Peter Schattschneider

TU Wien | TU Wien · Institute of Solid State Physics

Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or of a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as com...

The topological charge m of vortex electrons spans an infinite-dimensional Hilbert space. Selecting a two-dimensional subspace spanned by m = ± 1 , a beam electron in a transmission electron microscope (TEM) can be considered as a quantum bit (qubit) freely propagating in the column. A combination of electron optical quadrupole lenses can serve as...

Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compar...

The topological charge $m$ of vortex electrons spans an infinite-dimensional Hilbert space. Selecting a two-dimensional subspace spanned by $m=\pm 1$, a beam electron in a transmission electron microscope (TEM) can be considered as a quantum bit (qubit) freely propagating in the column. A combination of electron optical cylinder lenses can serve as...

The established technique of electron energy-loss spectrometry (EELS) in the electron microscope has surpassed the task of chemical microanalysis. Some aspects of EELS, such as low energy losses for optical studies, have a long tradition and we see them re-emerge after a long period of oblivion. Other aspects such as coherence of inelastically scat...

In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called π/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in commercial transmission electron microscope (T...

In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called $\pi$/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in electron optics. A viable work-around are...

Energy-loss magnetic chiral dichroism (EMCD) is a versatile method for measuring magnetism down to the atomic scale in transmission electron microscopy (TEM). As the magnetic signal is encoded in the phase of the electron wave, any process distorting this characteristic phase is detrimental for EMCD. For example, elastic scattering gives rise to a...

The increasing importance of phase shaping in electron microscopy, including holographic masks and mode converters, justifies a reconsideration of electron wave propagation in magnetic lenses. The standard procedure, proposed by Glaser in 1952, needs a two-step procedure — the parameters needed in the propagator must be obtained beforehand via ray...

We propose to use the topological charge instead of the spin variable to span a two-dimensional Hilbert space for beam electrons in a transmission electron microscope (TEM). In this basis, an electron can be considered as a qbit freely floating in vacuum. We show how a combination of magnetic quadrupoles with a magnetic drift tube can serve as a un...

In optics, mode conversion is an elegant way to switch between Hermite Gaussian and Laguerre Gaussian beam profiles and thereby impart orbital angular momentum onto the beam and to create vortices. In optics such vortex beams can be produced in a setup consisting of two identical cylinder lenses. In electron optics, quadrupole lenses can be used fo...

Treating Coulomb scattering of two free electrons in a stationary approach, we explore the momentum and spin entanglement created by the interaction. We show that a particular discretisation provides an estimate of the von Neumann entropy of the one-electron reduced density matrix from the experimentally accessible Shannon entropy. For spinless dis...

In optics, mode conversion is an elegant way to switch between Hermite Gaussian and Laguerre Gaussian beam profiles and thereby impart orbital angular momentum onto the beam and to create vortices. In optics such vortex beams can be produced in a setup consisting of two identical cylinder lenses. In electron optics, quadrupole lenses can be used fo...

Treating Coulomb scattering of two free electrons in a stationary approach, we explore the momentum and spin entanglement created by the interaction. We show that a particular discretisation provides an estimate of the von Neumann entropy of the one-electron reduced density matrix from the experimentally accessible Shannon entropy. For spinless dis...

Interaction of the probe with the specimen in an electron microscope inevitably leads to entanglement between the probe and the scatterer. In spite of the importance of entanglement in many areas of modern physics, this subject has not been touched in the literature. Here, we develop some ideas about entanglement in electron microscopy for a number...

Zusammenfassung Elektronenvortices sind junge Spieler auf dem weiten Gebiet der Teilchen‐ und Festkörperphysik mit enormem Entwicklungspotenzial. Wie optische Vortices tragen sie Bahndrehimpuls. Da sie im Elektronenmikroskop auf atomare Dimensionen fokussiert werden können, ähneln sie frei im Raum propagierenden Atomorbitalen. Im Magnetfeld erlaube...

