Stefan Löffler

Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction.

By focusing electrons on probes with a diameter of 50 pm, aberration-corrected scanning transmission electron microscopy (STEM) is currently crossing the border to probing subatomic details. A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field-induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright-field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary GaN as an ideal model system. We then present a detailed experimental study of SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. With this interpretation and upgraded instrumentation, STEM is capable of quantifying atomic electric fields and high-contrast imaging of light atoms.

Is magnetic chiral dichroism feasible with electron vortices

We discuss the feasibility of detecting magnetic transitions with focused electron vortex probes, suggested by selection rules for the magnetic quantum number. We theoretically estimate the dichroic signal strength in the L2,3 edge of ferromagnetic d metals. It is shown that under realistic conditions, the dichroic signal is undetectable for nanoparticles larger than ∼1nm. This is confirmed by a key experiment with nanometer-sized vortices.

Ultrafast VLS growth of epitaxial β-Ga2O3 nanowires

Well-defined monoclinic nanostructures of beta- Ga(2)O(3) were grown in a chemical vapor deposition apparatus using metallic gallium and oxygen as sources. Stable growth conditions were deduced for nanorods, nanoribbons, nanowires and cones. The types of nanostructures are determined by the growth temperature. We suppose that the vapor-solid growth mechanism rules the growth of nanoribbons and rods. For the nanowires we observed catalytic gold droplets atop, characteristic for the VLS growth mechanism with an extremely high growth rate of up to 10 microm min(-1). Nanowires grown on Al(2)O(3) substrates showed an excellent tendency to grow epitaxially, mapping the hexagonal symmetry of Al(2)O(3)(0001).

Imaging the dynamics of free-electron Landau states

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.

Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy

This study sheds light on the prerequisites, possibilities, limitations and interpretation of high-resolution differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). We draw particular attention to the well-established DPC technique based on segmented annular detectors and its relation to recent developments based on pixelated detectors. These employ the expectation value of the momentum transfer as a reliable measure of the angular deflection of the STEM beam induced by an electric field in the specimen. The influence of scattering and propagation of electrons within the specimen is initially discussed separately and then treated in terms of a two-state channeling theory. A detailed simulation study of GaN is presented as a function of specimen thickness and bonding. It is found that bonding effects are rather detectable implicitly, e.g., by characteristics of the momentum flux in areas between the atoms than by directly mapping electric fields and charge densities. For strontium titanate, experimental charge densities are compared with simulations and discussed with respect to experimental artifacts such as scan noise. Finally, we consider practical issues such as figures of merit for spatial and momentum resolution, minimum electron dose, and the mapping of larger-scale, built-in electric fields by virtue of data averaged over a crystal unit cell. We find that the latter is possible for crystals with an inversion center. Concerning the optimal detector design, this study indicates that a sampling of 5mrad per pixel is sufficient in typical applications, corresponding to approximately 10×10 available pixels.

Circular dichroism in the electron microscope: Progress and applications "invited…

According to theory, x-ray magnetic circular dichroism in a synchrotron is equivalent to energy loss magnetic chiral dichroism (EMCD) in a transmission electron microscope (TEM). After a synopsis of the development of EMCD, the theoretical background is reviewed and recent results are presented, focusing on the study of magnetic nanoparticles for ferrofluids and Heusler alloys for spintronic devices. Simulated maps of the dichroic strength as a function of atom position in the crystal allow evaluating the influence of specimen thickness and sample tilt on the experimental EMCD signal. Finally, the possibility of direct observation of chiral electronic transitions with atomic resolution in a TEM is discussed.

Sub-nanometer free electrons with topological charge

The holographic mask technique is used to create freely moving electrons with quantized angular momentum. With electron optical elements they can be focused to vortices with diameters below the nanometer range. The understanding of these vortex beams is important for many applications. Here, we produce electron vortex beams and compare them to a theory of electrons with topological charge. The experimental results show excellent agreement with simulations. As an immediate application, fundamental experimental parameters like spherical aberration and partial coherence are determined.

Breakdown of the dipole approximation in core losses

The validity of the dipole approximations commonly used in the inelastic scattering theory for transmission electron microscopy is reviewed. Both experimental and numerical arguments are presented, emphasizing that the dipole approximations cause significant errors of the order of up to 25% even at small momentum transfer. This behavior is attributed mainly to non-linear contributions to the dynamic form factor due to the overlap of wave functions.

Elastic propagation of fast electron vortices through crystals

Stefan Löffler and Peter Schattschneider 2 Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria∗ University Service Center for Transmission Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria Abstract The propagation of electron beams carrying angular momentum in crystals is studied using a multislice approach for the model system Fe. It is found that the vortex beam is distorted strongly due to elastic scattering. Consequently, the expectation value of the angular momentum as well as the local vortex components change with the initial position of the vortex and the propagation depth, making numerical simulations indispensable when analyzing experiments.The propagation of electron beams carrying angular momentum in crystals is studied using a multislice approach for the model system Fe. It is found that the vortex beam is distorted strongly due to elastic scattering. Consequently, the expectation value of the angular momentum as well as the local vortex components change with the initial position of the vortex and the propagation depth, making numerical simulations indispensable when analysing experiments.

A pure state decomposition approach of the mixed dynamic form factor for mapping atomic orbitals

We demonstrate how the mixed dynamic form factor (MDFF) can be interpreted as a quadratic form. This makes it possible to use matrix diagonalization methods to reduce the number of terms that need to be taken into account when calculating the inelastic scattering of electrons in a crystal. It also leads in a natural way to a new basis that helps elucidate the underlying physics. The new method is applied to several cases to show its versatility. In particular, predictions are made for directly imaging atomic orbitals in crystals.