains of metallic nanoparticles sustain strongly confined surface plasmons with relatively low dielectric losses. To exploit these properties in applications, such as waveguides, the fabrication of long chains of low disorder and a thorough understanding of the plasmon-mode properties, such as dispersion relations, are indispensable. Here, we use a wrinkled template for directed self-assembly to assemble chains of gold nanoparticles. With this up-scalable method, chain lengths from two particles (140 nm) to 20 particles (1500 nm) and beyond can be fabricated. Electron energy-loss spectroscopy supported by boundary element simulations, finite-difference time-domain, and a simplified dipole coupling model reveal the evolution of a band of plasmonic waveguide modes from degenerated single-particle modes in detail. In striking difference from plasmonic rod-like structures, the plasmon band is confined in excitation energy, which allows light manipulations below the diffraction limit. The non-degenerated surface plasmon modes show suppressed radiative losses for efficient energy propagation over a distance of 1500 nm. �� 2019 American Chemical Society.

Inspired by chains of ferrimagnetic nanocrystals (NCs) in magnetotactic bacteria (MTB), the synthesis and detailed characterization of ferrimagnetic magnetite NC chain-like assemblies is reported. An easy green synthesis route in a thermoreversible gelatin hydrogel matrix is used. The structure of these magnetite chains prepared with and without gelatin is characterized by means of transmission electron microscopy, including electron tomography (ET). These structures indeed bear resemblance to the magnetite assemblies found in MTB, known for their mechanical flexibility and outstanding magnetic properties and known to crystallographically align their magnetite NCs along the strongest magnetization easy axis. Using electron holography (EH) and angular dependent magnetic measurements, the magnetic interaction between the NCs and the generation of a magnetically anisotropic material can be shown. The electro- and magnetostatic modeling demonstrates that in order to precisely determine the magnetization (by means of EH) inside chain-like NCs assemblies, their exact shape, arrangement and stray-fields have to be considered (ideally obtained using ET). �� 2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Chemistry of materials 31(8), 2795 - 2806 (2019). doi:10.1021/acs.chemmater.8b05017, High-quality single crystals of MnBi2Te4 are grown for the first time by slow cooling within a narrow range between the melting points of Bi$_2$Te$_3$ (586 °C) and MnBi$_2$Te$_4$ (600 °C). Single-crystal X-ray diffraction and electron microscopy reveal ubiquitous antisite defects in both cation sites and, possibly, Mn vacancies (Mn$_{0.85(3)}$Bi$_{2.10(3)}$Te$_4$). Thermochemical studies complemented with high-temperature X-ray diffraction establish a limited high-temperature range of phase stability and metastability at room temperature. Nevertheless, the synthesis of MnBi$_2$Te$_4$ can be scaled-up as powders can be obtained at subsolidus temperatures and quenched at room temperature. Bulk samples exhibit long-range antiferromagnetic ordering below 24 K. The Mn(II) out-of-plane magnetic state is confirmed by the magnetization, X-ray photoemission, X-ray absorption, and linear dichroism measurements. The compound shows a metallic type of resistivity in the range 4.5–300 K and is an n-type conductor that reaches a thermoelectric figure of merit up to ZT = 0.17. Angle-resolved photoemission experiments show a surface state forming a gapped Dirac cone, thus strengthening MnBi$_2$Te$_4$ as a promising candidate for the intrinsic magnetic topological insulator, in accordance with theoretical predictions. The developed synthetic protocols enable further experimental studies of a crossover between magnetic ordering and nontrivial topology in bulk MnBi$_2$Te$_4$., Published by American Chemical Society, Washington, DC

Envisaged applications of Skyrmions in magnetic memory and logic devices crucially depend on the stability and mobility of these topologically nontrivial magnetic textures in thin films. We present for the first time quantitative maps of the magnetic induction that provide evidence for a 3D modulation of the Skyrmionic spin texture. The projected in-plane magnetic induction maps as determined from in-line and off-axis electron holography carry the clear signature of Bloch Skyrmions. However, the magnitude of this induction is much smaller than the values expected for homogeneous Bloch Skyrmions that extend throughout the thickness of the film. This finding can only be understood if the underlying spin textures are modulated along the out-of-plane $z$ direction. The projection of (the in-plane magnetic induction of) helices is further found to exhibit thickness-dependent lateral shifts, which show that this $z$ modulation is accompanied by an (in-plane) modulation along the $x$ and $y$ directions.