The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100 %. Increasing the detector size, the polarisat...

We discuss the feasibility of detecting spin polarized electronic transitions with a vortex filter. This approach does not rely on the principal condition of the standard electron energy-loss magnetic chiral dichroism (EMCD) technique, the precise alignment of the crystal in order to use it as a beam splitter, and thus would pave the way for the ap...

Circular dichroism is related to some physical property of a medium with handedness. For instance, magnetism breaks the symmetry of the interaction of matter with left- and right-handed circularly polarized photons. This effect is routinely used in the synchrotron-based X-ray magnetic circular dichroism (XMCD) technique for the study of magnetic ma...

Electron energy‐loss magnetic chiral dichroism (EMCD), which is the electron wave analogue of X‐ray magnetic circular dichroism (XMCD), offers the possibility to study magnetic properties at the nanoscale in a TEM. The relatively young method of EMCD [1] was already refined to such an extent that it is possible to probe magnetic moments of thin fil...

The world as we know it is shaped by electronic states. Be it optical, electrical, or magnetic properties, thermal conductivity, or chemical bonding: almost all macroscopic properties can be traced back to the electronic states on the nanoscale. It is all the more surprising that they remained mostly elusive from an experimental perspective so far....

Sr 14‐x Ca x Cu 24 O 41 is a fascinating member in the family of cuprates, not only because of its peculiar crystal structure where two distinct units, corner‐shared CuO 2 chains and edge‐shared Cu 2 O 3 ladders, coexist within the unit cell but also because it is the only known superconductor with a non two‐dimensional CuO 2 plane structure. Indee...

Holographic masks (HMs) with dislocation gratings placed in the condenser system of a TEM have been proven to be a reliable and robust method to impart quantized orbital angular momentum (OAM), as well as quantized magnetic moment onto the imaging electrons [1]. These so‐called electron vortex beams (EVBs) gathered a lot of attention due to some un...

The image intensity in high-angle annular dark field STEM images shows a strong chemical sensitivity. As it is also influenced by specimen thickness, crystal orientation as well as characteristics of illumination and detector, a standard-free quantification of composition requires a comparison with accurate image simulation, for which we use the fr...

The electrons' wavefront can be arbitrarily shaped by placing holographic masks (HMs) in the condenser system of a TEM. Using HMs with dislocation gratings, it is possible to impart quantized orbital angular momentum (OAM), as well as quantized magnetic moment onto the imaging electrons [1]. Due to their OAM, some peculiar effects can be observed f...

Spin filtering of an unpolarized beam in a TEM is a fascinating field of research. Bohr conjectured that it is impossible to spin filter an electron beam or, using Bohr words, “to observe the spin of the electron, separated fully from its orbital momentum, by means of experiments based on the concept of classical particle trajectories”[1]. However,...

Energy loss magnetic chiral dichroism (EMCD), established in 2006 [1] celebrates its 10 th anniversary. EMCD is the TEM equivalent of the X‐ray magnetic circular dichroism (XMCD) technique routinely applied on synchrotron beam lines for the study of magnetic moments. The EMCD signal is detected as an asymmetry in the energy filtered diffraction pat...

Despite the statement of Bohr and Pauli that Stern‐Gerlach based spin separation for electrons cannot work [1], it has been argued that spin separation or filtering of electrons is possible in particular geometries [2,3]. The argument has been debated, see e.g. [4], and it seems that the effect exists but is too small to be exploited with present d...

Electron energy-loss magnetic chiral dichroism (EMCD) allows for the quantification of magnetic properties of materials at the nanometer scale. It is shown that with the support of simulations that help to identify the optimal conditions for a successful experiment and upon implementing measurement routines that effectively reduce the noise floor,...

Transmission electron microscopy has been a promising candidate for mapping atomic orbitals for a long time. Here, we explore its capabilities by a first-principles approach. For the example of defected graphene, exhibiting either an isolated vacancy or a substitutional nitrogen atom, we show that three different kinds of images are to be expected,...

