Higher-order skyrmions and antiskyrmions are topologically protected spin textures with an integer topological charge other than $\pm 1$ and nucleate from topological point defects in regular Bloch walls, known as vertical Bloch lines. So far, they have only been observed using Lorentz transmission electron microscopy. In this work, we show that higher-order spin textures coexisting in Co/Ni multilayers at room temperature can be visualized by high-resolution magnetic force microscopy (MFM). The experimental results are supported by micromagnetic simulations confirming that different spin objects give rise to distinct MFM contrast in full agreement to our observations.
We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we te…
In non-centrosymmetric magnets the chiral Dzyaloshinskii-Moriya exchange stabilizes Skyrmion-strings as excitations which may condense into multiply modulated phases. Such extended Skyrmionic textures are determined by the stability of the localized "solitonic" Skyrmion cores and their geometrical incompatibility which frustrates regular space-filling. We present numerically exact solutions for Skyrmion lattices and formulate basic properties of the Skyrmionic states.
A type of vortex spin texture with skyrmionic core and a series of circle spin stripes was obtained in thin nanodisk of the chiral magnets with Dzyaloshinskii-Moriya interaction and uniaxial anisotropy by means of micromagnetic approach and Monte Carlo simulation. The size of skyrmionic core can be modulated continuously by controlling the disk size. Moreover, in some certain values of the disk size, this vortex state may be spontaneous ground state even without the help of the external magnetic field and thermal fluctuation. In addition, the uniaxial anisotropy is able to stabilize this vorte…
Magnetic skyrmions have the potential to provide solutions for low-power, high-density data storage and processing. One of the major challenges in developing skyrmion-based devices is the skyrmions' magnetic stability in confined helimagnetic nanostructures. Through a systematic study of equilibrium states, using a full three-dimensional micromagnetic model including demagnetisation effects, we demonstrate that skyrmionic textures are the lowest energy states in helimagnetic thin film nanostructures at zero external magnetic field and in absence of magnetocrystalline anisotropy. We also report…
Skyrmions are topological solitons that emerge in many physical contexts. In magnetism, they appear as textures of the spin-density field stabilized by different competing interactions and characterized by a topological charge that counts the number of times the order parameter wraps the sphere. They can behave as classical objects, when the spin texture varies slowly on the scale of the microscopic lattice of the magnet. However, the fast development of experimental tools to create and stabilize skyrmions in thin magnetic films has lead to a rich variety of textures, sometimes of atomistic si…
High-resolution tunneling electron spin transport properties (longitudinal spin current (LSC) and spin transfer torque (STT) maps) of topologically distinct real-space magnetic skyrmionic textures are reported by employing a 3D-WKB combined scalar charge and vector spin transport theory in the framework of spin-polarized scanning tunneling microscopy (SP-STM). For our theoretical investigation metastable skyrmionic spin structures with various topological charges ($Q=-3,-2,-1,0,1,2$) in the (Pt$_{0.95}$Ir$_{0.05}$)/Fe/Pd(111) ultrathin magnetic film are considered. Using an out-of-plane magnet…
The intrinsic magnetism observed in two-dimensional (2D) van der Waals (vdW) materials provides a unique opportunity for exploring the 2D topological magnetic textures, in particular skyrmionic magnetic textures (SMTs) including skyrmion and its topological equivalents. Since the experimental discovery of skyrmions in the 2D vdW materials and their heterostructures, a critical challenge lies in the control of these SMTs to translate their intriguing features into spintronic applications. Here, we review the recent experimental and theoretical progresses on the modulations of SMTs in 2D vdW mon…
Different from the skyrmion driven by the Dzyaloshinskii-Moriya interaction in non-centrosymmetric materials, the skyrmionic texture in centrosymmetric magnet may possess the extra internal degrees of freedom, which greatly enrich its morphologies, imply the continuous deformation allowed by topological protection, and enable flexible tunability and potential functionality. To describe the internal degree of freedom to full extent, the conventional integer-valued scalar vorticity is extended into a vector vorticity with continuous rotation allowed. The further simplified vorticity angle, toget…
The correct identification of topological magnetic objects in experiments is an important issue. In the present work we report on the characterization of metastable skyrmionic spin structures with various topological charges ($Q=-3,-2,-1,0,+1,+2$) in the (Pt$_{1-x}$Ir$_{x}$)Fe/Pd(111) ultrathin magnetic film by performing spin-polarized scanning tunneling microscopy (SP-STM) calculations. We find that an out-of-plane magnetized tip already results in distinguished SP-STM contrasts for the different skyrmionic structures corresponding to their symmetries. Our work also establishes an understand…
