Direct observation of Σ7 domain boundary core structure in magnetic skyrmion lattice

Phase imaging in scanning transmission electron microscopy using bright-field balanced divergency method

We introduce a phase imaging mechanism for scanning transmission electron microscopy that exploits the complementary intensity changes of transmitted disks at different scattering angles. For scanning transmission electron microscopy, this method provides a straightforward, dose-efficient, and noise-robust phase imaging, from atomic resolution to intermediate length scales, as a function of scattering angles and probe defocus. At atomic resolution, we demonstrate that the phase imaging using the method can detect both light and heavy atomic columns. Furthermore, we experimentally apply the method to the imaging of nanoscale magnetic phases in FeGe samples. Compared with conventional methods, phase retrieval using the new method has higher effective spatial resolution and robustness to non-phase background contrast. Our method complements traditional phase imaging modalities in electron microscopy and has the potential to be extended to other scanning transmission techniques and to characterize many emerging material systems.

Thermal Hysteresis and Ordering Behavior of Magnetic Skyrmion Lattices

The physics of phase transitions in two-dimensional (2D) systems underpins research in diverse fields including statistical mechanics, nanomagnetism, and soft condensed matter. However, many aspects of 2D phase transitions are still not well understood, including the effects of interparticle potential, polydispersity, and particle shape. Magnetic skyrmions are chiral spin-structure quasi-particles that form two-dimensional lattices. Here, we show, by real-space imaging using in situ cryo-Lorentz transmission electron microscopy coupled with machine learning image analysis, the ordering behavior of Néel skyrmion lattices in van der Waals Fe₃GeTe₂. We demonstrate a distinct change in the skyrmion size distribution during field-cooling, which leads to a loss of lattice order and an evolution of the skyrmion liquid phase. Remarkably, the lattice order is restored during field heating and demonstrates a thermal hysteresis. This behavior is explained by the skyrmion energy landscape and demonstrates the potential to control the lattice order in 2D phase transitions.

Control of structure and spin texture in the van der Waals layered magnet CrSBr

Controlling magnetism at nanometer length scales is essential for realizing high-performance spintronic, magneto-electric and topological devices and creating on-demand spin Hamiltonians probing fundamental concepts in physics. Van der Waals (vdW)-bonded layered magnets offer exceptional opportunities for such spin texture engineering. Here, we demonstrate nanoscale structural control in the layered magnet CrSBr with the potential to create spin patterns without the environmental sensitivity that has hindered such manipulations in other vdW magnets. We drive a local phase transformation using an electron beam that moves atoms and exchanges bond directions, effectively creating regions that have vertical vdW layers embedded within the initial horizontally vdW bonded exfoliated flakes. We calculate that the newly formed two-dimensional structure is ferromagnetically ordered in-plane with an energy gap in the visible spectrum, and weak antiferromagnetism between the planes, suggesting possibilities for creating spin textures and quantum magnetic phases.

Atomically sharp domain walls in an antiferromagnet

The interest in understanding scaling limits of magnetic textures such as domain walls spans the entire field of magnetism from its physical fundamentals to applications in information technologies. Here, we explore antiferromagnetic CuMnAs in which imaging by x-ray photoemission reveals the presence of magnetic textures down to nanoscale, reaching the detection limit of this established microscopy in antiferromagnets. We achieve atomic resolution by using differential phase-contrast imaging within aberration-corrected scanning transmission electron microscopy. We identify abrupt domain walls in the antiferromagnetic film corresponding to the Néel order reversal between two neighboring atomic planes. Our work stimulates research of magnetic textures at the ultimate atomic scale and sheds light on electrical and ultrafast optical antiferromagnetic devices with magnetic field-insensitive neuromorphic functionalities.

Real-space visualization of intrinsic magnetic fields of an antiferromagnet

Characterizing magnetic structures down to atomic dimensions is central to the design and control of nanoscale magnetism in materials and devices. However, real-space visualization of magnetic fields at such dimensions has been extremely challenging. In recent years, atomic-resolution differential phase contrast scanning transmission electron microscopy (DPC STEM)¹ has enabled direct imaging of electric field distribution even inside single atoms². Here we show real-space visualization of magnetic field distribution inside antiferromagnetic haematite (α-Fe₂O₃) using atomic-resolution DPC STEM in a magnetic-field-free environment³. After removing the phase-shift component due to atomic electric fields and improving the signal-to-noise ratio by unit-cell averaging, real-space visualization of the intrinsic magnetic fields in α-Fe₂O₃ is realized. These results open a new possibility for real-space characterization of many magnetic structures.

