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

Bending skyrmion strings under two-dimensional thermal gradients

Magnetic skyrmions are topologically protected magnetization vortices that form three-dimensional strings in chiral magnets. With the manipulation of skyrmions being key to their application in devices, the focus has been on their dynamics within the vortex plane, while the dynamical control of skyrmion strings remained uncharted territory. Here, we report the effective bending of three-dimensional skyrmion strings in the chiral magnet MnSi in orthogonal thermal gradients using small angle neutron scattering. This dynamical behavior is achieved by exploiting the temperature-dependent skyrmion Hall effect, which is unexpected in the framework of skyrmion dynamics. We thus provide experimental evidence for the existence of magnon friction, which was recently proposed to be a key ingredient for capturing skyrmion dynamics, requiring a modification of Thiele's equation. Our work therefore suggests the existence of an extra degree of freedom for the manipulation of three-dimensional skyrmions.

Bloch Point Quadrupole Constituting Hybrid Topological Strings Revealed with Electron Holographic Vector Field Tomography

Topological magnetic (anti)skyrmions are robust string-like objects heralded as potential components in next-generation topological spintronics devices due to their low-energy manipulability via stimuli such as magnetic fields, heat, and electric/thermal current. While these 2D topological objects are widely studied, intrinsically 3D electron-spin real-space topology remains less explored despite its prevalence in bulky magnets. 2D-imaging studies reveal peculiar vortex-like contrast in the core regions of spin textures present in antiskyrmion-hosting thin plate magnets with S4 crystal symmetry, suggesting a more complex 3D real-space structure than the 2D model suggests. Here, holographic vector field electron tomography captures the 3D structure of antiskyrmions in a single-crystal, precision-doped (Fe0.63Ni0.3Pd0.07)3P (FNPP) lamellae at room temperature and zero field. These measurements reveal hybrid string-like solitons composed of skyrmions with topological number W = -1 on the lamellae's surfaces and an antiskyrmion (W = + 1) connecting them. High-resolution images uncover a Bloch point quadrupole (four magnetic (anti)monopoles that are undetectable in 2D imaging) which enables the observed lengthwise topological transitions. Numerical calculations corroborate the stability of hybrid strings over their conventional (anti)skyrmion counterparts. Hybrid strings result in topological tuning, a tunable topological Hall effect, and the suppression of skyrmion Hall motion, disrupting existing paradigms within spintronics.

Observation by SANS and PNR of pure Néel-type domain wall profiles and skyrmion suppression below room temperature in magnetic [Pt/CoFeB/Ru]10 multilayers

We report investigations of the magnetic textures in periodic multilayers [Pt(1 nm)/(CoFeB(0.8 nm)/Ru(1.4 nm)]10 using polarised neutron reflectometry (PNR) and small-angle neutron scattering (SANS). The multilayers are known to host skyrmions stabilized by Dzyaloshinskii-Moriya interactions induced by broken inversion symmetry and spin-orbit coupling at the asymmetric interfaces. From depth-dependent PNR measurements, we observed well-defined structural features and obtained the layer-resolved magnetization profiles. The in-plane magnetization of the CoFeB layers calculated from fitting of the PNR profiles is found to be in excellent agreement with magnetometry data. Using SANS as a bulk probe of the entire multilayer, we observe long-period magnetic stripe domains and skyrmion ensembles with full orientational disorder at room temperature. No sign of skyrmions is found below 250 K, which we suggest is due to an increase of an effective magnetic anisotropy in the CoFeB layer on cooling that suppresses skyrmion stability. Using polarised SANS at room temperature, we prove the existence of pure Néel-type windings in both stripe domain and skyrmion regimes. No Bloch-type winding admixture, i.e. an indication for hybrid windings, is detected within the measurement sensitivity, in good agreement with expectations according to our micromagnetic modelling of the multilayers. Our findings using neutron techniques provide valuable microscopic insights into the rich magnetic behavior of skyrmion-hosting multilayers, which are essential for the advancement of future skyrmion-based spintronic devices.

