Control of morphology and formation of highly geometrically confined magnetic skyrmions

Demonstration of Controlled Skyrmion Injection Across a Thickness Step

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Thermal Stability of Skyrmion Tubes in Nanostructured Cuboids

Magnetic skyrmions in bulk materials are typically regarded as two-dimensional structures. However, they also exhibit three-dimensional configurations, known as skyrmion tubes, that elongate and extend in-depth. Understanding the configurations and stabilization mechanism of skyrmion tubes is crucial for the development of advanced spintronic devices. However, the generation and annihilation of skyrmion tubes in confined geometries are still rarely reported. Here, we present direct imaging of skyrmion tubes in nanostructured cuboids of a chiral magnet FeGe using Lorentz transmission electron microscopy (TEM), while applying an in-plane magnetic field. It is observed that skyrmion tubes stabilize in a narrow field-temperature region near the Curie temperature (Tc). Through a field cooling process, metastable skyrmion tubes can exist in a larger region of the field-temperature diagram. Combining these experimental findings with micromagnetic simulations, we attribute these phenomena to energy differences and thermal fluctuations. Our results could promote topological spintronic devices based on skyrmion tubes.

Room-Temperature Zero-Field kπ-Skyrmions and Their Field-Driven Evolutions in Chiral Nanodisks

Target skyrmion, characterized by a central skyrmion surrounded by a series of concentric cylinder domains known as kπ-skyrmions (k ≥ 2), holds promise as a novel storage state in next-generation memories. However, target skyrmions comprising one or more concentric cylindrical domains have not been observed in chiral magnets, particularly at room temperature. In this study, we experimentally achieved kπ-skyrmions (k = 2, 3, and 4) with diameters of ∼220, 320, and 410 nm, respectively, and room-temperature stability under zero magnetic field by tightly confining these topological spin textures in β-Mn-type Co8Zn10Mn2 nanodisks. The magnetic configurations and their field-driven evolutions were simultaneously investigated by using in situ off-axis electron holography. In combination with numerical simulations, we further investigated the dependence of kmax on the nanodisk diameter. These findings highlight the potential of kπ-skyrmions as information carriers and offer insights into manipulation of kπ-skyrmions in the future.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

All-Electrical 9-Bit Skyrmion-Based Racetrack Memory Designed with Laser Irradiation

Racetrack memories with magnetic skyrmions have recently been proposed as a promising storage technology. To be appealing, several challenges must still be faced for the deterministic generation of skyrmions, their high-fidelity transfer, and accurate reading. Here, we realize the first proof-of-concept of a 9-bit skyrmion racetrack memory with all-electrical controllable functionalities implemented in the same device. The key ingredient is the generation of a tailored nonuniform distribution of magnetic anisotropy via laser irradiation in order to (i) create a well-defined skyrmion nucleation center, (ii) define the memory cells hosting the information coded as the presence/absence of skyrmions, and (iii) improve the signal-to-noise ratio of anomalous Hall resistance measurements. This work introduces a strategy to unify previous findings and predictions for the development of a generation of racetrack memories with robust control of skyrmion nucleation and position, as well as effective skyrmion electrical detection.

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.

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.

Local Manipulation of Skyrmion Nucleation in Microscale Areas of a Thin Film with Nitrogen-Ion Implantation

Precise manipulation of skyrmion nucleation in microscale or nanoscale areas of thin films is a critical issue in developing high-efficient skyrmionic memories and logic devices. Presently, the mainstream controlling strategies focus on the application of external stimuli to tailor the intrinsic attributes of charge, spin, and lattice. This work reports effective skyrmion manipulation by controllably modifying the lattice defect through ion implantation, which is potentially compatible with large-scale integrated circuit technology. By implanting an appropriate dose of nitrogen ions into a Pt/Co/Ta multilayer film, the defect density was effectively enhanced to induce an apparent modulation of magnetic anisotropy, consequently boosting the skyrmion nucleation. Furthermore, the local control of skyrmions in microscale areas of the macroscopic film was realized by combining the ion implantation with micromachining technology, demonstrating a potential application in both binary storage and multistate storage. These findings provide a new approach to advancing the functionalization and application of skyrmionic devices.