Thin TEM specimen are regarded as weak objects (WPO), if the amplitude variation of the electron wave by the specimen can be neglected and the phase modulation is very small (≪π). Large classes of topical materials can be described in this approximation, such as most 2D materials, organic semiconductor materials or biological specimen. Due to the lack of amplitude (and hence intensity) contrast, conventional TEM (CTEM) investigations on WPOs are commonly performed under a certain defocus, which transfers part of the phase information to the recorded intensity. This intermixing contrast transfer from amplitude to phase and vice versa is commonly described by the phase contrast transfer function (PCTF), while the non-mixing contrast transfer for amplitude and phase is referred to as amplitude contrast transfer function (ACTF). Due to the transfer gap in the PCTF, the CTEM contrast transfer at low spatial frequencies is degraded in defocused images of WPOs (Fig. 1). By employing electron holography, however, both amplitude and phase of the electron wave can be reconstructed without a transfer gap. Having the whole wave information also enables the a-posteriori correction of geometric aberrations as it was already proposed in D. Gabor’s seminal paper from 1948 [1]. The realization of his idea, however, remains challenging in the absence of additional knowledge about the sample, due to the lack of a criterion for a successful aberration correction.

This chapter gives a brief introduction into the history of holography and tomography as well as transmission electron microscopy. It is shown that all three concepts are closely linked and cross-fertilized each other in their development. Going one step further, the introduction provides a red ribbon on how holography and tomography may be combined in the transmission electron microscope to facilitate the 3D reconstruction of physical fields as well as quantum states as discussed in this volume.

Plasmonic nanostructures and -devices are rapidly transforming light manipulation technology by allowing to modify and enhance optical fields on sub-wavelength scales. Advances in this field rely heavily on the development of new characterization methods for the fundamental nanoscale interactions. However, the direct and quantitative mapping of transient electric and magnetic fields characterizing the plasmonic coupling has been proven elusive to date. Here we demonstrate how to directly measure the inelastic momentum transfer of surface plasmon modes via the energy-loss filtered deflection of a focused electron beam in a transmission electron microscope. By scanning the beam over the sample we obtain a spatially and spectrally resolved deflection map and we further show how this deflection is related quantitatively to the spectral component of the induced electric and magnetic fields pertaining to the mode. In some regards this technique is an extension to the established differential phase contrast into the dynamic regime., Characterizing plasmonic coupling has proven elusive. Here, the authors obtain a spectrally resolved deflection map related to a focused electron beam, which has excited a surface plasmon resonance, and relate this deflection to the spectral component of the induced electric and magnetic fields pertaining to the mode.

This chapter provides the foundations of paraxial quantum mechanics as valid for relativistic electrons traveling along the optical axis of a Transmission Electron Microscope. Starting point is a derivation of relativistic paraxial wave dynamics from first principles. This description is subsequently generalized to the concepts of the density operator and the quantum mechanical phase space, including their paraxial dynamics. Quantum mechanical phase space is represented by the Wigner function, simultaneously describing the properties of the electron beam in position and diffraction (Fourier) space. The phase space representation of the imaging process and the unified description of different holographic schemes discussed in Chapters 4 and 5 are founded in these principles.

Semiconductors with native ferromagnetism barely exist and defined nanostructures are almost unknown. This lack impedes the exploration of a new class of materials characterized by a direct combination of effects on the electronic system caused by quantum confinement effects with magnetism. A good example is EuO for which currently no reliable routes for nanoparticle synthesis can be established. Bottom-up approaches applicable to other oxides fail because of the labile oxidation state +II. Instead of targeting a direct synthesis, the two steps—“structure control” and “chemical transformation”—are separated. The generation of a transitional, hybrid nanophase is followed by its conversion into EuO under full conservation of all morphological features. Hierarchical EuO materials are now accessible in the shape of oriented nanodisks stacked to tubular particles. Magnetically, the coupling of either vortex or onion states has been found. An unexpected temperature dependence is governed by thermally activated transitions between these states. published

In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the Phase Grating Approximation, have reached their limits in current and forsee- able applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.

