Observation of nanoscale magnetic fields using twisted electron beams

Structured electrons with chiral mass and charge

Chirality is a phenomenon with widespread relevance in fundamental physics, material science, chemistry, optics, and spectroscopy. In this work, we show that a free electron can be converted by the field cycles of laser light into a right-handed or left-handed coil of mass and charge. In contrast to phase-vortex beams, our electrons maintained a flat de Broglie wave but obtained their chirality from the shape of their expectation value in space and time. Measurements of wave function densities by attosecond gating revealed the three-dimensional shape of coils and double coils with left-handed or right-handed pitch. Engineered elementary particles with such or related chiral geometries should be useful for applications in chiral sensing, free-electron quantum optics, particle physics or electron microscopy.

Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy

In a scanning transmission electron microscope (STEM), producing a high-resolution image generally requires an electron beam focused to the smallest point possible. However, the magnetic lenses used to focus the beam are unavoidably imperfect, introducing aberrations that limit resolution. Modern STEMs overcome this by using hardware aberration correctors comprised of many multipole elements, but these devices are complex, expensive, and can be difficult to tune. We demonstrate a design for an electrostatic phase plate that can act as an aberration corrector. The corrector is comprised of annular segments, each of which is an independent two-terminal device that can apply a constant or ramped phase shift to a portion of the electron beam. We show the improvement in image resolution using an electrostatic corrector. Engineering criteria impose that much of the beam within the probe-forming aperture be blocked by support bars, leading to large probe tails for the corrected probe that sample the specimen beyond the central lobe. We also show how this device can be used to create other STEM beam profiles such as vortex beams and probes with a high degree of phase diversity, which improve information transfer in ptychographic reconstructions.

The influence of residual plural scattering after deconvolution in electron magnetic chiral dichroism

This work investigated the existence and influence of residual plural scattering in electron magnetic chiral dichroism (EMCD) spectra. A series of low-loss, conventional core-loss, and q-resolved core-loss spectra at Fe-L2,3 edges were detected from areas of different thicknesses in a plane-view sample of Fe/MgO (001) thin film. It reveals by comparison that there remains noticeable plural scattering in q-resolved spectra acquired at two particular chiral positions after deconvolution, and the residual scattering is more significant in thicker areas than thinner ones. Accordingly, the orbital-to-spin moment ratio extracted from EMCD spectra, which is the difference between the two q-resolved spectra after deconvolution, would be in principle increased with increasing sample thickness. The randomly fluctuated moment ratios displayed in our experiments are greatly attributed to a slight and irregular variation of local diffraction conditions due to the bending effect and imperfect epitaxy in detected areas. We suggest EMCD spectra should be acquired from sufficiently thin samples to minimize the plural scattering effect in originally detected spectra before any deconvolution. In addition, great care should be taken for slight misorientation and imperfect epitaxy when performing EMCD investigation on epitaxial thin films using a nano beam.

Generation of Perfect Electron Vortex Beam with a Customized Beam Size Independent of Orbital Angular Momentum

The electron vortex beam (EVB)-carrying quantized orbital angular momentum (OAM) plays an essential role in a series of fundamental research. However, the radius of the transverse intensity profile of a doughnut-shaped EVB strongly depends on the topological charge of the OAM, impeding its wide applications in electron microscopy. Inspired by the perfect vortex in optics, herein, we demonstrate a perfect electron vortex beam (PEVB), which completely unlocks the constraint between the beam size and the beam's OAM. We design nanoscale holograms to generate PEVBs carrying different quanta of OAM but exhibiting almost the same beam size. Furthermore, we show that the beam size of the PEVB can be readily controlled by only modifying the design parameters of the hologram. The generation of PEVB with a customized beam size independent of the OAM can promote various in situ applications of free electrons carrying OAM in electron microscopy.