Current-Induced Reversible Split of Elliptically Distorted Skyrmions in Geometrically Confined Fe3 Sn2 Nanotrack

Skyrmions are swirling spin textures with topological characters promising for future spintronic applications. Skyrmionic devices typically rely on the electrical manipulation of skyrmions with a circular shape. However, manipulating elliptically distorted skyrmions can lead to numerous exotic magneto-electrical functions distinct from those of conventional circular skyrmions, significantly broadening the capability to design innovative spintronic devices. Despite the promising potential, its experimental realization so far remains elusive. In this study, the current-driven dynamics of the elliptically distorted skyrmions in geometrically confined magnet Fe3 Sn2 is experimentally explored. This study finds that the elliptical skyrmions can reversibly split into smaller-sized circular skyrmions at a current density of 3.8 × 1010 A m-2 with the current injected along their minor axis. Combined experiments with micromagnetic simulations reveal that this dynamic behavior originates from a delicate interplay of the spin-transfer torque, geometrical confinement, and pinning effect, and strongly depends on the ratio of the major axis to the minor axis of the elliptical skyrmions. The results indicate that the morphology is a new degree of freedom for manipulating the current-driven dynamics of skyrmions, providing a compelling route for the future development of spintronic devices.

Confinement of Skyrmions in Nanoscale FeGe Device-like Structures

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions but that a complex device geometry changes the skyrmion behavior, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. The impact of edges in complex shapes is observed to be significant in changing the behavior of the magnetic textures formed. This could allow methods to be developed to control both the position and number of skyrmions within device structures.

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.

Unveiling the three-dimensional magnetic texture of skyrmion tubes

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion-skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles

The concept of topology has dramatically expanded the research landscape of magnetism, leading to the discovery of numerous magnetic textures with intriguing topological properties. A magnetic skyrmion is an emergent topological magnetic texture with a string-like structure in three dimensions and a disk-like structure in one and two dimensions. Skyrmions in zero dimensions have remained elusive due to challenges from many competing orders. Here, by combining electron holography and micromagnetic simulations, we uncover the real-space magnetic configurations of a skyrmionic vortex structure confined in a B20-type FeGe tetrahedral nanoparticle. An isolated skyrmionic vortex forms at the ground state and this texture shows excellent robustness against temperature without applying a magnetic field. Our findings shed light on zero-dimensional geometrical confinement as a route to engineer and manipulate individual skyrmionic metastructures.

Unveiling the Emergent Traits of Chiral Spin Textures in Magnetic Multilayers

Magnetic skyrmions are topologically wound nanoscale textures of spins whose ambient stability and electrical manipulation in multilayer films have led to an explosion of research activities. While past efforts focused predominantly on isolated skyrmions, recently ensembles of chiral spin textures, consisting of skyrmions and magnetic stripes, are shown to possess rich interactions with potential for device applications. However, several fundamental aspects of chiral spin texture phenomenology remain to be elucidated, including their domain wall (DW) structure, thermodynamic stability, and morphological transitions. Here the evolution of these textural characteristics are unveiled on a tunable multilayer platform-wherein chiral interactions governing spin texture energetics can be widely varied-using a combination of full-field electron and soft X-ray microscopies with numerical simulations. With increasing chiral interactions, the emergence of Néel helicity, followed by a marked reduction in domain compressibility, and finally a transformation in the skyrmion formation mechanism are demonstrated. Together with an analytical model, these experiments establish a comprehensive microscopic framework for investigating and tailoring chiral spin texture character in multilayer films.