Off-axis electron holography (EH) is a powerful method for mapping projected electric potentials, such as built-in potentials in semiconductor devices, in two dimensions (2D) at nanometer resolution. However, not well-defined thickness profiles, surface effects, and composition changes of the sample under investigation complicate the interpretation of the projected potentials. Here, we demonstrate how these problems can be overcome by combining EH with tomographic techniques, that is, electron holographic tomography (EHT), reconstructing electric potentials in 3D. We present EHT reconstructions of an n-type MOSFET including its dopant-related built-in potentials inside the device, as well as of a GaAs/AlGaAs core-multishell nanowire containing a 5 nm thick quantum well tube.

Tomographic techniques play a crucial role in imaging methods such as transmission electron microscopy (TEM) due to their unique capabilities to reconstruct three-dimensional object information. However, the accuracy of the two standard tomographic reconstruction techniques, the weighted back-projection (W-BP) and the simultaneous iterative reconstruction technique (SIRT) is reduced under common experimental restrictions, such as limited tilt range or noise. We demonstrate that the combination of W-BP and SIRT leads to an improved tomographic reconstruction technique: the weighted SIRT. Convergence, resolution and reconstruction error of the W-SIRT are analyzed by a detailed analytical, numerical, and experimental comparison with established methods. Our reconstruction technique is not restricted to TEM tomography but can be applied to all problems sharing single axis imaging geometry.

The exact knowledge about intrinsic electrostatic potentials and in particular their three-dimensional distribution at the nanometer scale is a key prerequisite for understanding the solid state properties. Electron holographic tomography (EHT), the combination of off-axis holography with tomography in the transmission electron microscope, provides a unique access to this information. We review the development and application of automated EHT to reconstruct 3D potentials in nanostructures such as the mean inner potential of a material or the diffusion potential across p–n junctions in semiconductors. We also discuss future challenges of the 3D reconstruction of electric crystal potentials at atomic resolution and magnetostatic fields as well as ways to overcome present limitations of the method.

Based on a recent claim [Phys. Rev. Lett. 116, 127203 (2016)] that electron vortex can be used to image magnetism at the nanoscale in elastic scattering experiments, using transmission electron microscopy, a comprehensive computational study is performed to study magnetic effects in the paraxial regime of elastic electron scattering in magnetic solids. Magnetic interactions from electron vortex beams, spin polarized electron beams and beams with phase aberrations are considered, as they pass through ferromagnetic FePt or antiferromagnetic LaMnAsO. The magnetic signals are obtained by comparing the intensity over a disk in the diffraction plane for beams with opposite angular momentum or aberrations. The strongest magnetic signals are obtained from vortex beams with large orbital angular momentum, where relative magnetic signals above $10^{-3}$ are indicated for $10\hbar$ orbital angular momentum, meaning that relative signals of one percent could be expected with the even larger orbital angular momenta, which have been produced in experimental setups. All results indicate that beams with low acceleration voltage and small convergence angles yield stronger magnetic signals, which is unfortunately problematic for the possibility of high spatial resolution imaging. Nevertheless, under atomic resolution conditions, relative magnetic signals in the order of $10^{-4}$ are demonstrated, corresponding to an increase with one order of magnitude compared to previous work.

The loss of the quantum phase information in the measurement process constitutes a fundamental limitation to transmission electron microscopy as the electron wave's phase often contains valuable information about the studied specimen. Phase retrieval from focal series is a holographic technique that seeks to recover the lost information from a set of images recorded at different defoci. In spite of its widespread use, especially for wave reconstruction at atomic resolution, a number of fundamental properties (e.g., regarding the conditions for a unique wave function reconstruction) the magnitude of the reconstruction error and the influence of inconsistencies or incomplete data are not well understood. Here, we elaborate on the fundamentals of the technique, making extensive use of the tomographic representation of a focal series as tilt series in phase space. Using this perspective, we discuss, among others, requirements for the focal series for a unique reconstruction, such as the focus interval ranging from the far field at underfocus to the far field at overfocus or the focus step size. We reveal that the prominent Gerchberg–Saxton iterative projection algorithm corresponds to a numerical integration of the quantum Hamilton–Jacobi equation in the small focus step limit. Moreover, we show that the topology of the starting guess divides the solution space of the Gerchberg–Saxton algorithm into equivalence classes, which mitigates the impact of the incompleteness of typical focal series data. To facilitate a focal series reconstruction meeting these theoretical requirements, such as the long range focus interval, we develop a dedicated calibration procedure facilitating the determination of unknown electron optical parameters such as the focal length of the principal imaging lens or the position of object and image planes. The findings are demonstrated with an example of a focal series reconstruction of an electron vortex beam.

