Hopfion rings in a cubic chiral magnet.

Magnetic skyrmions and hopfions are topological solitons1-well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions2,3 are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions4-9 are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging10 and has only been reported in a synthetic material11. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion-hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets.

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography.

The operation of nanoscale electronic devices is related intimately to the three-dimensional (3D) charge density distributions within them. Here, we demonstrate the quantitative 3D mapping of the charge density and long-range electric field associated with an electrically biased carbon fiber nanotip with a spatial resolution of approximately 5 nm using electron holographic tomography in the transmission electron microscope combined with model-based iterative reconstruction. The approach presented here can be applied to a wide range of other nanoscale materials and devices.

Counting Point Defects at Nanoparticle Surfaces by Electron Holography.

Metal oxide nanoparticles exhibit outstanding catalytic properties, believed to be related to the presence of oxygen vacancies at the particle's surface. However, little quantitative information is known about concentrations of point defects inside and at surfaces of these nanoparticles, due to the challenges in achieving an atomically resolved experimental access. By employing off-axis electron holography, we demonstrate, using MgO nanoparticles as an example, a methodology that discriminates between mobile charge induced by electron beam irradiation and immobile charge associated with deep traps induced by point defects as well as distinguishes between bulk and surface point defects. Counting the immobile charge provides a quantification of the concentration of F2+ centers induced by oxygen vacancies at the MgO nanocube surfaces.

Manipulation of dipolar magnetism in low-dimensional iron oxide nanoparticle assemblies.

The manipulation of magnetic states in nanoparticle supercrystals promises new pathways to design nanocrystalline magnetic materials and devices. Trench-patterned silicon substrates were used as templates to guide the self-assembly of iron oxide nanoparticles. Grazing incidence small angle X-ray scattering shows that the nanoparticles form a long-range ordered structure along the trench direction while in the direction perpendicular to the trenches, no coherent structure is observable. Electron holography provides evidence of an ordered magnetic state of nanoparticle moments in the remanent state after the application of a saturation magnetic field parallel to the trenches. However, a disordered magnetic state was observed in a perpendicular geometry. Hysteresis loops indicate that the nanoparticle moments form a superferromagnetic state for the geometry parallel to the trenches. Memory effect investigations reveal that the disordered magnetic state corresponds to a collective superspin glass state in the perpendicular geometry, while the superferromagnetic state in the parallel geometry suppresses the superspin glass state.

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.

Boosting the Thermoelectric Performance of (Na,K)-Codoped Polycrystalline SnSe by Synergistic Tailoring of the Band Structure and Atomic-Scale Defect Phonon Scattering.

We report the high thermoelectric performance of p-type polycrystalline SnSe obtained by the synergistic tailoring of band structures and atomic-scale defect phonon scattering through (Na,K)-codoping. The energy offsets of multiple valence bands in SnSe are decreased after Na doping and further reduced by (Na,K)-codoping, resulting in an enhancement in the Seebeck coefficient and an increase in the power factor to 492 µW m-1 K-2. The lattice thermal conductivity of polycrystalline SnSe is decreased by the introduction of effective phonon scattering centers, such as point defects and antiphase boundaries. The lattice thermal conductivity of the material is reduced to values as low as 0.29 W m-1 K-1 at 773 K, whereas ZT is increased from 0.3 for 1% Na-doped SnSe to 1.2 for 1% (Na,K)-codoped SnSe.

Direct Imaging of a Zero-Field Target Skyrmion and Its Polarity Switch in a Chiral Magnetic Nanodisk.

A target Skyrmion is a flux-closed spin texture that has twofold degeneracy and is promising as a binary state in next generation universal memories. Although its formation in nanopatterned chiral magnets has been predicted, its observation has remained challenging. Here, we use off-axis electron holography to record images of target Skyrmions in a 160-nm-diameter nanodisk of the chiral magnet FeGe. We compare experimental measurements with numerical simulations, demonstrate switching between two stable degenerate target Skyrmion ground states that have opposite polarities and rotation senses, and discuss the observed switching mechanism.

High thermoelectric performance realized in a BiCuSeO system by improving carrier mobility through 3D modulation doping.

We report a greatly enhanced thermoelectric performance in a BiCuSeO system, realized by improving carrier mobility through modulation doping. The heterostructures of the modulation doped sample make charge carriers transport preferentially in the low carrier concentration area, which increases carrier mobility by a factor of 2 while maintaining the carrier concentration similar to that in the uniformly doped sample. The improved electrical conductivity and retained Seebeck coefficient synergistically lead to a broad, high power factor ranging from 5 to 10 µW cm(-1) K(-2). Coupling the extraordinarily high power factor with the extremely low thermal conductivity of ∼0.25 W m(-1) K(-1) at 923 K, a high ZT ≈ 1.4 is achieved in a BiCuSeO system.

