A new way of producing electron vortex probes for STEM

Defect Contrast with 4D-STEM: Understanding Crystalline Order with Virtual Detectors and Beam Modification

Material properties strongly depend on the nature and concentration of defects. Characterizing these features may require nano- to atomic-scale resolution to establish structure-property relationships. 4D-STEM, a technique where diffraction patterns are acquired at a grid of points on the sample, provides a versatile method for highlighting defects. Computational analysis of the diffraction patterns with virtual detectors produces images that can map material properties. Here, using multislice simulations, we explore different virtual detectors that can be applied to the diffraction patterns that go beyond the binary response functions that are possible using ordinary STEM detectors. Using graphene and lead titanate as model systems, we investigate the application of virtual detectors to study local order and in particular defects. We find that using a small convergence angle with a rotationally varying detector most efficiently highlights defect signals. With experimental graphene data, we demonstrate the effectiveness of these detectors in characterizing atomic features, including vacancies, as suggested in simulations. Phase and amplitude modification of the electron beam provides another process handle to change image contrast in a 4D-STEM experiment. We demonstrate how tailored electron beams can enhance signals from short-range order and how a vortex beam can be used to characterize local symmetry.

Making the Most of your Electrons: Challenges and Opportunities in Characterizing Hybrid Interfaces with STEM

Inspired by the unique architectures composed of hard and soft materials in natural and biological systems, synthetic hybrid structures and associated soft-hard interfaces have recently evoked significant interest. Soft matter is typically dominated by fluctuations even at room temperature, while hard matter (which often serves as the substrate or anchor for the soft component) is governed by rigid mechanical behavior. This dichotomy offers considerable opportunities to leverage the disparate properties offered by these components across a wide spectrum spanning from basic science to engineering insights with significant technological overtones. Such hybrid structures, which include polymer nanocomposites, DNA functionalized nanoparticle superlattices and metal organic frameworks to name a few, have delivered promising insights into the areas of catalysis, environmental remediation, optoelectronics, medicine, and beyond. The interfacial structure between these hard and soft phases exists across a variety of length scales and often strongly influence the functionality of hybrid systems. While scanning/transmission electron microscopy (S/TEM) has proven to be a valuable tool for acquiring intricate molecular and nanoscale details of these interfaces, the unusual nature of hybrid composites presents a suite of challenges that make assessing or establishing the classical structure-property relationships especially difficult. These include challenges associated with preparing electron-transparent samples and obtaining sufficient contrast to resolve the interface between dissimilar materials given the dose sensitivity of soft materials. We discuss each of these challenges and supplement a review of recent developments in the field with additional experimental investigations and simulations to present solutions for attaining a nano or atomic-level understanding of these interfaces. These solutions present a host of opportunities for investigating and understanding the role interfaces play in this unique class of functional materials.

A semi-classical theory of magnetic inelastic scattering in transmission electron energy loss spectroscopy

The feasibility of detecting magnetic excitations using monochromated electron energy loss spectroscopy in the transmission electron microscope is examined. Inelastic scattering cross-sections are derived using a semi-classical electrodynamic model, and applied to AC magnetic susceptibility measurements and magnon characterization. Consideration is given to electron probes with a magnetic moment, such as vortex beams, where additional inelastic scattering can take place due to the change in magnetic potential energy of the incident electron in a non-uniform magnetic field. This so-called 'Stern-Gerlach' energy loss can be used to enhance the strength of the scattering by increasing the orbital angular momentum of the vortex beam, and enables separation of magnetic from non-magnetic (i.e. dielectric) energy losses, thus providing a promising experimental route for detecting magnons. AC magnetic susceptibility measurements are however not feasible using Stern-Gerlach energy losses for a vortex beam.

Alignment of electron optical beam shaping elements using a convolutional neural network

A convolutional neural network is used to align an orbital angular momentum sorter in a transmission electron microscope. The method is demonstrated using simulations and experiments. As a result of its accuracy and speed, it offers the possibility of real-time tuning of other electron optical devices and electron beam shaping configurations.

