P. Schattschneider

Production and application of electron vortex beams

Vortex beams (also known as beams with a phase singularity) consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Vortex photon beams are widely used in applications such as optical tweezers to manipulate micrometre-sized particles and in micro-motors to provide angular momentum, improving channel capacity in optical and radio-wave information transfer, astrophysics and so on. Very recently, an experimental realization of vortex beams formed of electrons was demonstrated. Here we describe the creation of vortex electron beams, making use of a versatile holographic reconstruction technique in a transmission electron microscope. This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope. We demonstrate how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties. Our results show that electron vortex beams hold promise for new applications, in particular for analysing and manipulating nanomaterials, and can be easily produced.

Detection of magnetic circular dichroism using a transmission electron microscope

A material is said to exhibit dichroism if its photon absorption spectrum depends on the polarization of the incident radiation. In the case of X-ray magnetic circular dichroism (XMCD), the absorption cross-section of a ferromagnet or a paramagnet in a magnetic field changes when the helicity of a circularly polarized photon is reversed relative to the magnetization direction. Although similarities between X-ray absorption and electron energy-loss spectroscopy in a transmission electron microscope (TEM) have long been recognized, it has been assumed that extending such equivalence to circular dichroism would require the electron beam in the TEM to be spin-polarized. Recently, it was argued on theoretical grounds that this assumption is probably wrong. Here we report the direct experimental detection of magnetic circular dichroism in a TEM. We compare our measurements of electron energy-loss magnetic chiral dichroism (EMCD) with XMCD spectra obtained from the same specimen that, together with theoretical calculations, show that chiral atomic transitions in a specimen are accessible with inelastic electron scattering under particular scattering conditions. This finding could have important consequences for the study of magnetism on the nanometre and subnanometre scales, as EMCD offers the potential for such spatial resolution down to the nanometre scale while providing depth information—in contrast to X-ray methods, which are mainly surface-sensitive.

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.

First-principles theory of chiral dichroism in electron microscopy applied to 3d ferromagnets

Recently it was demonstrated [Schattschneider , Nature 441, 486 (2006)], that an analog of the x-ray magnetic circular dichroism experiment can be performed with the transmission electron microscope. The new phenomenon has been named energy-loss magnetic chiral dichroism. In this work we present a detailed ab initio study of the chiral dichroism in the Fe, Co, and Ni transition elements. We discuss the methods used for the simulations together with the validity and accuracy of the treatment, which, in principle, can apply to any given crystalline specimen. The dependence of the dichroic signal on the sample thickness, accuracy of the detector position, and the size of convergence and collection angles are calculated.

The orientation dependent simulation of ELNES

We describe a program that allows the simulation of energy-loss near edge structure (ELNES). As an extension to the WIEN97 package (a full potential linearized augmented plane wave package for calculating crystal properties) [1] it permits to separate different contributions to the inelastic scattering cross section according to the character of the final state, explicitly taking into account projection onto scattering vector and integration over collection and convergence angle. Thus the program facilitates analysis of ELNES under precisely defined experimental conditions, and allows the investigation of anisotropic effects in ELNES from crystal structures. Dipole-allowed as well as dipole-forbidden transitions can be analyzed with this program.

A proposal for dichroic experiments in the electron microscope

Building upon the similarities between inelastic electron scattering and X-ray absorption we show that dichroism can be observed in electron energy loss spectrometry (EELS) in the transmission electron microscope (TEM). Natural or magnetic linear dichroism can be studied in electron scattering experiment with definite wave vector transfer in the interaction.The detection of circular dichroism in the TEM relies on interferometric EELS in a particular scattering geometry that allows extraction of the mixed dynamic form factor from energy loss spectra. Similarities between dichroic signals in energy loss near edge structures and X-ray absorption near edge structures are discussed, and a new experimental setup for dichroic measurements in the TEM is proposed.

Experimental application of sum rules for electron energy loss magnetic chiral dichroism

We present a derivation of the orbital and spin sum rules for magnetic circular dichroic spectra measured by electron energy loss spectroscopy in a transmission electron microscope. These sum rules are obtained from the differential cross section calculated for symmetric positions in the diffraction pattern. Orbital and spin magnetic moments are expressed explicitly in terms of experimental spectra and dynamical diffraction coefficients. We estimate the ratio of spin to orbital magnetic moments and discuss first experimental results for the Fe L2,3 edge.

The physical significance of the mixed dynamic form factor

We show that the mixed dynamic form factor for inelastic scattering of fast electrons in crystals is closely related to the density matrix of the probe electron and to that of the scatterer. With this insight it is possible to calculate both energy filtered diffraction patterns and energy spectroscopic high-resolution images. As an example we discuss the Si-K and -L edges.

Atomic scale electron vortices for nanoresearch

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 A. This unique way to prepare free electrons to a state resembling atomic orbitals is fascinating from a fundamental physics point of view and opens the road for magnetic mapping with atomic resolution in an electron microscope.

Improvement of energy loss near edge structure calculation using Wien2k

The density functional theory (DFT) is a recognised method for the calculation of electronic properties of materials. As such it can also be used for the calculation of energy loss near edge structures. Some care has to be taken since the DFT is intended for ground state calculation. The effect of the core hole left by the excited electron is different in an insulator and in a metal and can be observed in both cases. For an insulator (MgO, Si), a supercell calculation is needed while in the case of copper, extremely good agreement with experiment can be obtained with a partial core hole calculation. In the particular case of the WIEN code (APW method) we show that calculation of low lying edges (Si L at 99eV) where the initial state is not strongly localised can only be done within the dipole approximation and with some care. Random alloys (CuNi) have been calculated previously using a supercell; we show that a particular version of the virtual crystal approximation gives promising results.