Origin of the high performance in GeTe-based thermoelectric materials upon Bi2Te3 doping.

As a lead-free material, GeTe has drawn growing attention in thermoelectrics, and a figure of merit (ZT) close to unity was previously obtained via traditional doping/alloying, largely through hole carrier concentration tuning. In this report, we show that a remarkably high ZT of ∼1.9 can be achieved at 773 K in Ge0.87Pb0.13Te upon the introduction of 3 mol % Bi2Te3. Bismuth telluride promotes the solubility of PbTe in the GeTe matrix, thus leading to a significantly reduced thermal conductivity. At the same time, it enhances the thermopower by activating a much higher fraction of charge transport from the highly degenerate Σ valence band, as evidenced by density functional theory calculations. These mechanisms are incorporated and discussed in a three-band (L + Σ + C) model and are found to explain the experimental results well. Analysis of the detailed microstructure (including rhombohedral twin structures) in Ge0.87Pb0.13Te + 3 mol % Bi2Te3 was carried out using transmission electron microscopy and crystallographic group theory. The complex microstructure explains the reduced lattice thermal conductivity and electrical conductivity as well.

Steady motion of 80-nm-size skyrmions in a 100-nm-wide track.

The current-driven movement of magnetic skyrmions along a nanostripe is essential for the advancement and functionality of a new category of spintronic devices resembling racetracks. Despite extensive research into skyrmion dynamics, experimental verification of current-induced motion of ultra-small skyrmions within an ultrathin nanostripe is still pending. Here, we unveil the motion of individual 80 nm-size skyrmions in an FeGe track with an ultrathin width of 100 nm. The skyrmions can move steadily along the track over a broad range of current densities by using controlled pulse durations of as low as 2 ns. The potential landscape, arising from the magnetic edge twists in such a geometrically confined system, introduces skyrmion inertia and ensures efficient motion with a vanishing skyrmion Hall angle. Our results showcase the steady motion of skyrmions in an ultrathin track, offering a practical pathway for implementing skyrmion-based spintronic devices.

Pseudopolymorphic Phase Engineering for Improved Thermoelectric Performance in Copper Sulfides.

Polymorphism (and its extended form - pseudopolymorphism) in solids is ubiquitous in mineralogy, crystallography, chemistry/biochemistry, materials science, and the pharmaceutical industries. Despite the difficulty of controlling (pseudo-)polymorphism, the realization of specific (pseudo-)polymorphic phases and associated boundary structures is an efficient route to enhance material performance for energy conversion and electromechanical applications. Here, this work applies the pseudopolymorphic phase (PP) concept to a thermoelectric copper sulfide, Cu2- x S (x ≤ 0.25), via CuBr2 doping. A peak ZT value of 1.25 is obtained at 773 K in Cu1.8 S + 3 wt% CuBr2 , which is 2.3 times higher than that of a pristine Cu1.8 S sample. Atomic-resolution scanning transmission electron microscopy confirms the transformation of pristine Cu1.8 S low digenite into PP-engineered high digenite, as well as the formation of (semi-)coherent interfaces between different PPs, which is expected to enhance phonon scattering. The results demonstrate that PP engineering is an effective approach for achieving improved thermoelectric performance in Cu-S compounds. It is also expected to be useful in other materials.

Direct observation of tensile-strain-induced nanoscale magnetic hardening.

Magnetoelasticity is the bond between magnetism and mechanics, but the intricate mechanisms via which magnetic states change due to mechanical strain remain poorly understood. Here, we provide direct nanoscale observations of how tensile strain modifies magnetic domains in a ferromagnetic Ni thin plate using in situ Fresnel defocus imaging, off-axis electron holography and a bimetallic deformation device. We present quantitative measurements of magnetic domain wall structure and its transformations as a function of strain. We observe the formation and dissociation of strain-induced periodic 180° magnetic domain walls perpendicular to the strain axis. The magnetization transformation exhibits stress-determined directional sensitivity and is reversible and tunable through the size of the nanostructure. In this work, we provide direct evidence for expressive and deterministic magnetic hardening in ferromagnetic nanostructures, while our experimental approach allows quantifiable local measurements of strain-induced changes in the magnetic states of nanomaterials.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet.

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb3 S6  using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Prospect for measuring two-dimensional van der Waals magnets by electron magnetic chiral dichroism.