Evolution of Emergent Monopoles into Magnetic Skyrmion Strings

Topological defects are fundamental concepts in physics, but little is known about the transition between distinct types across different dimensionalities. In topological magnetism, as in field theory, the transition between 1D strings and 0D monopoles is a key process whose observation has remained elusive. Here, we introduce a novel mechanism that allows for the controlled stabilization of emergent monopoles and show that magnetic skyrmion strings can be folded into monopoles. Conversely, they act as seeds out of which the entire string structure can unfold, containing its complete information. In chiral magnets, this process can be observed by resonant elastic X-ray scattering when the objects are in proximity to a polarized ferromagnet, whereby a pure monopole lattice is emerging on the surface. Our experimental proof of the reversible evolution from monopole to string sheds new light on topological defects and establishes the emergent monopole lattice as a new 3D topological phase.

Small-angle neutron scattering of long-wavelength magnetic modulations in reduced sample dimensions

Magnetic small-angle neutron scattering (SANS) is ideally suited to providing direct reciprocal-space information on long-wavelength magnetic modulations, such as helicoids, solitons, merons or skyrmions. SANS of such structures in thin films or micro-structured bulk materials is strongly limited by the tiny scattering volume vis a vis the prohibitively high background scattering by the substrate and support structures. Considering near-surface scattering just above the critical angle of reflection, where unwanted signal contributions due to substrate or support structures become very small, it is established that the scattering patterns of the helical, conical, skyrmion lattice and fluctuation-disordered phases in a polished bulk sample of MnSi are equivalent for conventional transmission and near-surface SANS geometries. This motivates the prediction of a complete repository of scattering patterns expected for thin films in the near-surface SANS geometry for each orientation of the magnetic order with respect to the scattering plane.

Real-Space Observations of Three-Dimensional Antiskyrmions and Skyrmion Strings

Nanometric topological spin textures, such as skyrmions (Sks) and antiskyrmions (antiSks), have attracted much attention recently. However, most studies have focused on two-dimensional spin textures in films with inherent or synthetic antisymmetric spin-exchange interaction, termed Dzyaloshinskii-Moriya interaction, although three-dimensional (3D) topological spin textures, such as antiSks composed of alternating Bloch- and Néel-type spin spirals, chiral bobbers carrying emergent magnetic monopoles, and deformed Sk strings, are ubiquitous. To elucidate these textures, we have developed a 3D nanometric magnetic imaging technique, tomographic Lorentz transmission electron microscopy (TEM). The approach enables the visualization of the 3D shape of magnetic objects and their 3D vector field mapping. Here we report 3D vector field maps of deformed Sk-strings and antiSk using the technique. This research approach will lead to discoveries and understanding of fertile 3D magnetic structures in a broad class of magnets, providing insight into 3D topological magnetism.

Chiral surface spin textures in Cu2OSeO3 unveiled by soft X-ray scattering in specular reflection geometry

Resonant elastic soft X-ray magnetic scattering (XRMS) is a powerful tool to explore long-periodic spin textures in single crystals. However, due to the limited momentum transfer range imposed by long wavelengths of photons in the soft x-ray region, Bragg diffraction is restricted to crystals with the large lattice parameters. Alternatively, small-angle X-ray scattering has been involved in the soft energy X-ray range which, however, brings in difficulties with the sample preparation that involves focused ion beam milling to thin down the crystal to below a few hundred nm thickness. We show how to circumvent these restrictions using XRMS in specular reflection from a sub-nanometer smooth crystal surface. The method allows observing diffraction peaks from the helical and conical spin modulations at the surface of a Cu   2 OSeO   3 single crystal and probing their corresponding chirality as contributions to the dichroic scattered intensity. The results suggest a promising way to carry out XRMS studies on a plethora of noncentrosymmetric systems hitherto unexplored with soft X-rays due to the absence of the commensurate Bragg peaks in the available momentum transfer range.