Beam shaping and probe characterization in the scanning electron microscope

Here we demonstrate the use of nanofabricated grating holograms to diffract and shape electrons in a scanning electron microscope. The diffraction grating is placed in an aperture in the column. The entire diffraction pattern can be passed through the objective lens and projected onto the specimen, or an intermediate aperture can be used to select particular diffracted beams. We discuss several techniques for characterizing the diffraction pattern. The grating designs can incorporate features that can influence the phase and intensity of the diffracted SEM probe. We demonstrate this by producing electron vortex beams.

Fabrication of phase masks from amorphous carbon thin films for electron-beam shaping

Background: Electron-beam shaping opens up the possibility for novel imaging techniques in scanning (transmission) electron microscopy (S(T)EM). Phase-modulating thin-film devices (phase masks) made of amorphous silicon nitride are commonly used to generate a wide range of different beam shapes. An additional conductive layer on such a device is required to avoid charging under electron-beam irradiation, which induces unwanted scattering events. Results: Phase masks of conductive amorphous carbon (aC) were successfully fabricated with optical lithography and focused ion beam milling. Analysis by TEM shows the successful generation of Bessel and vortex beams. No charging or degradation of the aC phase masks was observed. Conclusion: Amorphous carbon can be used as an alternative to silicon nitride for phase masks at the expense of a more complex fabrication process. The quality of arbitrary beam shapes could benefit from the application of phase masks made of amorphous C.

Magnetic measurement by electron magnetic circular dichroism in the transmission electron microscope

Magnetic measurement by transmitted electrons at nanometer or even atomic scale is always an attractive and challenging issue in the transmission electron microscope. Electron magnetic circular dichroism, proposed in 2003 and realized in 2006, opens a new insight into the measurement of local magnetic properties. Later, it is developed into a powerful technique for quantitative magnetic measurement with site specificity and element specificity at high spatial resolution over years of efforts, both in the aspect of theory and experiments. The novel technique has been widely applied to the characterization of magnetic materials now. This present review gives an overview of its development and applications in the past fifteen years since its invention. The theory of electron magnetic circular dichroism and its development are reviewed. The diffraction geometry and experimental setups are summarized. The general way for quantitative measurement of magnetic parameters is presented with typical cases. Representative breakthroughs in method development and applications over a wide range of materials are then described. Finally, prospects for future development are briefly discussed.

Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams

A general orbital-angular-momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of vortex generating elements such as spiral zone plate holograms, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks.

Atom size electron vortex beams with selectable orbital angular momentum

The decreasing size of modern functional magnetic materials and devices cause a steadily increasing demand for high resolution quantitative magnetic characterization. Transmission electron microscopy (TEM) based measurements of the electron energy-loss magnetic chiral dichroism (EMCD) may serve as the needed experimental tool. To this end, we present a reliable and robust electron-optical setup that generates and controls user-selectable single state electron vortex beams with defined orbital angular momenta. Our set-up is based on a standard high-resolution scanning TEM with probe aberration corrector, to which we added a vortex generating fork aperture and a miniaturized aperture for vortex selection. We demonstrate that atom size probes can be formed from these electron vortices and that they can be used for atomic resolution structural and spectroscopic imaging - both of which are prerequisites for future atomic EMCD investigations.

Detecting magnetic ordering with atomic size electron probes

Although magnetism originates at the atomic scale, the existing spectroscopic techniques sensitive to magnetic signals only produce spectra with spatial resolution on a larger scale. However, recently, it has been theoretically argued that atomic size electron probes with customized phase distributions can detect magnetic circular dichroism. Here, we report a direct experimental real-space detection of magnetic circular dichroism in aberration-corrected scanning transmission electron microscopy (STEM). Using an atomic size-aberrated electron probe with a customized phase distribution, we reveal the checkerboard antiferromagnetic ordering of Mn moments in LaMnAsO by observing a dichroic signal in the Mn L-edge. The novel experimental setup presented here, which can easily be implemented in aberration-corrected STEM, opens new paths for probing dichroic signals in materials with unprecedented spatial resolution.