The use of phase plates in the back focal plane of a microscope is a well-established technique in optical microscopy to increase the contrast of weakly interacting samples and is gaining interest in electron microscopy as well. In this paper we study the spiral phase plate (SPP), also called helical, vortex, or two-dimensional Hilbert phase plate, which adds an angularly dependent phase of the form ${e}^{i\ensuremath{\ell}{\ensuremath{\phi}}_{k}}$ to the exit wave in Fourier space. In the limit of large collection angles, we analytically calculate that the average of a pair of $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ SPP filtered images is directly proportional to the gradient squared of the exit wave, explaining the edge contrast previously seen in optical SPP work. We discuss the difference between a clockwise-anticlockwise pair of SPP filtered images and derive conditions under which the modulus of the wave's gradient can be seen directly from one SPP filtered image. This work provides the theoretical background to interpret images obtained with a SPP, thereby opening new perspectives for new experiments to study, for example, magnetic materials in an electron microscope.

Electron vortex beams hold great promise for development in transmission electron microscopy, but have yet to be widely adopted. This is partly due to the complex set of interactions that occur between a beam carrying orbital angular momentum (OAM) and a sample. Herein, the system is simplified to focus on the interaction between geometrical symmetries, OAM and topology. We present multiple simulations, alongside experimental data to study the behaviour of a variety of electron vortex beams after interacting with apertures of different symmetries, and investigate the effect on their OAM and vortex structure, both in the far-field and under free-space propagation., Comment: 11 pages

We present the synthesis of Co2FeGa Heusler nanowires and the results of our investigations on their three-dimensional (3D) electric and magnetic internal and external fields mapped by electron holographic tomography (EHT). These fields will be of great importance in next-generation nanomagnets integrated in spintronics and memory devices. The Co2FeGa nanowires with a L21 ordered structure are prepared by a SBA-15 silica-assisted method. The magnetic dipole-like stray fields of several Co2FeGa nanowires are revealed by holographically reconstructed phase images. Based on the measured magnetic phase shifts of an individual nanowire and its 3D reconstruction using EHT, we obtain an internal magnetic induction with a magnitude of 1.15 T and a nonmagnetic surface layer of 10 nm thickness. Furthermore, we also reconstruct the 3D distribution of the electrostatic potential of the same nanowire.

Elastic scattering of electron vortex beams on magnetic materials leads to a weak magnetic contrast due to Zeeman interaction of orbital angular momentum of the beam with magnetic fields in the sample. The magnetic signal manifests itself as a redistribution of intensity in diffraction patterns due to a change of sign of the orbital angular moment. While in the atomic resolution regime the magnetic signal is most likely under the detection limits of present transmission electron microscopes, for electron probes with high orbital angular momenta, and correspondingly larger spatial extent, its detection is predicted to be feasible., Comment: 5 pages, 3 figures

cited By 0; International audience; We present the state of the art in strain mapping at the nanoscale using aberration - corrected high - resolution transmission electron microscopy, HRTEM and HAADF - STEM, and dark - field electron holography (DFEH) [1]. In particular, we will focus on the examination of localized strains around defects. A broader comparison of TEM strain mapping techniques can be found i n a recent review [2]. High - resolution images can be analysed by geometric phase analysis (GPA) [3] or applying peak - finding routines to determine the positions of individual atomic columns. GPA is best adapted to measuring the deformation of the crystall ine lattice, as the example concerning a five - fold twinned Pt nanoparticle will show (Figure 1). These star - shaped particles [4] have a disclination - like strain fields around their centres, as found for Au nanoparticles [5]. In multiferroic materials, peak - finding can be used to determine the relative displacements of atom columns within a unit cell [6]. The local polarization and strain can be mapped around dislocations and in the vicinity of domain walls (Figure 2). DFEH was developed to measure strain over wide fields of view to high precision and nanometre spatial resolution. We have nevertheless been applying the technique to the study of quantum dots to relatively high resolution [7]. As with any TEM technique the samples are necessarily thin which allows some of the strain to be relaxed: the well - known thin film effect. In addition, dynamical scattering effects the strain information [8]. These issues will be addressed using a combination of finite - element modelin g (FEM) and dynamical - scattering simulations. This overview will, in addition, show results from the recently installed I2TEM microscope (Hitachi), an instrument specifically designed for DFEH experiments and aberration - corrected HRTEM over wide fields of view and for in - situ experiments (Figure 3).