Chirality flips of skyrmion bubbles

The investigation of three-dimensional magnetic textures and chirality switching has attracted enormous interest from the perspective of fundamental research. Here, the three-dimensional magnetic structures of skyrmion bubbles in the centrosymmetric magnet MnNiGa were reconstructed with the vector field tomography approach via Lorentz transmission electron microscopy. The magnetic configuration of the bubbles was determined based on the reconstructed magnetic induction (B-field) at their surfaces and centers. We found that the bubbles easily switched their chirality but preserved their polarity to retain their singularity in the matrix of the material. Our results offer valuable insights into the chirality behavior of skyrmion bubbles.

Axially Bound Magnetic Skyrmions: Glueing Topological Strings Across an Interface

A major challenge in topological magnetism lies in the three-dimensional (3D) exploration of their magnetic textures. A recent focus has been the question of how 2D skyrmion sheets vertically stack to form distinct types of 3D topological strings. Being able to manipulate the vertical coupling should therefore provide a route to the engineering of topological states. Here, we present a new type of axially bound magnetic skyrmion string state in which the strings in two distinct materials are glued together across their interface. With quasi-tomographic resonant elastic X-ray scattering, the 3D skyrmion profiles before and after their binding across the interface were unambiguously determined and compared. Their attractive binding is accompanied by repulsive twisting; i.e., the coupled skyrmions mutually affect each other via a compensating twisting. This state exists in chiral magnet-magnetic thin film heterostructures, providing a new arena for the engineering of 3D topological 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.

Using small-angle scattering to guide functional magnetic nanoparticle design

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

Direct visualization of the three-dimensional shape of skyrmion strings in a noncentrosymmetric magnet

Magnetic skyrmions are topologically stable swirling spin textures that appear as particle-like objects in two-dimensional (2D) systems. Here, utilizing scalar magnetic X-ray tomography under applied magnetic fields, we report the direct visualization of the three-dimensional (3D) shape of individual skyrmion strings in the room-temperature skyrmion-hosting non-centrosymmetric compound Mn_1.4Pt_0.9Pd_0.1Sn. Through the tomographic reconstruction of the 3D distribution of the [001] magnetization component on the basis of transmission images taken at various angles, we identify a skyrmion string running through the entire thickness of the sample, as well as various defect structures, such as the interrupted and Y-shaped strings. The observed point defect may represent the Bloch point serving as an emergent magnetic monopole, as proposed theoretically. Our tomographic approach with a tunable magnetic field paves the way for direct visualization of the structural dynamics of individual skyrmion strings in 3D space, which will contribute to a better understanding of the creation, annihilation and transfer of these topological objects.

Superposition of Emergent Monopole and Antimonopole in CoTb Thin Films

A three-dimensional singular point that consists of two oppositely aligned emergent monopoles is identified in continuous CoTb thin films, as confirmed by complementary techniques of resonant elastic x-ray scattering, Lorentz transmission electron microscopy, and scanning transmission x-ray microscopy. This new type of topological defect can be regarded as a superposition of an emergent magnetic monopole and an antimonopole, around which the source and drain of the magnetic flux overlap in space. We experimentally prove that the observed spin twist seen in Lorentz transmission electron microscopy reveals the cross section of the superimposed three-dimensional structure, providing a straightforward strategy for the observation of magnetic singularities. Such a quasiparticle provides an excellent platform for studying the rich physics of emergent electromagnetism.

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Chiral Spin Textures in Amorphous Iron-Germanium Thick Films

Topological solitary fields, such as magnetic and polar skyrmions, are envisioned to revolutionize microelectronics. These configurations have been stabilized in solid-state materials with a global inversion symmetry breaking, which translates in magnetic materials into a vector spin exchange known as the Dzyaloshinskii-Moriya interaction (DMI), as well as spin chirality selection and isotropic solitons. This work reports experimental evidence of 3D chiral spin textures, such as helical spins and skyrmions with different chirality and topological charge, stabilized in amorphous Fe-Ge thick films. These results demonstrate that structurally and chemically disordered materials with a random DMI can resemble inversion symmetry broken systems with similar magnetic properties, moments, and states. Disordered systems are distinguished from systems with global inversion symmetry breaking by their degenerate spin chirality that allows for forming isotropic and anisotropic topological spin textures at remanence, while offering greater flexibility in materials synthesis, voltage, and strain manipulation.