TU Wien（维也纳工业大学）；University of Vienna（维也纳大学）；University of Augsburg（奥格斯堡大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）；Technical University of Munich（慕尼黑工业大学）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Institut Universitaire de France (IUF)（法国高等研究院）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Forschungszentrum Jülich（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林赫尔姆霍兹材料与能源中心）；Thales（泰雷兹集团）；Université Paris-Saclay（巴黎萨克雷大学）
Three-dimensional (3D) topological spin textures emerge as promising quasi-particles for encoding information in future spintronic devices. The third dimension provides more malleability regarding their magnetic properties as well as more flexibility for potential applications. However, the stabilization and characterization of such quasi-particles in easily implementable systems remain a work in progress. Here we observe a new type of 3D magnetic textures that we called skyrmionic cocoons that sits in the interior of magnetic thin films multilayers and possesses a characteristic ellipsoidal s…
Magnetic skyrmions and skyrmion bags are nano-scale spin textures whose stability, size and ease of manipulation make them strong contenders for next generation data and logic applications. Skyrmion bags are composite skyrmions of any integer topological degree and this means they have emergent properties not present in unitary degree skyrmions. Here we present models and theoretical descriptions demonstrating the process of skyrmionic division where a skyrmion or skyrmion bag can be divided into two or more skyrmionic structures. This exciting result could pave the way to entirely new types o…
We study a two-dimensional electron gas exchanged-coupled to a system of classical magnetic ions. For large Rashba spin-orbit coupling a single electron can become self-trapped in a skyrmion spin texture self-induced in the magnetic ions system. This new quasiparticle carries electrical and topological charge as well as a large spin, and we named it as magnetic skyrmionic polaron. We study the range of parameters; temperature, exchange coupling, Rashba coupling and magnetic field, for which the magnetic skyrmionic polaron is the fundamental state in the system. The dynamics of this quasipartic…
Novel types of barrel-shaped chiral skyrmions can exist as isolated topological defects or as bound states in magnetic nanolayers with intrinsic and surface/interface induced chirality. The equilibrium parameters of chiral modulations calculated as functions of applied fields, layer thicknesses, and values of surface and volume uniaxial anisotropies allow to find optimal parameters for skyrmionic states in magnetic nanolayers. Our findings also show that in cholesteric cells with homeotropic anchoring smooth skyrmionic textures can be induced as an intriguing alternative to common disclination…
We report that in cylindrical nanorods skyrmion chains, i.e., three-dimensional spin textures, emerge dynamically, as revealed by micromagnetic simulations. The skyrmion-chain state occurs when the diameter of the rod is larger than the helical pitch length of the material, and the number of skyrmions on the chain is proportional to the length of the nanorod. This finding provides a deeper understanding of the interplay between geometry and skyrmionic symmetry, and shows how spatial confinement can stabilize spontaneous topological spin textures.
The magnetic field-driven evolution of chiral spin textures in thin helimagnet nanodisk with varied size are investigated by means of Monte Carlo simulation. It is demonstrated that the complex spin texture may simply be regarded as the superposition of the edged state with in plane spin orientation perpendicular or parallel to the edge and the bulk state with the features similar to two-dimensional chiral magnetic films. With the increase of the external field, the proportion of the parallel spins of the edge state increases, and the spin textures finally transfers into edged magnetic vortex.…
Skyrmionic textures are being extensively investigated due to the occurrence of novel topological magnetic phenomena and their promising applications in a new generation of spintronic devices that take advantage of the robust topological stability of their spin structures. The development of practical devices relies on a detailed understanding of how skyrmionic structures can be formed, transferred, detected and annihilated. In this work, our considerations go beyond static skyrmions and theoretically show that the formation/annihilation of both skyrmions and antiskyrmions is enabled by the tr…
Magnetic topological defects, including vortices and Skyrmions, can be stabilized as equilibrium structures by tuning intrinsic magnetic interactions and stray field geometries. Here, employing rapid quench conditions, we report the observation of a light-induced metastable magnetic texture, which consists of a dense nanoscale network of vortices and antivortices and exhibits glass-like properties. Our results highlight the emergence of complex ordering regimes in optically driven magnetic systems, opening up new pathways to harness ultrafast far-from-equilibrium relaxation processes.