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.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

py4DSTEM: A Software Package for Four-Dimensional Scanning Transmission Electron Microscopy Data Analysis

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

Two-dimensional characterization of three-dimensional magnetic bubbles in Fe3Sn2 nanostructures

We report differential phase contrast scanning transmission electron microscopy (TEM) of nanoscale magnetic objects in Kagome ferromagnet Fe3Sn2 nanostructures. This technique can directly detect the deflection angle of a focused electron beam, thus allowing clear identification of the real magnetic structures of two magnetic objects including three-ring and complex arch-shaped vortices in Fe3Sn2 by Lorentz-TEM imaging. Numerical calculations based on real material-specific parameters well reproduced the experimental results, showing that the magnetic objects can be attributed to integral magnetizations of two types of complex three-dimensional (3D) magnetic bubbles with depth-modulated spin twisting. Magnetic configurations obtained using the high-resolution TEM are generally considered as two-dimensional (2D) magnetic objects previously. Our results imply the importance of the integral magnetizations of underestimated 3D magnetic structures in 2D TEM magnetic characterizations.

Nanometre imaging of Fe3GeTe2 ferromagnetic domain walls

Fe₃GeTe₂ is a layered crystal which has recently been shown to maintain its itinerant ferromagnetic properties even when atomically thin. Here, differential phase contrast scanning transmission electron microscopy is used to investigate the domain structure in a Fe₃GeTe₂ cross-sectional lamella at temperatures ranging from 95 to 250 K and at nanometre spatial resolution. Below the experimentally determined Curie temperature (T _C) of 191 K, stripe domains magnetised along 〈0001〉, bounded with 180^◦ Bloch type domain walls, are observed, transitioning to mixed Bloch-Néel type where the cross-sectional thickness is reduced below 50 nm. When warming towards T _C, these domains undergo slight restructuring towards uniform size, before abruptly fading at T _C. Localised loss of ferromagnetic order is seen over time, hypothesised to be a frustration of ferromagnetic order from ambient oxidation and basal cracking, which could enable selective modification of the magnetic properties for device applications.

Toward quantitative electromagnetic field imaging by differential-phase-contrast scanning transmission electron microscopy

Differential-phase-contrast scanning transmission electron microscopy (DPC STEM) is a technique to directly visualize local electromagnetic field distribution inside materials and devices at very high spatial resolution. Owing to the recent progress in the development of high-speed segmented and pixelated detectors, DPC STEM now constitutes one of the major imaging modes in modern aberration-corrected STEM. While qualitative imaging of electromagnetic fields by DPC STEM is readily possible, quantitative imaging by DPC STEM is still under development because of the several fundamental issues inherent in the technique. In this report, we review the current status and future prospects of DPC STEM for quantitative electromagnetic field imaging from atomic scale to mesoscopic scale.

Recent advances in small-angle electron diffraction and Lorentz microscopy

We describe small-angle electron diffraction (SmAED) and Lorentz microscopy using a conventional transmission electron microscope. In SmAED, electron diffraction patterns with a wide-angular range on the order of 1 × 10-2 rad to 1 × 10-7 rad can be obtained. It is demonstrated that magnetic information of nanoscale magnetic microstructures can be obtained by Fresnel imaging, Foucault imaging and SmAED. In particular, we report magnetic microstructures associated with magnetic stripes and magnetic skyrmions revealed by Lorentz microscopy with SmAED. SmAED can be applied to the analysis of microstructures in functional materials such as dielectric, ferromagnetic and multiferroic materials.

Tilted X-Ray Holography of Magnetic Bubbles in MnNiGa Lamellae

Nanoscopic lamellae of centrosymmetric ferromagnetic alloys have recently been reported to host the biskyrmion spin texture; however, this has been disputed as the misidentication of topologically trivial type-II magnetic bubbles. Here we demonstrate resonant soft X-ray holographic imaging of topological magnetic states in lamellae of the centrosymmetric alloy (Mn_1-xNi_x)_0.65Ga_0.35 (x = 0.5), showing the presence of magnetic stripes evolving into single core magnetic bubbles. We observe rotation of the stripe phase via the nucleation and destruction of disclination defects. This indicates the system behaves as a conventional uniaxial ferromagnet. By utilizing the holography with extended reference by autocorrelation linear differential operator (HERALDO) method, we show tilted holographic images at 30° incidence confirming the presence of type-II magnetic bubbles in this system. This study demonstrates the utility of X-ray imaging techniques in identifying the topology of localized structures in nanoscale magnetism.