Robust skyrmion mediated reversal of ferromagnetic nanodots of 20 nm lateral dimension with high Ms and observable DMI

Implementation of skyrmion based energy efficient and high-density data storage devices requires aggressive scaling of skyrmion size. Ferrimagnetic materials are considered to be a suitable platform for this purpose due to their low saturation magnetization (i.e. smaller stray field). However, this method of lowering the saturation magnetization and scaling the lateral size of skyrmions is only applicable where the skyrmions have a smaller lateral dimension compared to the hosting film. Here, we show by performing rigorous micromagnetic simulation that the size of skyrmions, which have lateral dimension comparable to their hosting nanodot can be scaled by increasing saturation magnetization. Also, when the lateral dimension of nanodot is reduced and thereby the skyrmion confined in it is downscaled, there remains a challenge in forming a stable skyrmion with experimentally observed Dzyaloshinskii–Moriya interaction (DMI) values since this interaction has to facilitate higher canting  per spin to complete a 360° rotation along the diameter. In our study, we found that skyrmions can be formed in 20 nm lateral dimension nanodots with high saturation magnetization (1.30–1.70 MA/m) and DMI values (~ 3 mJ/m²) that have been reported to date. This result could stimulate experiments on implementation of highly dense skyrmion devices. Additionally, using this, we show that voltage controlled magnetic anisotropy based switching mediated by an intermediate skyrmion state can be achieved in the soft layer of a ferromagnetic p-MTJ of lateral dimensions 20 nm with sub 1 fJ/bit energy in the presence of room temperature thermal noise with reasonable DMI ~ 3 mJ/m².

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.

Evolution and competition between chiral spin textures in nanostripes with D 2d symmetry

Chiral spin textures are of considerable interest for applications in spintronics. It has recently been shown that magnetic materials with D _2d symmetry can sustain several distinct spin textures. Here, we show, using Lorentz transmission electron microscopy, that single and double chains of antiskyrmions can be generated at room temperature in nanostripes less than 0.5 μm in width formed from the D _2d Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn. Typically, truncated helical spin textures are formed in low magnetic fields, whose edges are terminated by half antiskyrmions. These evolve into chains of antiskyrmions with increasing magnetic field. Single chains of these objects are located in the middle of the nanostripes even when the stripes are much wider than the antiskyrmions. Moreover, the chains can even include elliptical Bloch skyrmions depending on details of the applied magnetic field history. These findings make D _2d materials special and highly interesting for applications such as magnetic racetrack memory storage devices.

Off-axis electron holography of Néel-type skyrmions in multilayers of heavy metals and ferromagnets

Magnetic skyrmions are complex swirling spin structures that are of interest for applications in energy-efficient memories and logic technologies. Multilayers of heavy metals and ferromagnets have been shown to host magnetic skyrmions at room temperature. Lorentz transmission electron microscopy is often used to study magnetic domain structures in multilayer samples using mainly Fresnel defocus imaging. Here, off-axis electron holography is used to obtain in-focus electron optical phase images of Néel-type domains and skyrmions in an Ir/Fe/Co/Pt multilayer sample. The preparation of the sample, reconstruction of the holograms and influence of sample tilt angle on the signal-to-noise ratio in the phase images are discussed. A good agreement is found between images of individual skyrmions that are stabilized using an external magnetic field and simulated images based on theoretical models of Néel-type skyrmions.

A cartridge-based turning specimen holder with wireless tilt angle measurement for magnetic induction mapping in the transmission electron microscope

Magnetic induction mapping in the transmission electron microscope using phase contrast techniques such as off-axis electron holography and differential phase contrast imaging often requires the separation of the magnetic contribution to the recorded signal from the electrostatic contribution. When using off-axis electron holography, one of the experimental approaches that can be used to achieve this separation is to evaluate half of the difference between phase shift images that have been recorded before and after turning the sample over. Here, we introduce a cartridge-based sample mounting system, which is based on an existing on-axis tomography specimen holder and can be used to turn a sample over inside the electron microscope, thereby avoiding the need to remove the holder from the microscope to turn the sample over manually. We present three cartridge designs, which are compatible with all pole piece designs and can be used to support conventional 3-mm-diameter sample grids, Si₃N₄-based membrane chips and needle-shaped specimens. We make use of a wireless inclinometer that has a precision of 0.1° to monitor the sample holder tilt angle independently of the microscope goniometer readout. We also highlight the need to remove geometrical image distortions when aligning pairs of phase shift images that have been recorded before and after turning the sample over. The capabilities of the cartridge-based specimen holder and the turning approach are demonstrated by using off-axis electron holography to record magnetic induction maps of lithographically-patterned soft magnetic Co elements, a focused ion beam milled hard magnetic Nd-Fe-B lamella and an array of four Fe₃O₄ nanocrystals.