Measurement of Atomic Electric Fields by Scanning Transmission Electron Microscopy (STEM) Employing Ultrafast Detectors - Volume 22 Issue S3 - Knut Müller-Caspary, Florian F. Krause, Armand Béché, Martial Duchamp, Marco Schowalter, Stefan Löffler, Vadim Migunov, Florian Winkler, Martin Huth, Robert Ritz, Sebastian Ihle, Martin Simson, Henning Ryll,...

Quantifying Magnetism on the nm Scale: EMCD on Individual FePt Nanoparticles - Volume 22 Issue S3 - Sebastian Schneider, Darius Pohl, Stefan Löffler, Deepa Kasinathan, Jan Rusz, Peter Schattschneider, Ludwig Schultz, Bernd Rellinghaus

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on the {\AA}ngstr\"om scale in bulk ruti...

Energy-loss magnetic chiral dichroism (EMCD) allows for the quantification of magnetic properties of materials at the nanometer scale. It is shown that with the support of simulations that help to identify the optimal conditions for a successful experiment and upon implementing measurement routines that effectively reduce the noise floor, EMCD meas...

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 b...

Understanding the physical properties of the chain-ladder Sr3Ca11Cu24O41 hole-doped superconductor has been precluded by the unknown hole distribution among chains and ladders. We use electron energy-loss spectrometry (EELS) in a scanning transmission electron microscope (STEM) at atomic resolution to directly separate the contributions of chains a...

We report the high-resolution electron Compton profiles of graphite along three main crystallographic directions of [101¯0], [112¯0], and [0001] by recording electron energy-loss spectra at a large momentum transfer using a transmission electron microscope. A significant anisotropy is observed. The experimental results are in good agreement with th...

The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized. In the limit of infinitely small detectors on axis, the spin polarisation tends to 100 % . Increasing the detector size, the polarisation decreases rapi...

The Surprising Dynamics of Electron Vortex Beams - Volume 21 Issue S3 - Stefan Loffler, Thomas Schachinger, Michael Stoger-Pollach, Peter Schattschneider

Aberration corrected STEM-EELS study of the hole distribution in cuprate superconductors - Volume 21 Issue S3 - M. Bugnet, G. Radtke, S. Loffler, P. Schattschneider, D. Hawthorn, G. A. Sawatzky, G. A. Botton

Standard electron optics predicts Larmor image rotation in the magnetic lens field of a TEM. Introducing the possibility to produce electron vortex beams with quantized orbital angular momentum brought up the question of their rotational dynamics in the presence of a magnetic field. Recently, it has been shown that electron vortex beams can be prep...

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 fi...

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 dyn...

A Comment on the Letter by S. Lloyd et al., Phys. Rev. Lett. 109, 254801 (2012).

The validity of some assumptions included in the theoretical basis of several x-ray methods for the determination of concentration spectra in inhomogeneous solids, is analysed critically by theoretical considerations.

The analysis of X-ray reflections allows for the determination of the grain dimension in the direction of the bisector of the incident and scattered radiation. It is shown that correct results will be obtained only as long as the grain dimensions perpendicular to this direction are sufficiently large. The possible errors are estimated. The conditio...

A general expression for x-ray interference profiles of a binary alloy showing crystals of different concentration and thus different lattice dimensions is deduced. This expression contains previously reported relations as special cases, which are discussed briefly. It is not restricted to systems of total solid solubility or cubic lattice.

Oriented attachment has created a great debate about the description of crystal growth throughout the last decade. This aggregation-based model has successfully described biomineralization processes as well as forms of inorganic crystal growth, which could not be explained by classical crystal growth theory. Understanding the nanoparticle growth is...

Both the unoccupied and ground electronic states of graphite have been studied by electron energy-loss spectroscopy in a transmission electron microscope. Electron energy-loss near-edge structures of the K-edge of carbon have been investigated in detail for scattering angles from 0 to 2.8 mrad. The π* and σ* components were separated. The angular a...