Creation of a Chiral Bobber Lattice in Helimagnet-Multilayer Heterostructures

A chiral bobber is a localized three-dimensional magnetization configuration, terminated by a singularity. Chiral bobbers coexist with magnetic skyrmions in chiral magnets, lending themselves to new types of skyrmion-complementary bits of information. However, the on-demand creation of bobbers, as well as their direct observation remained elusive. Here, we introduce a new mechanism for creating a stable chiral bobber lattice state via the proximity of two skyrmion species with comparable size. This effect is experimentally demonstrated in a Cu_{2}OSeO_{3}/[Ta/CoFeB/MgO]_{4} heterostructure in which an exotic bobber lattice state emerges in the phase diagram of Cu_{2}OSeO_{3}. To unambiguously reveal the existence of the chiral bobber lattice state, we have developed a novel characterization technique, magnetic truncation rod analysis, which is based on resonant elastic x-ray scattering.

Revealing 3D magnetization of thin films with soft X-ray tomography: magnetic singularities and topological charges

The knowledge of how magnetization looks inside a ferromagnet is often hindered by the limitations of the available experimental methods which are sensitive only to the surface regions or limited in spatial resolution. Here we report a vector tomographic reconstruction based on soft X-ray transmission microscopy and magnetic dichroism data, which has allowed visualizing the three-dimensional magnetization in a ferromagnetic thin film heterostructure. Different non-trivial topological textures have been resolved and the determination of their topological charge has allowed us to identify a Bloch point and a meron-like texture. Our method relies only on experimental data and might be of wide application and interest in 3D nanomagnetism.

Although magnetic tomography has been used in the past to determine the 3D magnetization of materials its application to thin films remains challenging. Here the authors reconstruct the magnetization of a thin film, enabling the measurement of topological charges of magnetic singularities.

Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

Kerr effect anomaly in magnetic topological insulator superlattices

We report the magneto-optical Kerr effect (MOKE) study of magnetic topological insulator superlattice films with alternating transition-metal and rare-earth doping. We observe an unexpected hump in the MOKE hysteresis loops upon magnetization reversal at low temperatures, reminiscent of the topological Hall effect (THE) reported in transport measurements. The THE is commonly associated with the existence of magnetic skyrmions, i.e. chiral spin textures originating from topological defects in real space. Here, the observation of the effect is tied to ferromagnetic ordering in the rare-earth-doped layers of the superlattice. Our study may provide a new approach for the non-invasive optical investigation of skyrmions in magnetic films, complementary to electrical transport measurements, where the topological Hall signal is often the only hint of non-trivial magnetization patterns.

Real-Space Observation of Topological Defects in Extended Skyrmion-Strings

Exotic topological spin textures such as emergent magnetic monopole/anti-monopoles (hedgehog/anti-hedgehog) in the metastable extended skyrmion-strings attract much attention to the fundamental physics owing to their novel electromagnetic properties. However, the direct imaging of such spin textures is lacking. Here, we report the real-space observation of emergent magnetic monopoles involved in extended skyrmion-strings by Lorentz transmission electron microscopy (TEM) in combination with micromagnetic simulations. The in-plane extended skyrmion-strings are observed directly by Lorentz TEM to accompany the topological hedgehog-like defect, where the skyrmion-string terminates or merges with another skyrmion-string, as well as the surface-related defects where skyrmion-string bends 90° and ends on the surface. We also demonstrate the transformation of a metastabilized lattice of out-of-plane short skyrmion-strings into an in-plane array of extended skyrmion-strings by tuning the magnitude of oblique fields in a room-temperature helimagnet, revealing the stability of such topological spin textures and the possibility to control them.