Half-hedgehog spin textures in sub-100 nm soft magnetic nanodots

Topologically non-trivial structures such as magnetic skyrmions are nanometric spin textures of outstanding potential for spintronic applications due to their unique features. It is well known that Néel skyrmions of definite chirality are stabilized by the Dzyaloshinskii-Moriya exchange interaction (DMI) in bulk non-centrosymmetric materials or ultrathin films with strong spin-orbit coupling at the interface. In this work, we show that soft magnetic (permalloy) hemispherical nanodots are able to host three-dimensional chiral structures (half-hedgehog spin textures) with non-zero tropological charge. They are observed at room temperature, in absence of DMI interaction and they can be further stabilized by the magnetic field arising from the Magnetic Force Microscopy probe. Micromagnetic simulations corroborate the experimental data. Our work implies the existence of a new degree of freedom to create and manipulate complex 3D spin-textures in soft magnetic nanodots and opens up future possibilities to explore their magnetization dynamics.

Dynamics of chiral state transitions and relaxations in an FeGe thin plate via in situ Lorentz microscopy

Studying the magnetic transition between different topological spin textures in noncentrosymmetric magnets under external stimuli is an important topic in chiral magnetism. Here, using in situ Lorentz transmission electron microscopy (LTEM) we directly visualize the thermal-driven magnetic transitions and dynamic characteristics in FeGe thin plates. A novel protocol-dependent phase diagram of FeGe thin plates was obtained via pulsed laser excitation. Moreover, by setting the appropriate specimen temperature, the relaxation of chiral magnetic states in FeGe specimens was recorded and analyzed with an Arrhenius-type relaxation mechanism. We present the field-dependent activation energy barriers for chiral state transitions and the magnetic transition pathways of these spin textures for FeGe thin plates. Our results unveil the effects of thermal excitation on the topological spin texture transitions and provide useful information about magnetic dynamics of chiral magnetic state relaxation.

Visualizing Magnetic Structure in 3D Nanoscale Ni-Fe Gyroid Networks

Arrays of interacting 2D nanomagnets display unprecedented electromagnetic properties via collective effects, demonstrated in artificial spin ices and magnonic crystals. Progress toward 3D magnetic metamaterials is hampered by two challenges: fabricating 3D structures near intrinsic magnetic length scales (sub-100 nm) and visualizing their magnetic configurations. Here, we fabricate and measure nanoscale magnetic gyroids, periodic chiral networks comprising nanowire-like struts forming three-connected vertices. Via block copolymer templating, we produce Ni₇₅Fe₂₅ single-gyroid and double-gyroid (an inversion pair of single-gyroids) nanostructures with a 42 nm unit cell and 11 nm diameter struts, comparable to the exchange length in Ni-Fe. We visualize their magnetization distributions via off-axis electron holography with nanometer spatial resolution and interpret the patterns using finite-element micromagnetic simulations. Our results suggest an intricate, frustrated remanent state which is ferromagnetic but without a unique equilibrium configuration, opening new possibilities for collective phenomena in magnetism, including 3D magnonic crystals and unconventional computing.