Shaping of Electron Beams Using Sculpted Thin Films

Electron beam shaping by sculpted thin films relies on electron-matter interactions and the wave nature of electrons. It can be used to study physical phenomena of special electron beams and to develop technological applications in electron microscopy that offer new and improved measurement techniques and increased resolution in different imaging modes. In this Perspective, we review recent applications of sculpted thin films for electron orbital angular momentum sorting, improvements in phase contrast transmission electron microscopy, and aberration correction. For the latter, we also present new results of our work toward correction of the spherical aberration of Lorentz scanning transmission electron microscopes and suggest a method to correct chromatic aberration using thin films. This review provides practical insight for researchers in the field and motivates future progress in electron microscopy.

Parameterization of magnetic vector potentials and fields for efficient multislice calculations of elastic electron scattering

The multislice method, which simulates the propagation of the incident electron wavefunction through a crystal, is a well established method for analysing the multiple scattering effects that an electron beam may undergo. The inclusion of magnetic effects into this method proves crucial towards simulating enhanced magnetic interaction of vortex beams with magnetic materials, calculating magnetic Bragg spots or searching for magnon signatures, to name a few examples. Inclusion of magnetism poses novel challenges to the efficiency of the multislice method for larger systems, especially regarding the consistent computation of magnetic vector potentials A and magnetic fields B over large supercells. This work presents a tabulation of parameterized magnetic (PM) values for the first three rows of transition metal elements computed from atomic density functional theory (DFT) calculations, allowing for the efficient computation of approximate A and B across large crystals using only structural and magnetic moment size and direction information. Ferromagnetic b.c.c. (body-centred cubic) Fe and tetragonal FePt are chosen to showcase the performance of PM values versus directly obtaining A and B from the unit-cell spin density by DFT. The magnetic fields of b.c.c. Fe are well described by the PM approach while for FePt the PM approach is less accurate due to deformations in the spin density. Calculations of the magnetic signal, namely the change due to A and B of the intensity of diffraction patterns, show that the PM approach for both b.c.c. Fe and FePt is able to describe the effects of magnetism in these systems to a good degree of accuracy.

A sorter for electrons based on magnetic elements

The orbital angular momentum (OAM) sorter is an electron optical device for the measurement of an electron's OAM. It is based on two phase elements, which are referred to as an "unwrapper" and a "corrector" and are located in Fourier conjugate planes. The simplest implementation of the sorter is based on electrostatic phase elements, such as a charged needle for the unwrapper and electrodes with alternating charges or potentials for the corrector. Here, we use a formal analogy between phase shifts introduced by charges and vertical currents to propose alternative designs for the sorter elements, which are based on phase shifts introduced by magnetic fields. We use this concept to provide a general guide for phase element design, which promises to provide improved reliability of phase control in electron optics.

Experimental Demonstration of an Electrostatic Orbital Angular Momentum Sorter for Electron Beams

The component of orbital angular momentum (OAM) in the propagation direction is one of the fundamental quantities of an electron wave function that describes its rotational symmetry and spatial chirality. Here, we demonstrate experimentally an electrostatic sorter that can be used to analyze the OAM states of electron beams in a transmission electron microscope. The device achieves postselection or sorting of OAM states after electron-material interactions, thereby allowing the study of new material properties such as the magnetic states of atoms. The required electron-optical configuration is achieved by using microelectromechanical systems technology and focused ion beam milling to control the electron phase electrostatically with a lateral resolution of 50 nm. An OAM resolution of 1.5ℏ is realized in tests on controlled electron vortex beams, with the perspective of reaching an optimal OAM resolution of 1ℏ in the near future.

Positron annihilation localization by nanoscale magnetization

In positron emission tomography (PET), the finite range over which positrons travel before annihilating with an electron places a fundamental physical limit on the spatial resolution of PET images. After annihilation, the photon pair detected by the PET instrumentation is emitted from a location that is different from the positron-emitting source, resulting in image blurring. Here, we report on the localization of positron range, and hence annihilation quanta, by strong nanoscale magnetization of superparamagnetic iron oxide nanoparticles (SPIONs) in PET-MRI. We found that positron annihilations localize within a region of interest by up to 60% more when SPIONs are present (with [Fe] = 3 mM) compared to when they are not. The resulting full width at half maximum of the PET scans showed the spatial resolution improved by up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}≈ 30%. We also found evidence suggesting that the radiolabeled SPIONs produced up to a six-fold increase in ortho-positronium. These results may also have implications for emerging cancer theranostic strategies, where charged particles are used as therapeutic as well as diagnostic agents and improved dose localization within a tumor is a determinant of better treatment outcomes.