Achieving atomic resolution magnetic dichroism by controlling the phase symmetry of an electron probe

The calculations presented here reveal that an electron probe carrying orbital angular momentum is just a particular case of a wider class of electron beams that can be used to measure electron magnetic circular dichroism (EMCD) with atomic resolution. It is possible to obtain an EMCD signal with atomic resolution by simply breaking the symmetry of the electron probe phase distribution using the aberration-corrected optics of a scanning transmission electron microscope. The required phase distribution of the probe depends on the magnetic symmetry and crystal structure of the sample. The calculations indicate that EMCD signals utilizing the phase of the electron probe are as strong as those obtained by nanodiffraction methods.

Toward single mode, atomic size electron vortex beams

We propose a practical method of producing a single mode electron vortex beam suitable for use in a scanning transmission electron microscope (STEM). The method involves using a holographic "fork" aperture to produce a row of beams of different orbital angular momenta, as is now well established, magnifying the row so that neighboring beams are separated by about 1 µm, selecting the desired beam with a narrow slit, and demagnifying the selected beam down to 1-2 Å in size. We show that the method can be implemented by adding two condenser lenses plus a selection slit to a straight-column cold-field emission STEM. It can also be carried out in an existing instrument, the monochromated Nion high-energy-resolution monochromated electron energy-loss spectroscopy-STEM, by using its monochromator in a novel way. We estimate that atom-sized vortex beams with ≥ 20 pA of current should be attainable at 100-200 keV in either instrument.

A perturbation theory study of electron vortices in electromagnetic fields: the case of infinitely long line charge and magnetic dipole

The novel discovery of electron vortices carrying quantized orbital angular momentum motivated intensive research of their basic properties as well as applications, e.g. structural characterization of magnetic materials. In this paper, the fundamental interactions of electron vortices within infinitely long atomic-column-like electromagnetic fields are studied based on the relativistically corrected Pauli-Schrödinger equation and the perturbation theory. The relative strengths of three fundamental interactions, i.e. the electron-electric potential interaction, the electron-magnetic potential/field interaction and the spin-orbit coupling are discussed. The results suggest that the perturbation energies of the last two interactions are in an order of 10(3)-10(4) smaller than that of the first one for electron vortices. In addition, it is also found that the strengths of these interactions are strongly dependant on the spatial distributions of the electromagnetic field as well as the electron vortices.

Vortex beam production and contrast enhancement from a magnetic spiral phase plate

Electron vortex beam probes offer the possibility of mapping magnetic moments with atomic resolution. In this work we consider using the stray magnetic field produced from a narrow ferromagnetic rod magnetised along its long axis to produce a vortex beam probe, as an alternative to the currently used holographic apertures or gratings. We show through numerical modelling, electron holography observations and direct imaging of the electron probe, that a long narrow ferromagnetic rod induces a phase shift in the wave-function of passing electrons that approximately describes a helix in the regions near its ends. Directing this rod towards the optical axis of a charged-particle beam probe forming system at a limiting aperture position, with the free-end sufficiently close to the axis, is shown to offer a point spread function composed of vortex modes, with evidence of this appearing in observations of the electron probe formed from inserting a micro-fabricated CoFe rod into the beam path of a 300 keV transmission electron microscope (TEM). If the rod is arranged to contain the magnetic flux of h/e, thus producing a maximum phase shift of 2π, it produces a simple spiral-like phase contrast transfer function for weak phase objects. In this arrangement the ferromagnetic rod can be used as a phase plate, positioned at the objective aperture position of a TEM, yielding enhanced image contrast which is simulated to be intermediate between comparable Zernike and Hilbert phase plates. Though this aspect of the phase plate performance is not demonstrated here, agreement between our observations and models for the probe formed from an example rod containing a magnetic flux of ~2.35h/e, indicate this phase plate arrangement could be a simple means of enhancing contrast and gaining additional information from TEM imaged weak phase samples, while also offering the capability to produce vortex beam probes. However, steps still need to be taken to either remove or improve the support membrane for the rod in our experiments to reduce any effects from charging in the phase plate.