Scaling, rotation, and channeling behavior of helical and skyrmion spin textures in thin films of Te-doped Cu2OSeO3

Topologically nontrivial spin textures such as vortices, skyrmions, and monopoles are promising candidates as information carriers for future quantum information science. Their controlled manipulation including creation and annihilation remains an important challenge toward practical applications and further exploration of their emergent phenomena. Here, we report controlled evolution of the helical and skyrmion phases in thin films of multiferroic Te-doped Cu₂OSeO₃ as a function of material thickness, dopant, temperature, and magnetic field using in situ Lorentz phase microscopy. We report two previously unknown phenomena in chiral spin textures in multiferroic Cu₂OSeO₃: anisotropic scaling and channeling with a fixed-Q state. The skyrmion channeling effectively suppresses the recently reported second skyrmion phase formation at low temperature. Our study provides a viable way toward controlled manipulation of skyrmion lattices, envisaging chirality-controlled skyrmion flow circuits and enabling precise measurement of emergent electromagnetic induction and topological Hall effects in skyrmion lattices.

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.

Smectic Liquid-Crystalline Structure of Skyrmions in Chiral Magnet Co_{8.5}Zn_{7.5}Mn_{4}(110) Thin Film

The organizing of magnetic skyrmions shows several forms similar to atomic arrays of solid states. Using Lorentz transmission electron microscopy, we report the first direct observation of a stable liquid-crystalline structure of skyrmions in chiral magnet Co_{8.5}Zn_{7.5}Mn_{4}(110) thin film, caused by magnetic anisotropy and chiral surface twist. Elongated skyrmions are oriented and periodically arranged only in the ⟨110⟩ directions, whereas they exhibit short-range order along the ⟨001⟩ directions, indicating a smectic skyrmion state. In addition, skyrmions possess anisotropic interaction with an opposite sign depending on the crystal orientation, in contrast to existing isotropic interaction.

Electron Holography and Magnetotransport Measurements Reveal Stabilized Magnetic Skyrmions in Fe1-xCoxSi Nanowires

Magnetic skyrmions are topological spin textures that have shown promise for future nonvolatile memory devices. Herein, we report on the stability of magnetic skyrmions in alloyed cubic B20 Fe_1-xCo_xSi nanowires (NWs) determined using off-axis electron holography and magnetotransport measurements. This study presents the real space observation of one-dimensional skyrmion lattice in a NW of Fe_1-xCo_xSi which shows that the skyrmion phase in a Fe_0.75Co_0.25Si NW exists at lower applied magnetic fields (200 Oe) with a reduced domain size (28 ± 2 nm) in comparison to bulk and thin film samples. Magnetotransport measurements were used to observe the helimagnetic transition temperature dependence on the cobalt concentration in the Fe_1-xCo_xSi NWs. Field-dependent magnetoresistance measurements of Fe_1-xCo_xSi NWs under applied magnetic field parallel to the NW axis and their second derivative plots reveal the critical fields for the magnetic state transition at different temperatures. A representative magnetic phase diagram constructed with the results from transport measurements of a Fe_0.81Co_0.19Si NW clearly shows expanded stability region for magnetic skyrmions in the Fe_1-xCo_xSi NWs.

An achiral ferromagnetic/chiral antiferromagnetic bilayer system leading to controllable size and density of skyrmions

Magnetic skyrmions are topologically protected domain structures related to the Dzyaloshinskii-Moriya interaction (DMI). To understand how magnetic skyrmions occur under different circumstances, we propose a model for skyrmion formation in a bilayer system of ferromagnetic/antiferromagnetic (FM/AFM) films, in which the bulk DMI is only present in the AFM film. Micromagnetic simulations reveal that skyrmions are formed in this system due to the competition between the DMI and demagnetization energies. A critical interfacial exchange energy (A_i = 6.5 mJ/m²) is determined, above which the competition occurs at its full extent. More skyrmions are formed with increasing external magnetic field till a critical value above which the external field is too large and thus leading to the annihilation of skyrmions. The spacing between two skyrmions can be as small as 45 nm. Our results may give technological implications for future skyrmion applications.