The role of the crystal lattice, temperature and magnetic field for the spin structure formation in the 2D van der Waals magnet Fe5GeTe2 is a key open question. Using Lorentz transmission electron microscopy, we experimentally observe topological spin structures up to room temperature in the metastable pre-cooling and stable post-cooling phase of Fe5GeTe2. Over wide temperature and field ranges, skyrmionic magnetic bubbles form without preferred chirality, which is indicative of a centrosymmetric crystal structure. In the pre-cooling phase, these bubbles are observable even without the applica…
We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and anti-skyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show th…
A coherent superposition of many nuclear spin states can be prepared and manipulated via the hyperfine interaction with the electronic spins by varying the Landau level filling factor through the gate voltage in appropriately designed Quantum Hall Ferromagnet. During the manipulation periods the 2D electron system forms spatially large Skyrmionic spin textures, where many nuclear spins follow locally the electron spin polarization. It is shown that the collective spin rotation of a single spin texture is gapless in the limit of zero Zeeman splitting, and may dominate the nuclear spins relaxati…
Magnetic skyrmions have been in the spotlight since their observation in technologically relevant systems at room temperature. More recently, there has been increasing interest in additional quasiparticles that may exist as stable/metastable spin textures in magnets, such as the skyrmionium and the anti-skyrmionite (i.e., a double-antiskyrmion-skyrmion pair) that have distinct topological characteristics. The next challenge and opportunity, at the same time, is to investigate the use of multiple magnetic quasiparticles as information carriers in a single device for next generation nanocomputin…
Recent observations of topological spin textures brought spintronics one step closer to new magnetic memories. Nevertheless, the existence of Skyrmions, as well as their stabilization, require very specific intrinsic magnetic properties which are usually fixed in magnets. Here we address the possibility to dynamically control their intrinsic magnetic interactions by varying the strength of a high-frequency laser field. It is shown that drastic changes can be induced in the antiferromagnetic exchange interactions and the latter can even be reversed to become ferromagnetic, provided the direct e…
When magnetic skyrmions are moved via currents, they do not strictly travel along the path of the current, instead their motion also gains a transverse component. This so-called skyrmion Hall effect can be detrimental in potential skyrmion devices because it drives skyrmions towards the edge of their hosting material where they face potential annihilation. Here we experimentally modify a skyrmion model system - an atomic Pd/Fe bilayer on Ir(111) - by decorating the film edge with ferromagnetic Co/Fe patches. Employing spin-polarized scanning tunneling microscopy, we demonstrate that this ferro…
Skyrmionic Transport and First Order Phase Transitions in Twisted Bilayer Graphene Quantum Hall Ferromagnet
Indian Institute of Technology, Kharagpur（印度理工学院哈格普尔分校）；S. N. Bose National Centre for Basic Sciences（S.N.玻色基础科学国家中心）；National Institute for Materials Science（日本国立材料研究所）
Magnetic skyrmion, a swirling spin texture, in chiral magnets is characterized by (i) nano-scale size ($\sim$1nm -- 100nm), (ii) topological stability, and (iii) gyro-dynamics. These features are shown to be advantageous for (a) high-density data-storage, (b) nonvolatile memory, and (c) ultra-low current and energy cost manipulation, respectively. By the numerical simulations of Landau-Lifshitz-Gilbert equation, the elementary functions of skyrmions are demonstrated aiming at the design principles of skyrmionic memory devices.
Magnetic skyrmions are nontrivial spin textures which resist external perturbations, being promising candidates for the next generation recording devices. Nevertheless, a major challenge in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures under ambient conditions and zero applied field. Here, we demonstrate for the first time the formation and stabilization of magnetic skyrmions on arrays of self-assembled hexagonal nanodomes taking advantage of the intrinsic properties of its curved geometry. Magnetic force microscopy images from the arrays of 100…
Complex magnetic exchange, anisotropy and skyrmionic textures in two-dimensional FeXZ$_{2}$ (\textit{X} = Nb, Ta and \textit{Z} = S, Se, Te) ferromagnets
We show that scanning electron microscopy with polarization analysis (SEMPA) that is sensitive to both in-plane magnetization components can be used to image the out-of-plane magnetized multi-domain state in multilayered chiral spin textures. By depositing a thin layer of Fe on top of the multilayer we image the underlying out-of-plane domain state through the mapping of its stray fields in the Fe. We also demonstrate that SEMPA can be used to image the domain wall chirality in these systems after milling away the capping layer and imaging the topmost magnetic layer directly.