The origin of post-peak spectra in electron energy loss near edge structure (ELNES) spectra of pure Ni and NiO is investigated through ab initio calculation. Contrary to the general view that post-peak spectra in ELNES are generated by transitions to continuum states, it is found that orbit hybridization is the main cause of post-peak spectra in th...

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 nanopa...

It was claimed (Lloyd et al., PRL 108 (2012) 074802) that energy loss magnetic chiral dichroism (EMCD) with electron vortex beams is feasible, and has even advantages over the standard setup with Bragg diffracted waves. In this Comment, we show that Lloyd et al. ignored an important constraint on the proposed selection rule for the transfer of angu...

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 el...

Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused by using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field...

Magnetic Circular Dichroism (MCD) is a phenomenon that occurs in magnetic materials whereby the intensity of transitions from core states to available states above the Fermi energy depends on the circular polarization of the exciting radiation. This is due to the fact that spin-orbit coupling breaks the degeneracy of core states with different tota...

Nanoparticle syntheses utilizing biomimetic approaches have advanced in recent years. Polypeptides, with their ability to influence inorganic crystal growth, are a topic of great interest. Their effect on the particle formation has not been completely understood yet. Here we report a bioinspired synthesis of cobalt ferrite nanoparticles carried out...

We report site-specific energy loss magnetic dichroism measurements of the technologically interesting Heusler alloy Ni2MnSn. In addition, we confirm the theoretical prediction that under certain conditions, two different atoms on inequivalent lattice sites give dichroic signals with opposite signs. With this, it is possible to distinguish the magn...

We investigate the influence of the film thickness on the martensitic transformation for the example of Ni-Mn-Sn thin films. Epitaxial films with thicknesses ranging from 100 nm down to 10 nm were deposited on MgO by co-sputtering on heated substrates. The martensitic transformation is investigated using temperature dependent x-ray diffraction, mag...

A mode converter for electron vortex beams is described. Numerical simulations, confirmed by experiment, show that the converter transforms a vortex beam with topological charge $m=\pm 1$ into beams closely resembling Hermite-Gaussian HG$_{10}$ and HG$_{01}$ modes. The converter can be used as a mode discriminator or filter for electron vortex beam...

The density of states and the energy loss near-edge structure of the oxygen K edge in NiO are calculated using different models for the exchange-correlation functional. The results are compared to each other and to experimentally acquired energy loss spectra. It is found that only when using the modified Becke-Johnson potential are the calculated s...

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...

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions,...

In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These...

The coupling between Angstrom-sized electron probes and spin polarised electronic transitions shows that the inelastically scattered probe is in a mixed state containing electron vortices with non-zero orbital angular momentum. These electrons create an asymmetric intensity distribution in energy filtered diffraction patterns, giving access to maps...

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 th...

Electron vortex beams were only recently discovered and their potential as a probe for magnetism in materials was shown. Here we demonstrate a method to produce electron vortex beams with a diameter of less than 1.2 angstrom. This unique way to prepare free electrons to a state resembling atomic orbitals is fascinating from a fundamental physics po...

Inversion procedures for the recovery of inelastic single scattering probabilities from energy loss spectra are reviewed. It is shown that all three procedures in question (termed Fourier, convolution and matrix approach, respectively) yield unique solutions. Conditions of convergence are compared. From numerical and experimental considerations it...

SUMMARYA recently developed method based on matrix analysis for the removal of plural scattering from angle-resolved energy loss spectra is tested. A single loss function, Lorentzian in the energy and Gaussian in the angular variable is assumed as input for the test. Multiple scattering probabilities are simulated by summing up n-fold self-convolut...

The recent creation of electron vortex beams and their first practical application motivates a better understanding of their properties. Here, we develop the theory of free electron vortices with quantized angular momentum, based on solutions of the Schrödinger equation for cylindrical boundary conditions. The principle of transformation of a plane...