Manipulating the Topology of Nanoscale Skyrmion Bubbles by Spatially Geometric Confinement

The discovery of magnetic skyrmion bubbles in centrosymmetric magnets has been receiving increasing interest from the research community, due to the fascinating physics of topological spin textures and its possible applications to spintronics. However, key challenges remain, such as how to manipulate the nucleation of skyrmion bubbles to exclude the trivial bubbles or metastable skyrmion bubbles that usually coexist with skyrmion bubbles in the centrosymmetric magnets. Here, we report having performed this task by applying spatially geometric confinement to a centrosymmetric frustrated Fe₃Sn₂ magnet. We demonstrate that the spatially geometric confinement can indeed stabilize the skyrmion bubbles by effectively suppressing the formation of trivial bubbles and metastable skyrmion bubbles. We also show that the critical magnetic field for the nucleation of the skyrmion bubbles in the confined Fe₃Sn₂ nanostripes is drastically less, by an order of magnitude, than that required in the thin plate without geometrical confinement. By analyzing how the width and thickness of the nanostripes affect the spin textures of skyrmion bubbles, we infer that the topological transition of skyrmion bubbles is closely related to the dipole-dipole interaction, which we find is consistent with theoretical simulations. The results presented here bring us closer to achieving the fabrication of skyrmion-based racetrack memory devices.

Architecture of nanoscale ferroelectric domains in GaMo4S8

Local-probe imaging of the ferroelectric domain structure and auxiliary bulk pyroelectric measurements were conducted at low temperatures with the aim to clarify the essential aspects of the orbitally driven phase transition in GaMo₄S₈, a lacunar spinel crystal that can be viewed as a spin-hole analogue of its GaV₄S₈ counterpart. We employed multiple scanning probe techniques combined with symmetry and mechanical compatibility analysis to uncover the hierarchical domain structures, developing on the 10-100 nm scale. The identified domain architecture involves a plethora of ferroelectric domain boundaries and junctions, including primary and secondary domain walls in both electrically neutral and charged configurations, and topological line defects transforming neutral secondary walls into two oppositely charged ones.

Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures

Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Moriya interactions and the geometry of nanostructures, stabilize hopfions. We demonstrate knots in emergent field lines and computer simulate Lorentz transmission electron microscopy images of such solitonic configurations to guide their experimental discovery in magnetic solids.

Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet

It is commonly assumed that surfaces modify the properties of stable materials within the top few atomic layers of a bulk specimen only. Exploiting the polarization dependence of resonant elastic X-ray scattering to go beyond conventional diffraction and imaging techniques, we have determined the depth dependence of the full 3D spin structure of skyrmions-that is, topologically nontrivial whirls of the magnetization-below the surface of a bulk sample of Cu₂OSeO₃ We found that the skyrmions change exponentially from pure Néel- to pure Bloch-twisting over a distance of several hundred nanometers between the surface and the bulk, respectively. Though qualitatively consistent with theory, the strength of the Néel-twisting at the surface and the length scale of the variation observed experimentally exceed material-specific modeling substantially. In view of the exceptionally complete quantitative theoretical account of the magnetic rigidities and associated static and dynamic properties of skyrmions in Cu₂OSeO₃ and related materials, we conclude that subtle changes of the materials properties must exist at distances up to several hundred atomic layers into the bulk, which originate in the presence of the surface. This has far-reaching implications for the creation of skyrmions in surface-dominated systems and identifies, more generally, surface-induced gradual variations deep within a bulk material and their impact on tailored functionalities as an unchartered scientific territory.

Direct Observation of Twisted Surface skyrmions in Bulk Crystals

Magnetic skyrmions in noncentrosymmetric helimagnets with D_{n} symmetry are Bloch-type magnetization swirls with a helicity angle of ±90°. At the surface of helimagnetic thin films below a critical thickness, a twisted skyrmion state with an arbitrary helicity angle has been proposed; however, its direct experimental observation has remained elusive. Here, we show that circularly polarized resonant elastic x-ray scattering is able to unambiguously measure the helicity angle of surface skyrmions, providing direct experimental evidence that a twisted skyrmion surface state also exists in bulk systems. The exact surface helicity angles of twisted skyrmions for both left- and right-handed chiral bulk Cu_{2}OSeO_{3}, in the single as well as in the multidomain skyrmion lattice state, are determined, revealing their detailed internal structure. Our findings suggest that a skyrmion surface reconstruction is a universal phenomenon, stemming from the breaking of translational symmetry at the interface.