Magnetic-structure imaging in polycrystalline materials by specimen-tilt series averaged DPC STEM

Differential phase contrast (DPC) imaging in scanning transmission electron microscopy is a technique to visualize electromagnetic field distribution inside specimens at high spatial resolution. However, diffraction contrast strongly hampers electromagnetic contrast in DPC images especially in polycrystalline samples. In this paper, we develop an imaging technique to effectively suppress diffraction contrast in DPC images. It is shown that a magnetic structure in a Nd-Fe-B permanent magnet was clearly visualized by averaging 64 DPC images with various specimen-tilt conditions. This is because the diffraction contrast in DPC images sensitively and randomly varies with crystal orientation and thus almost vanishes by averaging specimen-tilt image series. We further investigated two types of residual diffraction contrast in the tilt-series averaged DPC images: weak contrast inside grains and strong contrast at grain boundaries. We found that the former can be suppressed by averaging more DPC images, whereas the latter can be suppressed by the tilt-series averaging with wider range of specimen tilt. The tilt-series averaging method enables DPC to visualize electromagnetic structures even inside polycrystalline materials.

Electrostatic potential imaging of phase-separated structures in organic materials via differential phase contrast scanning transmission electron microscopy

Electron staining is generally performed prior to observing organic materials via transmission electron microscopy (TEM) to enhance image contrast. However, electron staining can deteriorate organic materials. Here, we demonstrate electrostatic potential imaging of organic materials via differential phase contrast (DPC) scanning transmission electron microscopy (STEM) without electron staining. Electrostatic potential imaging drastically increases the contrast between different materials. Phase-separated structures in a poly (3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) blend that are impossible to observe using conventional STEM are clearly visualized. Furthermore, annealing behavior of the phase-separated structures is directly observed. The morphological transformations in the samples are consistent with their physical parameters, including their glass transition and melting temperatures. Our results indicate that electrostatic potential imaging is highly effective for observing organic materials.

Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition

Tensor singular value decomposition (SVD) is a method to find a low-dimensional representation of data with meaningful structure in three or more dimensions. Tensor SVD has been applied to denoise atomic-resolution 4D scanning transmission electron microscopy (4D STEM) data. On data simulated from a SrTiO₃ [100] perfect crystal and a Si [110] edge dislocation, tensor SVD achieved an average peak signal-to-noise ratio (PSNR) of ~40 dB, which matches or exceeds the performance of other denoising methods, with processing times at least 100 times shorter. On experimental data from SrTiO₃ [100] and LiZnSb [112¯0]/GaSb [110] samples, tensor SVD denoises multiple GB 4D STEM data sets in ten minutes on a typical personal computer. Denoising with tensor SVD improves both convergent beam electron diffraction patterns and virtual-aperture annular dark field images.

Suppressing dynamical diffraction artefacts in differential phase contrast scanning transmission electron microscopy of long-range electromagnetic fields via precession

It is well known that dynamical diffraction varies with changes in sample thickness and local crystal orientation (due to sample bending). In differential phase contrast scanning transmission electron microscopy (DPC-STEM), this can produce contrast comparable to that arising from the long-range electromagnetic fields probed by this technique. Through simulation we explore the scale of these dynamical diffraction artefacts and introduce a metric for the magnitude of their contribution to the contrast. We show that precession over an angular range of a few milliradian can suppress this contribution to the contrast by one-to-two orders of magnitude. Our exploration centres around a case study of GaAs near the [011] zone-axis orientation using a probe-forming aperture semiangle on the order of 0.1 mrad at 300 keV, but the trends found and methodology used are expected to apply more generally.