Generation and detection of spin-orbit coupled neutron beams

Spin-orbit coupling of light has come to the fore in nanooptics and plasmonics, and is a key ingredient of topological photonics and chiral quantum optics. We demonstrate a basic tool for incorporating analogous effects into neutron optics: the generation and detection of neutron beams with coupled spin and orbital angular momentum. The 3He neutron spin filters are used in conjunction with specifically oriented triangular coils to prepare neutron beams with lattices of spin-orbit correlations, as demonstrated by their spin-dependent intensity profiles. These correlations can be tailored to particular applications, such as neutron studies of topological materials.

Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields

Vortex-carrying matter waves, such as chiral electron beams, are of significant interest in both applied and fundamental science. Continuous-wave electron vortex beams are commonly prepared via passive phase masks imprinting a transverse phase modulation on the electron's wavefunction. Here, we show that femtosecond chiral plasmonic near fields enable the generation and dynamic control on the ultrafast timescale of an electron vortex beam. The vortex structure of the resulting electron wavepacket is probed in both real and reciprocal space using ultrafast transmission electron microscopy. This method offers a high degree of scalability to small length scales and a highly efficient manipulation of the electron vorticity with attosecond precision. Besides the direct implications in the investigation of nanoscale ultrafast processes in which chirality plays a major role, we further discuss the perspectives of using this technique to shape the wavefunction of charged composite particles, such as protons, and how it can be used to probe their internal structure.

Electric Quadrupole Moment and the Tensor Magnetic Polarizability of Twisted Electrons and a Potential for their Measurements

For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron. The tensor magnetic polarizability of the twisted electron can be measured in a magnetic storage ring because a beam with an initial orbital tensor polarization acquires a horizontal orbital vector polarization. The electric quadrupole moment is rather large and strongly influences the dynamics of the intrinsic orbital angular momentum (OAM). Three different methods of its measurements, freezing the intrinsic orbital angular momentum and two resonance methods, are proposed. The existence of the quadrupole moment of twisted electrons can lead to practical applications.

Relativistic Quantum Dynamics of Twisted Electron Beams in Arbitrary Electric and Magnetic Fields

Relativistic quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields are constructed for the first time. This allows us to change the controversial contemporary situation when the nonrelativistic approximation is used for relativistic twisted electrons. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. A critical experiment for a verification of the results obtained is proposed. The new important effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Magnetic characterization of cobalt nanowires and square nanorings fabricated by focused electron beam induced deposition

The magnetic properties of nanowires (NWs) and square nanorings, which were deposited by focused electron beam induced deposition (FEBID) of a Co carbonyl precursor, are studied using off-axis electron holography (EH), Lorentz transmission electron microscopy (L-TEM) and magnetic force microscopy (MFM). EH shows that NWs deposited using beam energies of 5 and 15 keV have the characteristics of magnetic dipoles, with larger magnetic moments observed for NWs deposited at lower energy. L-TEM is used to image magnetic domain walls in NWs and nanorings and their motion as a function of applied magnetic field. The NWs are found to have almost square hysteresis loops, with coercivities of ca. 10 mT. The nanorings show two different magnetization states: for low values of the applied in-plane field (0.02 T) a horseshoe state is observed using L-TEM, while for higher values of the applied in-plane field (0.3 T) an onion state is observed at remanence using L-TEM and MFM. Our results confirm the suitability of FEBID for nanofabrication of magnetic structures and demonstrate the versatility of TEM techniques for the study and manipulation of magnetic domain walls in nanostructures.