Detection of the Chiral Spin Structure in Ferromagnetic SrRuO3 Thin Film

SrRuO₃ (SRO) thin films and their heterostructure have attracted much attention because of the recently demonstrated fascinating properties, such as topological Hall effect and skyrmions. Critical to the understanding of those SRO properties is the study of the spin configuration. Here, we conduct resonant soft X-ray scattering (RSXS) at the oxygen K edge to investigate the spin configuration of a four-unit-cell SRO film that was grown epitaxially on a single-crystal SrTiO₃. The RSXS signal under a magnetic field (∼0.4 tesla) clearly shows a magnetic dichroism pattern around the specular reflection. Model calculations on the RSXS signal demonstrate that the magnetic dichroism pattern originates from a Néel-type chiral spin structure in this SRO thin film. We believe that the observed spin structure of the SRO system is a critical piece of information for understanding its intriguing magnetic and transport properties.

Imaging three-dimensional magnetic systems with x-rays

Recent progress in nanofabrication and additive manufacturing have facilitated the building of nanometer-scale three-dimensional (3D) structures, that promise to lead to an emergence of new functionalities within a number of fields, compared to state-of-the-art two dimensional systems. In magnetism, the move to 3D systems offers the possibility for novel magnetic properties not available in planar systems, as well as enhanced performance, both of which are key for the development of new technological applications. In this review paper we will focus our attention on 3D magnetic systems and how their magnetic configuration can be retrieved using x-ray magnetic nanotomography. We will start with an introduction to magnetic materials, and their relevance to our everyday life, along with the growing impact that they will have in the coming years in, for example, reducing energy consumption. We will then briefly introduce common methods used to study magnetic materials, such as electron holography, neutron and x-ray imaging. In particular, we will focus on x-ray magnetic circular dichroism (XMCD) and how it can be used to image magnetic moment configurations. As a next step we will introduce tomography for 3D imaging, and how it can be adapted to study magnetic materials. Particular attention will be given to explaining the reconstruction algorithms that can be used to retrieve the magnetic moment configuration from the experimental data, as these represent one of the main challenges so far, as well as the different experimental geometries that are available. Recent experimental results will be used as specific examples to guide the reader through each step in order to make sure that the paper will be accessible for those interested in the topic that do not have a specialized background on magnetic imaging. Finally, we will describe the future prospects of such studies, identifying the current challenges facing the field, and how these can be tackled. In particular we will highlight the exciting possibilities offered by the next generation of synchrotron sources which will deliver diffraction limited beams, as well as with the extension of well-established methodologies currently implemented for the study of two-dimensional magnetic materials to achieve higher dimensional investigations.

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.

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.

Magnetic skyrmions in FePt nanoparticles having Reuleaux 3D geometry: a micromagnetic simulation study

The magnetization reversal in magnetic FePt nanoelements having Reuleaux 3D geometry is studied using micromagnetic simulations employing Finite Element discretizations. Magnetic skyrmions are revealed in different systems generated by the variation of the magnitude of the magnetocrystalline anisotropy which was kept normal to the nanoelement's base and parallel to the applied external field. The topological quantity of skyrmion number is computed in order to characterize micromagnetic configurations exhibiting skyrmionic formations. Micromagnetic configurations with a wide range of skyrmion numbers between -3 and 3 are indicative for the existence of one or multiple skyrmions that have been detected and stabilized in a range of external fields. Internal magnetic structures are shown consisting of Bloch type skyrmionic entities in the bulk altered to Néel skyrmions on the nanoelement's bottom and top base surfaces. The actual sizes of the formed skyrmions and the internal magnetization structures were computed. In particular, the sizes of the generated and persistent skyrmions were calculated as functions of the magnetocrystalline anisotropy value and of the applied external magnetic field. It is shown that the size of skyrmions is linearly dependent on the external field value. The slope of the linear curve can be controlled by the magnetocrystalline anisotropy value. The magnetic skyrmions can be created for FePt magnetic systems lacking of chiral interactions by designing the geometry-shape of the nanoparticle and by controlling the value of magnetocrystalline anisotropy.