Machine Learning Magnetic Parameters from Spin Configurations

Hamiltonian parameters estimation is crucial in condensed matter physics, but is time- and cost-consuming. High-resolution images provide detailed information of underlying physics, but extracting Hamiltonian parameters from them is difficult due to the huge Hilbert space. Here, a protocol for Hamiltonian parameters estimation from images based on a machine learning (ML) architecture is provided. It consists in learning a mapping between spin configurations and Hamiltonian parameters from a small amount of simulated images, applying the trained ML model to a single unexplored experimental image to estimate its key parameters, and predicting the corresponding materials properties by a physical model. The efficiency of the approach is demonstrated by reproducing the same spin configuration as the experimental one and predicting the coercive field, the saturation field, and even the volume of the experiment specimen accurately. The proposed approach paves a way to achieve a stable and efficient parameters estimation.

Spontaneous creation and annihilation dynamics and strain-limited stability of magnetic skyrmions

Magnetic skyrmions are topological magnetic spin structures exhibiting particle-like behaviour. They are of strong interest from a fundamental viewpoint and for application, where they have potential to act as information carriers in future low-power computing technologies. Importantly, skyrmions have high physical stability because of topological protection. However, they have potential to deform according to their local energy environment. Here we demonstrate that, in regions of high exchange energy density, skyrmions may exhibit such extreme deformation that spontaneous merging with nearest neighbours or spawning new skyrmions is favoured to attain a lower energy state. Using transmission electron microscopy and a high-speed imaging detector, we observe dynamics involving distinct configurational states, in which transitions are accompanied by spontaneous creation or annihilation of skyrmions. These observations raise important questions regarding the limits of skyrmion stability and topological charge conservation, while also suggesting a means of control of skyrmion creation and annihilation.

Mechanisms of Skyrmion and Skyrmion Crystal Formation from the Conical Phase

Real-space topological magnetic structures such as skyrmions and merons are promising candidates for information storage and transport. However, the microscopic mechanisms that control their formation and evolution are still unclear. Here, using in situ Lorentz transmission electron microscopy, we demonstrate that skyrmion crystals (SkXs) can nucleate, grow, and evolve from the conical phase in the same ways that real nanocrystals form from vapors or solutions. More intriguingly, individual skyrmions can also "reproduce" by division in a mitosis-like process that allows them to annihilate SkX lattice imperfections, which is not available to crystals made of mass-conserving particles. Combined string method and micromagnetic calculations show that competition between repulsive and attractive interactions between skyrmions governs particle-like SkX growth, but nonconservative SkX growth appears to be defect mediated. Our results provide insights toward manipulating magnetic topological states by applying established crystal growth theory, adapted to account for the new process of skyrmion mitosis.

Giant Topological Hall Effect and Superstable Spontaneous Skyrmions below 330 K in a Centrosymmetric Complex Noncollinear Ferromagnet NdMn2Ge2

Skyrmions with topologically nontrivial spin textures are promising information carriers in next-generation ultralow power consumption and high-density spintronic devices. To promote their further development and utilization, the search for new room temperature skyrmion-hosting materials is crucial. Considering that most of the previous skyrmion-hosting materials are noncollinear magnets, here, the detection of the topological Hall effect (THE) and the discovery of skyrmions at room temperature are first reported in a centrosymmetric complex noncollinear ferromagnet NdMn₂Ge₂. Below 330 K, the compound can host stable Bloch-type skyrmions with about 75 nm diameter in a wide window of magnetic field and temperature, including zero magnetic field and room temperature. Moreover, the skyrmions can induce a giant topological Hall effect in a wide temperature range with a maximum value of -2.05 μΩ cm. These features make the compound attractive for both fundamental research and potential application in novel spintronic devices.

Imaging and quantification of charged domain walls in BiFeO3

Charged domain walls in ferroelectrics hold great promise for the design of novel electronic devices due to their enhanced local conductivity. In fact, charged domain walls show unique properties including the possibility of being created, moved and erased by an applied voltage. Here, we demonstrate that the charged domain walls are constituted by a core region where most of the screening charge is localized and such charge accumulation is responsible for their enhanced conductivity. In particular, the link between the local structural distortions and charge screening phenomena in 109° tail-to-tail domain walls of BiFeO3 is elucidated by a series of multiscale analysis performed by means of scanning probe techniques, including conductive atomic force microscopy (cAFM) and atomic resolution differential phase contrast scanning transmission electron microscopy (DPC-STEM). The results prove that an accumulation of oxygen vacancies occurs at the tail-to-tail domain walls as the leading charge screening process. This work constitutes a new insight in understanding the behavior of such complex systems and lays down the fundaments for their implementation into novel nanoelectronic devices.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Elliptical Bloch skyrmion chiral twins in an antiskyrmion system