A model for a new electron vortex beam production method is proposed and experimentally demonstrated. The technique calls on the controlled manipulation of the degrees of freedom of the lens aberrations to achieve a helical phase front. These degrees of freedom are accessible by using the corrector lenses of a transmission electron microscope. The vortex beam is produced through a particular alignment of these lenses into a specifically designed astigmatic state and applying an annular aperture in the condensor plane. Experimental results are found to be in good agreement with simulations., 5 pages, 4 figures

The performance of ferroelectric devices, for example, the ferroelectric field effect transistor, is reduced by the presence of crystal defects such as edge dislocations. For example, it is well-known that edge dislocations play a crucial role in the formation of ferroelectric dead-layers at interfaces and hence finite size effects in ferroelectric thin films. The detailed lattice structure including the relevant electro- mechanical coupling mechanisms in close vicinity of the edge dislocations is, however, not well-understood, which hampers device optimization. Here, we investigate edge dislocations in ferroelectric BiFeO3 by means of spherical aberration-corrected scanning transmission electron microscopy, a dedicated model-based structure analysis, and phase field simulations. Unit-cell-wise resolved strain and polarization profiles around edge dislocation reveal a wealth of material states including polymorph nanodomains and multiple domain walls characteristically pinned to the dislocation. We locally determine the piezoelectric tensor and identify piezoelectric coupling as the driving force for the observed phenomena, explaining, for example, the orientation of the domain wall with respect to the edge dislocation. Furthermore, an atomic model for the dislocation core is derived.

International audience; The microstructure of ion-implanted crystals is profoundly dictated by mechanical strain developing in interplay with structural defects. Understanding the origin of strain during the early stages of development is challenging and requires accurate measurements and modeling. Here, we investigate the mechanical strain in H-implanted Si. X-ray diffraction analysis is performed to measure the mesoscopic out-of-plane strain and dark-field electron holography to map strain in two-dimensions (2D) with nanometer spatial resolution. Supported by finite element method modeling, we propose that the mean strain field is explained by overlapping and averaging discrete strain fields generated by sub-nanoscopic defects that are intimately related to the H depth concentration.

International audience; A novel generalized linear transfer theory describing the signal and noise transfer in image detectors has been developed in Part I (Niermann, this issue, [1]) of this paper. Similar to the existing notion of a point spread function (PSF) describing the transfer of the first statistical moment (the average), a noise spread function (NSF) was introduced to characterize the spatially resolved transfer of noise (central second moment, covariance). Following the theoretic results developed in Part I (Niermann, this issue, [1]), a new experimental method based on single spot illumination has been developed and applied to measure 2D point and 4D noise spread functions of CCD cameras used in TEM. A dedicated oversampling method has been used to suppress aliasing in the measured quantities. We analyze the 4D noise spread with respect to electronic and photonic noise contributions.

Electron holography in the transmission electron microscope (TEM) offers the spatial and signal resolution for studying effects like Fermi level pinning or dopant concentration variations important for the design of modern electronic devices. To overcome the loss of information along the projection direction, surface effects, and surface damage due to TEM specimen preparation, we apply electron holographic tomography to analyze the 3D potential distribution of semiconductor samples prepared by focused-ion-beam. We observe mid-band gap pinning of the Fermi level at Si surfaces but valence band pinning at Ge surfaces. The pinning extends over tens of nanometers into the bulk.

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals-Yoshioka-equations-based forward propagation and the reciprocal wave method-are founded in two conceptually differing schemes-a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z-locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.