Three-dimensional frequency- and phase-multiplexed magneto-optical microscopy

We describe a new approach to scanning magneto-optical Kerr effect (MOKE) microscopy in which two opto-mechanical choppers modulate the spatial profile of a probe laser beam to separately encode all three magnetization components at different frequencies and phases in one signal. We demonstrate this multiplexed technique in two representative regimes: the equilibrium and non-equilibrium response of a magnetic vortex to a changing magnetic field. We observe the translation of the vortex state in equilibrium and the spiraling gyrotropic trajectory of the vortex position out of equilibrium. We compare the results to a traditional MOKE measurement and to micromagnetic simulations. We find that the multiplexed method presented here provides better agreement with simulation than previous methods and equal or better signal-to-noise ratio.

Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

Cubic chiral magnets, such as Cu_{2}OSeO_{3}, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Anatomy of Skyrmionic Textures in Magnetic Multilayers

Room temperature magnetic skyrmions in magnetic multilayers are considered as information carriers for future spintronic applications. Currently, a detailed understanding of the skyrmion stabilization mechanisms is still lacking in these systems. To gain more insight, it is first and foremost essential to determine the full real-space spin configuration. Here, two advanced X-ray techniques are applied, based on magnetic circular dichroism, to investigate the spin textures of skyrmions in [Ta/CoFeB/MgO]_n multilayers. First, by using ptychography, a high-resolution diffraction imaging technique, the 2D out-of-plane spin profile of skyrmions with a spatial resolution of 10 nm is determined. Second, by performing circular dichroism in resonant elastic X-ray scattering, it is demonstrated that the chirality of the magnetic structure undergoes a depth-dependent evolution. This suggests that the skyrmion structure is a complex 3D structure rather than an identical planar texture throughout the layer stack. The analyses of the spin textures confirm the theoretical predictions that the dipole-dipole interactions together with the external magnetic field play an important role in stabilizing sub-100 nm diameter skyrmions and the hybrid structure of the skyrmion domain wall. This combined X-ray-based approach opens the door for in-depth studies of magnetic skyrmion systems, which allows for precise engineering of optimized skyrmion heterostructures.

Organic enantiomeric high-T c ferroelectrics

For nearly 100 y, homochiral ferroelectrics were basically multicomponent simple organic amine salts and metal coordination compounds. Single-component homochiral organic ferroelectric crystals with high-Curie temperature (T _c) phase transition were very rarely reported, although the first ferroelectric Rochelle salt discovered in 1920 is a homochiral metal coordination compound. Here, we report a pair of single-component organic enantiomorphic ferroelectrics, (R)-3-quinuclidinol and (S)-3-quinuclidinol, as well as the racemic mixture (Rac)-3-quinuclidinol. The homochiral (R)- and (S)-3-quinuclidinol crystallize in the enantiomorphic-polar point group 6 (C ₆) at room temperature, showing mirror-image relationships in vibrational circular dichroism spectra and crystal structure. Both enantiomers exhibit 622F6-type ferroelectric phase transition with as high as 400 K [above that of BaTiO₃ (T _c = 381 K)], showing very similar ferroelectricity and related properties, including sharp step-like dielectric anomaly from 5 to 17, high saturation polarization (7 μC/cm²), low coercive field (15 kV/cm), and identical ferroelectric domains. Their racemic mixture (Rac)-3-quinuclidinol, however, adopts a centrosymmetric point group 2/m (C _2h), undergoing a nonferroelectric high-temperature phase transition. This finding reveals the enormous benefits of homochirality in designing high-T _c ferroelectrics, and sheds light on exploring homochiral ferroelectrics with great application.