Skyrmions and antiskyrmions are distinct topological chiral spin textures that have been observed in various material systems depending on the symmetry of the crystal structure. Here we show, using Lorentz transmission electron microscopy, that arrays of skyrmions can be stabilized in a tetragonal inverse Heusler with D_2d symmetry whose Dzyaloshinskii-Moriya interaction (DMI) otherwise supports antiskyrmions. These skyrmions can be distinguished from those previously found in several B20 systems which have only one chirality and are circular in shape. We find Bloch-type elliptical skyrmions with opposite chiralities whose major axis is oriented along two specific crystal directions: [010] and [100]. These structures are metastable over a wide temperature range and we show that they are stabilized by long-range dipole-dipole interactions. The possibility of forming two distinct chiral spin textures with opposite topological charges of ±1 in one material makes the family of D_2d materials exceptional.

Skyrmions and anti-skyrmions often exist in distinct material systems. Here, the authors observe elliptical skyrmions and anti-skyrmions with opposite topological charges in one tetragonal Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn with D_2d symmetry.

Robust Perpendicular Skyrmions and Their Surface Confinement

Magnetic skyrmions are two-dimensional magnetization swirls that stack in the form of tubes in the third dimension and which are proposed as prospective information carriers for nonvolatile memory devices due to their unique topological properties. From resonant elastic X-ray scattering measurements on Cu₂OSeO₃ with an in-plane magnetic field, we find that a state of perpendicularly ordered skyrmions forms, in stark contrast to the well-studied bulk state. The surface state is stable over a wide temperature range, unlike the bulk state in out-of-plane fields which is confined to a narrow region of the temperature-field phase diagram. In contrast to ordinary skyrmions found in the bulk, the surface state skyrmions result from the presence of magnetic interactions unique to the surface which stabilize them against external perturbations. The surface guiding makes the robust state particular interesting for racetracklike devices, ultimately allowing for much higher storage densities due to the smaller lateral footprint of the perpendicular skyrmions.

Emerging Electron Microscopy Techniques for Probing Functional Interfaces in Energy Materials

Interfaces play a fundamental role in many areas of chemistry. However, their localized nature requires characterization techniques with high spatial resolution in order to fully understand their structure and properties. State-of-the-art atomic resolution or in situ scanning transmission electron microscopy and electron energy-loss spectroscopy are indispensable tools for characterizing the local structure and chemistry of materials with single-atom resolution, but they are not able to measure many properties that dictate function, such as vibrational modes or charge transfer, and are limited to room-temperature samples containing no liquids. Here, we outline emerging electron microscopy techniques that are allowing these limitations to be overcome and highlight several recent studies that were enabled by these techniques. We then provide a vision for how these techniques can be paired with each other and with in situ methods to deliver new insights into the static and dynamic behavior of functional interfaces.

Stabilization and Reversal of Skyrmion Lattice in Ta/CoFeB/MgO Multilayers

Recently, magnetic skyrmion has attracted much attention due to its potential application in racetrack memory and other nanodevices. In bulk chiral magnets with non-centrosymmetric crystal structures, skyrmion lattice phase has been extensively observed. However, in film or multilayers with interfacial Dzyaloshinskii-Moriya interaction, individual skyrmion is often observed. Here, we report a short-ordered skyrmion lattice observed in [Ta(5.0 nm)/CoFeB(1.5 nm)/MgO(1.0 nm)]₁₅ multilayer in a remnant state. The structure, stabilization, and reversal of these skyrmions are discussed. Applying a slightly tilted in-plane magnetic field caused reversal of the skyrmion lattice. This reversal came from disappearance of skyrmions and nucleation of new skyrmions in the interstitial regions of the lattice. Also, we investigated how the skyrmion lattice depended on the CoFeB thickness. Our findings provide a pathway to stabilize and reverse the skyrmions in multilayers films.