Two-dimensional (2D) van der Waals magnets have drawn considerable attention in recent years triggered by the huge interest in novel magnetism and spintronic devices. Magnetic measurement of 2D van der Waals (vdW) magnets is crucial to understand the physical origin of magnetism in 2D limits. Therefore, advanced magnetic characterization techniques are highly required. However, only a limited number of such techniques are available due to the extremely small volume of 2D vdW magnets. Here, we introduce the electron magnetic chiral dichroism (EMCD) technique in transmission electron microscope (TEM) to measure 2D vdW crystals. In comparison with some other already-employed techniques in 2D magnets, EMCD is able to quantitatively measure magnetic parameters in three orthogonal directions at nanometer or even at atomic scale. We then perform EMCD simulations on several typical 2D vdW magnets with respect to the accelerating voltage, the number of atomic layers and beam tilt under zone axial orientation. The intensity and distribution of EMCD signals in three orthogonal directions are given in the diffraction plane, thereby providing an optimized design to achieve EMCD measurements. Finally, we discuss the signal-to-noise-ratio and required electron dose in order to obtain a measurable EMCD signal for 2D vdW magnets. Our results provide a feasibility analysis and guideline to measure 2D vdW magnets in future experiments.

Electron-beam-induced charging of an Al2O3 nanotip studied using off-axis electron holography.

Electrostatic charging of specimens during electron, photon or ion irradiation is a complicated and poorly understood phenomenon, which can affect the acquisition and interpretation of experimental data and alter the functional properties of the constituent materials. It is usually linked to secondary electron emission, but also depends on the geometry and electrical properties of the specimen. Here, we use off-axis electron holography in the transmission electron microscope to study electron-beam-induced charging of an insulating Al2O3 nanotip on a conducting support. The measurements are performed under parallel electron illumination conditions as a function of specimen temperature, electron dose, primary electron energy and surface cleanliness. We observe a lack of reproducibility of charge density measurements after cycling the specimen temperature. Surprisingly, we find both positively and negatively charged regions in closely adjacent parts of the specimen.

Magnetic skyrmion braids.

Skyrmions are vortex-like spin textures that form strings in magnetic crystals. Due to the analogy to elastic strings, skyrmion strings are naturally expected to braid and form complex three-dimensional patterns, but this phenomenon has not been explored yet. We found that skyrmion strings can form braids in cubic crystals of chiral magnets. This finding is confirmed by direct observations of skyrmion braids in B20-type FeGe using transmission electron microscopy. The theoretical analysis predicts that the discovered phenomenon is general for a wide family of chiral magnets. These findings have important implications for skyrmionics and propose a solid-state framework for applications of the mathematical theory of braids.

Magnetic Field Mapping using Off-Axis Electron Holography in the Transmission Electron Microscope.

Off-axis electron holography is a powerful technique that involves the formation of an interference pattern in a transmission electron microscope (TEM) by overlapping two parts of an electron wave, one of which has passed through a region of interest on a specimen and the other is a reference wave. The resulting off-axis electron hologram can be analyzed digitally to recover the phase difference between the two parts of the electron wave, which can then be interpreted to provide quantitative information about local variations in electrostatic potential and magnetic induction within and around the specimen. Off-axis electron holograms can be recorded while a specimen is subjected to external stimuli such as elevated or reduced temperature, voltage, or light. The protocol that is presented here describes the practical steps that are required to record, analyze, and interpret off-axis electron holograms, with a primary focus on the measurement of magnetic fields within and around nanoscale materials and devices. Presented here are the steps involved in the recording, analysis, and processing of off-axis electron holograms, as well as the reconstruction and interpretation of phase images and visualization of the results. Also discussed are the need for optimization of the specimen geometry, the electron optical configuration of the microscope, and the electron hologram acquisition parameters, as well as the need for the use of information from multiple holograms to extract the desired magnetic contributions from the recorded signal. The steps are illustrated through a study of specimens of B20-type FeGe, which contain magnetic skyrmions and were prepared with focused ion beams (FIBs). Prospects for the future development of the technique are discussed.

Quantitative measurement of charge accumulation along a quasi-one-dimensional W5O14 nanowire during electron field emission.

We use an electron holographic method to determine the charge distribution along a quasi-one-dimensional W5O14 nanowire during in situ field emission in a transmission electron microscope. The results show that the continuous charge distribution along the nanowire is not linear, but that there is an additional accumulation of charge at its apex. An analytical expression for this additional contribution to the charge distribution is proposed and its effect on the field enhancement factor and emission current is discussed.