Experimental observation of chiral magnetic bobbers in B20-type FeGe

Chiral magnetic skyrmions^1,2 are nanoscale vortex-like spin textures that form in the presence of an applied magnetic field in ferromagnets that support the Dzyaloshinskii-Moriya interaction (DMI) because of strong spin-orbit coupling and broken inversion symmetry of the crystal^3,4. In sharp contrast to other systems^5,6 that allow for the formation of a variety of two-dimensional (2D) skyrmions, in chiral magnets the presence of the DMI commonly prevents the stability and coexistence of topological excitations of different types ⁷ . Recently, a new type of localized particle-like object-the chiral bobber (ChB)-was predicted theoretically in such materials ⁸ . However, its existence has not yet been verified experimentally. Here, we report the direct observation of ChBs in thin films of B20-type FeGe by means of quantitative off-axis electron holography (EH). We identify the part of the temperature-magnetic field phase diagram in which ChBs exist and distinguish two mechanisms for their nucleation. Furthermore, we show that ChBs are able to coexist with skyrmions over a wide range of parameters, which suggests their possible practical applications in novel magnetic solid-state memory devices, in which a stream of binary data bits can be encoded by a sequence of skyrmions and bobbers.

Induction Mapping of the 3D-Modulated Spin Texture of Skyrmions in Thin Helimagnets

Envisaged applications of Skyrmions in magnetic memory and logic devices crucially depend on the stability and mobility of these topologically nontrivial magnetic textures in thin films. We present for the first time quantitative maps of the magnetic induction that provide evidence for a 3D modulation of the Skyrmionic spin texture. The projected in-plane magnetic induction maps as determined from in-line and off-axis electron holography carry the clear signature of Bloch Skyrmions. However, the magnitude of this induction is much smaller than the values expected for homogeneous Bloch Skyrmions that extend throughout the thickness of the film. This finding can only be understood if the underlying spin textures are modulated along the out-of-plane z direction. The projection of (the in-plane magnetic induction of) helices is further found to exhibit thickness-dependent lateral shifts, which show that this z modulation is accompanied by an (in-plane) modulation along the x and y directions.

Interaction of Individual Skyrmions in a Nanostructured Cubic Chiral Magnet

We report direct evidence of the field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high-resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of an external magnetic field the character of such long-range skyrmion interactions changes from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skyrmion-edge distances as a function of the applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. The important role of demagnetizing fields and the internal symmetry of three-dimensional magnetic skyrmions are discussed in detail.

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.

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.

Creation of Single Chain of Nanoscale Skyrmion Bubbles with Record-High Temperature Stability in a Geometrically Confined Nanostripe

Nanoscale topologically nontrivial spin textures, such as magnetic skyrmions, have been identified as promising candidates for the transport and storage of information for spintronic applications, notably magnetic racetrack memory devices. The design and realization of a single skyrmion chain at room temperature (RT) and above in the low-dimensional nanostructures are of great importance for future practical applications. Here, we report the creation of a single skyrmion bubble chain in a geometrically confined Fe₃Sn₂ nanostripe with a width comparable to the featured size of a skyrmion bubble. Systematic investigations on the thermal stability have revealed that the single chain of skyrmion bubbles can keep stable at temperatures varying from RT up to a record-high temperature of 630 K. This extreme stability can be ascribed to the weak temperature-dependent magnetic anisotropy and the formation of edge states at the boundaries of the nanostripes. The realization of the highly stable skyrmion bubble chain in a geometrically confined nanostructure is a very important step toward the application of skyrmion-based spintronic devices.

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.