Sub-Ångstrom electric field measurements on a universal detector in a scanning transmission electron microscope

Scanning transmission electron microscopy (STEM) excels in accessing atomic-scale structure and chemistry. Enhancing our ability to directly image the functionalities of local features in materials has become one of the most important topics in the future development of STEM. Recently, differential phase contrast (DPC) imaging has been utilized to map the internal electric and magnetic fields in materials from nanoscale features such as p-n junctions, skyrmions, and even from individual atoms. Here, we use an ultra-low noise SCMOS detector in as the diffraction plane camera to collect four-dimensional (4D) datasets. The high angular resolution, efficient high-SNR acquisition, and modifiability of the camera allow it to function as a universal detector, where STEM imaging configurations, such as DPC, bright field, annular bright field, and annular dark field can all be reconstructed from a single 4D dataset. By examining a distorted perovskite, DyScO3, which possesses projected lattice spacings as small as 0.83 Å, we demonstrate DPC spatial resolution almost reaching the information limit of a 100 keV electron beam. In addition, the perovskite has ordered O-coordinations with alternating octahedral tilts, which can be quantitatively measured with single degree accuracy by taking advantage of DPC's sensitivity to light atoms. The results, acquired on a standard Ronchigram camera as opposed to a specialized DPC detector, open up new opportunities to understand and design functional materials and devices that involve lattice and charge coupling at nano- and atomic-scales.

Quantification of Magnetic Surface and Edge States in an FeGe Nanostripe by Off-Axis Electron Holography

Whereas theoretical investigations have revealed the significant influence of magnetic surface and edge states on Skyrmonic spin texture in chiral magnets, experimental studies of such chiral states remain elusive. Here, we study chiral edge states in an FeGe nanostripe experimentally using off-axis electron holography. Our results reveal the magnetic-field-driven formation of chiral edge states and their penetration lengths at 95 and 240 K. We determine values of saturation magnetization M_{S} by analyzing the projected in-plane magnetization distributions of helices and Skyrmions. Values of M_{S} inferred for Skyrmions are lower by a few percent than those for helices. We attribute this difference to the presence of chiral surface states, which are predicted theoretically in a three-dimensional Skyrmion model. Our experiments provide direct quantitative measurements of magnetic chiral boundary states and highlight the applicability of state-of-the-art electron holography for the study of complex spin textures in nanostructures.

Direct Determination of Atomic Structure and Magnetic Coupling of Magnetite Twin Boundaries

Clarifying how the atomic structure of interfaces/boundaries in materials affects the magnetic coupling nature across them is of significant academic value and will facilitate the development of state-of-the-art magnetic devices. Here, by combining atomic-resolution transmission electron microscopy, atomistic spin-polarized first-principles calculations, and differential phase contrast imaging, we conduct a systematic investigation of the atomic and electronic structures of individual Fe₃O₄ twin boundaries (TBs) and determine their concomitant magnetic couplings. We demonstrate that the magnetic coupling across the Fe₃O₄ TBs can be either antiferromagnetic or ferromagnetic, which directly depends on the TB atomic core structures and resultant electronic structures within a few atomic layers. Revealing the one-to-one correspondence between local atomic structures and magnetic properties of individual grain boundaries will shed light on in-depth understanding of many interesting magnetic behaviors of widely used polycrystalline magnetic materials, which will surely promote the development of advanced magnetic materials and devices.

Stable Magnetic Skyrmion States at Room Temperature Confined to Corrals of Artificial Surface Pits Fabricated by a Focused Electron Beam

Stable confinement of elemental magnetic nanostructures, such as a single magnetic domain, is fundamental in modern magnetic recording technology. It is well-known that various magnetic textures can be stabilized by geometrical confinement using artificial nanostructures. The magnetic skyrmion, with novel spin texture and promise for future memory devices because of its topological protection and dimension at the nanometer scale, is no exception. So far, skyrmion confinement techniques using large-scale boundaries with limited geometries such as isolated disks and stripes prepared by conventional microfabrication techniques have been used. Here, we demonstrate an alternative technique confining skyrmions to artificial nanostructures (corrals) built from surface pits fabricated by a focused electron beam. Using aberration-corrected differential phase contrast scanning transmission electron microscopy, we directly visualized stable skyrmion states confined at a room temperature to corrals made of artificial surface pits on a thin plate of Co₈Zn₈Mn₄. We observed a stable single-skyrmion state confined to a triangular corral and a unique transition into a triple-skyrmions state depending on the perpendicular magnetic field. Furthermore, we made an array of stable single-skyrmion states by using concatenated triangular corrals. Artificial control of skyrmion states with the present technique should be a powerful way to realize future nonvolatile memory devices using skyrmions.

Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition

The helicity-orbital coupling is an intriguing feature of magnetic skyrmions in frustrated magnets. Here we explore the skyrmion dynamics in a frustrated magnet based on the J₁-J₂-J₃ classical Heisenberg model explicitly by including the dipole-dipole interaction. The skyrmion energy acquires a helicity dependence due to the dipole-dipole interaction, resulting in the current-induced translational motion with a fixed helicity. The lowest-energy states are the degenerate Bloch-type states, which can be used for building the binary memory. By increasing the driving current, the helicity locking-unlocking transition occurs, where the translational motion changes to the rotational motion. Furthermore, we demonstrate that two skyrmions can spontaneously form a bound state. The separation of the bound state forced by a driving current is also studied. In addition, we show the annihilation of a pair of skyrmion and antiskyrmion. Our results reveal the distinctive frustrated skyrmions may enable viable applications in topological magnetism.

Exploring the helicity-orbital coupling induced skyrmion properties is essential for the spintronic applications. Here the authors report the current controlled skyrmions and antiskyrmions dynamics with locking-unlocking helicity in frustrated magnets by including the dipole-dipole interaction in their model.

Direct Visualization of Local Electromagnetic Field Structures by Scanning Transmission Electron Microscopy

The functional properties of materials and devices are critically determined by the electromagnetic field structures formed inside them, especially at nanointerface and surface regions, because such structures are strongly associated with the dynamics of electrons, holes and ions. To understand the fundamental origin of many exotic properties in modern materials and devices, it is essential to directly characterize local electromagnetic field structures at such defect regions, even down to atomic dimensions. In recent years, rapid progress in the development of high-speed area detectors for aberration-corrected scanning transmission electron microscopy (STEM) with sub-angstrom spatial resolution has opened new possibilities to directly image such electromagnetic field structures at very high-resolution. In this Account, we give an overview of our recent development of differential phase contrast (DPC) microscopy for aberration-corrected STEM and its application to many materials problems. In recent years, we have developed segmented-type STEM detectors which divide the detector plane into 16 segments and enable simultaneous imaging of 16 STEM images which are sensitive to the positions and angles of transmitted/scattered electrons on the detector plane. These detectors also have atomic-resolution imaging capability. Using these segmented-type STEM detectors, we show DPC STEM imaging to be a very powerful tool for directly imaging local electromagnetic field structures in materials and devices in real space. For example, DPC STEM can clearly visualize the local electric field variation due to the abrupt potential change across a p-n junction in a GaAs semiconductor, which cannot be observed by normal in-focus bright-field or annular type dark-field STEM imaging modes. DPC STEM is also very effective for imaging magnetic field structures in magnetic materials, such as magnetic domains and skyrmions. Moreover, real-time imaging of electromagnetic field structures can now be realized through very fast data acquisition, processing, and reconstruction algorithms. If we use DPC STEM for atomic-resolution imaging using a sub-angstrom size electron probe, it has been shown that we can directly observe the atomic electric field inside atoms within crystals and even inside single atoms, the field between the atomic nucleus and the surrounding electron cloud, which possesses information about the atomic species, local chemical bonding and charge redistribution between bonded atoms. This possibility may open an alternative way for directly visualizing atoms and nanostructures, that is, seeing atoms as an entity of electromagnetic fields that reflect the intra- and interatomic electronic structures. In this Account, the current status of aberration-corrected DPC STEM is highlighted, along with some applications in real material and device studies.

Control of morphology and formation of highly geometrically confined magnetic skyrmions

The ability to controllably manipulate magnetic skyrmions, small magnetic whirls with particle-like properties, in nanostructured elements is a prerequisite for incorporating them into spintronic devices. Here, we use state-of-the-art electron holographic imaging to directly visualize the morphology and nucleation of magnetic skyrmions in a wedge-shaped FeGe nanostripe that has a width in the range of 45–150 nm. We find that geometrically-confined skyrmions are able to adopt a wide range of sizes and ellipticities in a nanostripe that are absent in both thin films and bulk materials and can be created from a helical magnetic state with a distorted edge twist in a simple and efficient manner. We perform a theoretical analysis based on a three-dimensional general model of isotropic chiral magnets to confirm our experimental results. The flexibility and ease of formation of geometrically confined magnetic skyrmions may help to optimize the design of skyrmion-based memory devices.

Proposals for skyrmion-based high-density memory devices require an understanding of the formation and shape of skyrmions in confined geometries. Here, the authors use electron holography to image magnetic textures in FeGe nanostripes and explore the parameters governing skyrmion morphology.

