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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., Comment: 7 pages, 5 figures

Envisaged applications of skyrmions in magnetic memory and logic devices crucially depend on the stability and mobility of these topologically non-trivial 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.

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.

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 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, that adds an angularly dependent phase of the form $e^{i\ell\phi}$ to the exit wave in Fourier space. In the limit of large collection angles, we analytically calculate that the average of a pair of $\ell=\pm1$ SPP images is directly proportional to the gradient squared of the exit wave, explaining the edge contrast previously seen in optical SPP work. The difference between a clockwise-anticlockwise pair of SPP images and conditions where this difference vanishes and the gradient of the exit wave can be seen from one single SPP image, are discussed. Finally, we demonstrate how with three images, one without and one with each of an $\ell=\pm1$ SPP, may give enough information to reconstruct both the amplitude and the phase of the exit wave. This work provides the theoretical background to interpret images obtained with a SPP and can help enable new experiments to study for example magnetic materials in an electron microscope., Comment: 7 pages, 4 figures

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

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

The phase problem can be considered as one of the cornerstones of quantum mechanics intimately connected to the detection process and the uncertainty relation. The latter impose fundamental limits on the manifold phase reconstruction schemes invented to date in particular at small magnitudes of the quantum wave. Here, we show that a rigorous solution of the Transport of Intensity Reconstruction (TIE) scheme in terms of a linear elliptic partial differential equation for the phase provides reconstructions even in the presence of wave zeros if particular boundary conditions (BCs) are given. We furthermore discuss how partial coherence hampers phase reconstruction and show that a modified version of the TIE reconstructs the curl-free current density at arbitrary (in-)coherence. This opens the way for a large variety of new applications in fields as diverse as astrophysics, geophysics, photonics, acoustics, and electron microscopy, where zeros in the respective wave field are a ubiquitous feature., Comment: 5 pages, 3 figures, includes correction as in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.199902

We investigate topological aspects of sub-nm electron vortex beams upon elastic propagation through atomic scattering potentials. Two main aspects can be distinguished: (i) Significantly reduced delocalization compared to a similar non-vortex beam if the beam centers on an atomic column and (ii) site symmetry dependent splitting of higher-order vortex beams. Furthermore, the results provide insight into the complex vortex line fabric within the elastically scattered wave containing characteristic vortex loops predominantly attached to atomic columns and characteristic twists of vortex lines around atomic columns., Comment: 10 pages, 6 figures

We report on the development of Electron Holographic Tomography towards a versatile potential measurement technique, overcoming several limitations, such as a limited tilt range, previously hampering a reproducible and accurate electrostatic potential reconstruction in three dimensions. Most notably, tomographic reconstruction is performed on optimally sampled polar grids taking into account symmetry and other spatial constraints of the nanostructure. Furthermore, holographic tilt series acquisition and alignment have been automated and adapted to three dimensions. We demonstrate 6 nm spatial and 0.2 V signal resolution by reconstructing various, previously hidden, potential details of a GaAs/AlGaAs core-shell nanowire. The improved tomographic reconstruction opens pathways towards the detection of minute potentials in nanostructures and an increase in speed and accuracy in related techniques such as X-ray tomography.

In TEM, a typical goal consists of making a small electron probe in the sample plane in order to obtain high spatial resolution in scanning transmission electron microscopy. In order to do so, the phase of the electron wave is corrected to resemble a spherical wave compensating for aberrations in the magnetic lenses. In this contribution we discuss the advantage of changing the phase of an electron wave in a specific way in order to obtain fundamentally different electron probes opening up new application in the (S)TEM. We focus on electron vortex states as a specific family of waves with an azimuthal phase signature and discuss their properties, production and applications. The concepts presented here are rather general and also different classes of probes can be obtained in a similar fashion showing that electron probes can be tuned to optimise a specific measurement or interaction.

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., Comment: 5 pages, 4 figures

We present a first-principles density functional study of the structural, electronic and magnetic properties of the ferroelectric domain walls in multiferroic BiFeO3. We find that domain walls in which the rotations of the oxygen octahedra do not change their phase when the polarization reorients are the most favorable, and of these the 109 degree domain wall centered around the BiO plane has the lowest energy. The 109 degree and 180 degree walls have a significant change in the component of their polarization perpendicular to the wall; the corresponding step in the electrostatic potential is consistent with a recent report of electrical conductivity at the domain walls. Finally, we show that changes in the Fe-O-Fe bond angles at the domain walls cause changes in the canting of the Fe magnetic moments which can enhance the local magnetization at the domain walls., Comment: 9 pages, 20 figures