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.

Both classical and quantum waves can form vortices: with helical phase fronts and azimuthal current densities. These features determine the intrinsic orbital angular momentum carried by localized vortex states. In the past 25 years, optical vortex beams have become an inherent part of modern optics, with many remarkable achievements and applications. In the past decade, it has been realized and demonstrated that such vortex beams or wavepackets can also appear in free electron waves, in particular, in electron microscopy. Interest in free-electron vortex states quickly spread over different areas of physics: from basic aspects of quantum mechanics, via applications for fine probing of matter (including individual atoms), to high-energy particle collision and radiation processes. Here we provide a comprehensive review of theoretical and experimental studies in this emerging field of research. We describe the main properties of electron vortex states, experimental achievements and possible applications within transmission electron microscopy, as well as the possible role of vortex electrons in relativistic and high-energy processes. We aim to provide a balanced description including a pedagogical introduction, solid theoretical basis, and a wide range of practical details. Special attention is paid to translate theoretical insights into suggestions for future experiments, in electron microscopy and beyond, in any situation where free electrons occur.

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.

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.