Probing nanocrystalline grain dynamics in nanodevices

Dynamical structural defects exist naturally in a wide variety of solids. They fluctuate temporally and hence can deteriorate the performance of many electronic devices. Thus far, the entities of these dynamic objects have been identified to be individual atoms. On the other hand, it is a long-standing question whether a nanocrystalline grain constituted of a large number of atoms can switch, as a whole, reversibly like a dynamical atomic defect (that is, a two-level system). This is an emergent issue considering the current development of nanodevices with ultralow electrical noise, qubits with long quantum coherence time, and nanoelectromechanical system sensors with ultrahigh resolution. We demonstrate experimental observations of dynamic nanocrystalline grains that repeatedly switch between two or more metastable coordinate states. We study temporal resistance fluctuations in thin ruthenium dioxide (RuO₂) metal nanowires and extract microscopic parameters, including relaxation time scales, mobile grain sizes, and the bonding strengths of nanograin boundaries. These material parameters are not obtainable by other experimental approaches. When combined with previous in situ high-resolution transmission electron microscopy, our electrical method can be used to infer rich information about the structural dynamics of a wide variety of nanodevices and new two-dimensional materials.

Electric field imaging of single atoms

In scanning transmission electron microscopy (STEM), single atoms can be imaged by detecting electrons scattered through high angles using post-specimen, annular-type detectors. Recently, it has been shown that the atomic-scale electric field of both the positive atomic nuclei and the surrounding negative electrons within crystalline materials can be probed by atomic-resolution differential phase contrast STEM. Here we demonstrate the real-space imaging of the (projected) atomic electric field distribution inside single Au atoms, using sub-Å spatial resolution STEM combined with a high-speed segmented detector. We directly visualize that the electric field distribution (blurred by the sub-Å size electron probe) drastically changes within the single Au atom in a shape that relates to the spatial variation of total charge density within the atom. Atomic-resolution electric field mapping with single-atom sensitivity enables us to examine their detailed internal and boundary structures.

The ability of scanning transmission electron microscopy (STEM) to image single atoms is becoming increasingly sophisticated. Here, the authors use differential phase contrast STEM to map the atomic electric fields within single Au atoms and SrTiO₃ crystals, a step toward visualizing such intra- and interatomic electronic structure as chemical bonds.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

Magnetic Skyrmion Formation at Lattice Defects and Grain Boundaries Studied by Quantitative Off-Axis Electron Holography

We use in situ Lorentz microscopy and off-axis electron holography to investigate the formation and characteristics of skyrmion lattice defects and their relationship to the underlying crystallographic structure of a B20 FeGe thin film. We obtain experimental measurements of spin configurations at grain boundaries, which reveal inversions of crystallographic and magnetic chirality across adjacent grains, resulting in the formation of interface spin stripes at the grain boundaries. In the absence of material defects, we observe that skyrmions lattices possess dislocations and domain boundaries, in analogy to atomic crystals. Moreover, the distorted skyrmions can flexibly change their size and shape to accommodate local geometry, especially at sites of dislocations in the skyrmion lattice. Our findings provide a detailed understanding of the elasticity of topologically protected skyrmions and their correlation with underlying material defects.

Jointed magnetic skyrmion lattices at a small-angle grain boundary directly visualized by advanced electron microscopy

The interactions between magnetic skyrmions and structural defects, such as edges, dislocations, and grain boundaries (GBs), which are all considered as topological defects, will be important issues when magnetic skyrmions are utilized for future memory device applications. To investigate such interactions, simultaneous visualization of magnetic skyrmions and structural defects at high spatial resolution, which is not feasible by conventional techniques, is essential. Here, taking advantages of aberration-corrected differential phase-contrast scanning transmission electron microscopy, we investigate the interaction of magnetic skyrmions with a small-angle GB in a thin film of FeGe_1−xSi_x. We found that the magnetic skyrmions and the small-angle GB can coexist each other, but a domain boundary (DB) was formed in the skyrmion lattice along the small-angle GB. At the core of the DB, unexpectedly deformed magnetic skrymions, which appear to be created by joining two portions of magnetic skyrmions in the adjacent lattices, were formed to effectively compensate misorientations between the two adjacent magnetic skyrmion lattices. These observations strongly suggest the flexible nature of individual magnetic skyrmions, and also the significance of defect engineering for future device applications.