Vorträge und Posterpräsentationen (mit Tagungsband-Eintrag):
S. Löffler, S. Sack, T. Schachinger:
"Electron vortices in solids - from crystalline to amorphous materials";
Vortrag: Microscopy Conference 2017,
Lausanne, Schweiz (eingeladen);
- 25.08.2017; in: "MC 2017 Lausanne - Microscopy Conference",
Introduction: Since their discovery [1,2], the interest in electron vortex beams (EVBs) has increased
dramatically. As their potential ranges from the detection of magnetic moments on the atomic scale  to
the manipulation of nanoparticles , they hold great promise for advances in many fields, particularly
physics and materials science. Most, if not all, future applications will use the interaction of EVBs with
samples. Therefore, it is vital to understand how such vortices are affected by materials.
Objectives: In this work, we are mostly concerned with the elastic scattering of EVBs in solids as the
inelastic interaction can readily be described using the mixed dynamic form factor (MDFF) approach
commonly used, e.g., in energy-loss magnetic chiral dichroism (EMCD). The elastic scattering has
already been studied to some extent for crystalline materials [5,6], where a transfer of orbital angular
momentum (OAM) and a significant deviation from OAM eigenstates was found. Here, we extend this
investigation to amorphous materials which are of huge practical importance. For example, due to the
lack of periodicity, classical EMCD is not possible with amorphous materials - but EVB-EMCD is,
provided that elastic scattering does not alter the probe electrons wave function substantially.
Materials and Methods: To investigate the propagation of the probe electron, we use the multislice
approach. On the one hand, we develop a general and unified theoretical framework based on the
multislice equation in cylindrical coordinates to derive conditions under which OAM is exchanged with the
sample, thus turning an Lz eigenstate into a coherent superposition of components with different OAM.
On the other hand, we use numerical simulations for common materials such as Si to elucidate the
underlying physics and support the theoretical calculations.
Results: As shown in Fig. 1, the expectation value of the Lz operator does not deviate much from the
nominal value of 1 ħ for reasonably thin amorphous specimens in stark contrast to the crystalline case
. At the same time, the contribution of the m=1 eigenstate steadily decreases while other orders
emerge. Due to the very similar contributions of m=1+Δm and m=1-Δm, the overall expectation value
remains nearly unchanged. These other OAM components can, however, influence the performance of
EMCD, nanoparticle manipulation, and similar techniques. For reasonably thin Si and atom-sized vortex
beams (Fig. 1), the decrease in m=1 intensity is not too dramatic, but for heaver elements and/or
different densities, stronger deviations are found. In addition, the convergence/divergence angle plays a
crucial role as differently-sized EVBs scatter differently.
Conclusion: In this work, we have investigated the elastic scattering behavior of electron vortex beams in
solids. Going from crystalline to amorphous materials, we have developed a general, unified theory
based on the multislice approach and performed numerical simulations. This gives new insights into the
behavior of EVBs and paves the way for their efficient use in novel, emerging techniques such as EVBEMCD
or nanoparticle manipulation. 
Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.