Measuring the orbital angular momentum of electron vortex beams using a forked grating

The present study experimentally examines how an electron vortex beam with orbital angular momentum (OAM) undergoes diffraction through a forked grating. The nth-order diffracted electron vortex beam after passing through a forked grating with a Burgers vector of 1 shows an OAM transfer of nℏ. Hence, the diffraction patterns become mirror asymmetric owing to the size difference between the electron beams. Such a forked grating, when used in combination with a pinhole located at the diffraction plane, could act as an analyzer to measure the OAM of input electrons.

Exploiting lens aberrations to create electron-vortex beams

A model for a new electron-vortex beam production method is proposed and experimentally demonstrated. The technique calls on the controlled manipulation of the degrees of freedom of the lens aberrations to achieve a helical phase front. These degrees of freedom are accessible by using the corrector lenses of a transmission electron microscope. The vortex beam is produced through a particular alignment of these lenses into a specifically designed astigmatic state and applying an annular aperture in the condenser plane. Experimental results are found to be in good agreement with simulations.

Observation of the Larmor and Gouy rotations with electron vortex beams

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 strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, when passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behavior is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.

Electron vortex production and control using aberration induced diffraction catastrophes

An aberration corrected electron microscope is used to create electron diffraction catastrophes, containing arrays of intensity zeros threading vortex cores. Vortices are ascribed to these arrays using catastrophe theory, scalar diffraction integrals, and experimentally retrieved phase maps. From measured wave function phases, obtained using focal-series phase retrieval, the orbital angular momentum density is mapped for highly astigmatic electron probes. We observe vortex rings and topological reconnections of nodal lines by tracking the vortex cores using the retrieved phases.

STEM_CELL: a software tool for electron microscopy: part 1--simulations

The software STEM_CELL, here presented, is a useful tool for (S) TEM simulation. In particular innovative solutions are presented in (1) the supercell manipulation and parameters setting (2) simulation execution through the modified Kirkland routines (3) simulation post-processing with extended output and comprehensive graphic tools (4) image contrast interpretation through a strain channeling equation accounting for strain effects in STEM-ADF.

Advanced electron microscopy for advanced materials

The idea of this Review is to introduce newly developed possibilities of advanced electron microscopy to the materials science community. Over the last decade, electron microscopy has evolved into a full analytical tool, able to provide atomic scale information on the position, nature, and even the valency atoms. This information is classically obtained in two dimensions (2D), but can now also be obtained in 3D. We show examples of applications in the field of nanoparticles and interfaces.

On-column 2p bound state with topological charge ±1 excited by an atomic-size vortex beam in an aberration-corrected scanning transmission electron microscope

Atomic-size vortex beams have great potential in probing the magnetic moment of materials at atomic scales. However, the limited depth of field of vortex beams constrains the probing depth in which the helical phase front is preserved. On the other hand, electron channeling in crystals can counteract beam divergence and extend the vortex beam without disrupting its topological charge. Specifically, in this article, we report that atomic vortex beams with topological charge ±1 can be coupled to the 2p columnar bound states and propagate for more than 50 nm without being dispersed and losing its helical phase front. We give numerical solutions to the 2p columnar orbitals and tabulate the characteristic size of the 2p states of two typical elements, Co and Dy, for various incident beam energies and various atomic densities. The tabulated numbers allow estimates of the optimal convergence angle for maximal coupling to 2p columnar orbital. We have also developed analytic formulae for beam energy, convergence angle, and hologram-dependent scaling for various characteristic sizes. These length scales are useful for the design of pitch-fork apertures and operations of microscopes in the vortex-beam imaging mode.