The coupling of electron spin to real-space magnetic textures leads to a variety of interesting magnetotransport effects. The skyrmionic spin textures often found in chiral B20-lattice magnets give rise, via real-space Berry phases, to the topological Hall effect, but it is typically rather small. Here, B20-ordered Fe$_{0.7}$Co$_{0.3}$Si epilayers display a giant topological Hall effect due to the combination of three favourable properties: they have a high spin-polarisation, a large ordinary Hall coefficient, and dense chiral spin textures. The topological Hall resistivity is as large as 820 …
In multiferroic materials, the microscopic magnetic and electric textures are strongly correlated with each other by magnetoelectric (ME) coupling. Therefore, topological electric dipole textures, such as ferroelectric (FE) dipole skyrmions and periodic FE dipole crystals, are expected to be induced if ferromagnetic (FM) skyrmions and FM skyrmionic crystals (or lattices so as to be abbreviated as SLs for convenience) can be stabilized. In the present work, a quantum computational approach is utilized to simulate the topological textures of FE SLs in a two-dimensional (2D) multiferroic system. …
When a foreign atom is placed on a surface of a metal, the surrounding sea of electrons responds screening the additional charge leading to oscillations or ripples. On surfaces, those electrons are sometimes confined to two-dimensional surface states, whose spin-degeneracy is lifted due to the Rashba effect arising from the spin-orbit interaction of electrons and the inversion asymmetric environment. It is believed that at least for a single adatom scanning tunneling microscopy measurements are insensitive to the Rashba splitting i.e. no signatures in the charge oscillations will be observed. …
The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potent…
Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have received tremendous attention as exotic textures in particle physics, cosmology, superfluids, and many other systems. Here we experimentally create and measure a topological 3D skyrmionic hopfion in fully structured light. By simultaneously tailoring the p…
We find numerically skyrmionic textures with skyrmion number Q=0 in ferromagnets with the Dzyaloshinskii-Moriya interaction and perpendicular anisotropy. These have the form of a skyrmion-antiskyrmion pair and may be called chiral droplets. They are stable in an infinite film as well as in disc-shaped magnetic elements. Droplets are found for values of the parameters close to the transition from the ferromagnetic to the spiral phase. We study their motion under spin-transfer torque. They move in the direction of the spin flow and, thus, their dynamics are drastically different than the Hall dy…
Realizing effective manipulation and explicit identification of topological spin textures are two crucial ingredients to make them as information carrier in spintronic devices with high storage density, high data handling speed and low energy consumption. Electric-field manipulation of magnetism has been achieved as a dissipationless method compared with traditional regulations. However, the magnetization is normally insensitive to the electric field since it does not break time-reversal symmetry directly, and distribution of topological magnetic quasiparticles is difficult to maintain due to …
We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a 3D topological insulator (TI), coupled by proximity effect. The magnetic texture of skyrmions can lead to confinement of Dirac states at the skyrmion radius, where out of plane magnetization vanishes. This confinement can result in charging of the skyrmion texture. The presence of bound states is robust in an external magnetic field, which is needed to stabilize skyrmions. It is expected that for relevant experimental parameters skyrmions will have a few bound states that can be tu…
We have observed peculiar magnetization textures in Ni$_{80}$Pd$_{20}$ nanostructures using three different imaging techniques: magnetic force microscopy, photoemission electron microscopy under polarized X-ray absorption, and scanning electron microscopy with polarization analysis. The appearances of diamond-like domains with strong lateral charges and of weak stripe structures bring into evidence the presence of both a transverse and a perpendicular anisotropy in these nanostrips. This anisotropy is seen to reinforce as temperature decreases, as testified by a simplified domain structure at …
The surfaces of antimony are characterized by the presence of spin-split states within the projected bulk band gap and the Fermi contour is thus expected to exhibit a spin texture. Using spin-resolved density functional theory calculations, we determine the spin polarization of the surface bands of Sb(110). The existence of the unconventional spin texture is corroborated by the investigations of the electron scattering on this surface. The charge interference patterns formed around single scattering impurities, imaged by scanning tunneling microscopy, reveal the absence of direct backscatterin…
Italian Institute of Technology（意大利理工学院）；University of Genoa（热那亚大学）；University of Groningen（格罗宁根大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 emergent matter science 中心）；Fundamental Quantum Science Program (FQSP), TRIP Headquarters, RIKEN（理化学研究所 基础量子科学计划（FQSP）TRIP总部）；Quantum Materials Theory（量子材料理论）
With the recent proposition of skyrmion utilization in racetrack memories at room temperature, skyrmionics has become a very attractive field. However, for the stability of skyrmions, it is essential to incorporate the Dzyaloshinskii-Moriya interaction (DMI) and the out-of-plane magnetic field into the system. In this work, we explore a system without these interactions. First, we propose a controlled way for the creation of magnetic skyrmions and skyrmioniums imprinted on a ferromagnetic nanotrack via a nanopatterned nanodisk with the magnetic vortex state. Then we investigate the detachment …
Quantization of topological charges determines the various topological spin textures that are expected to play a key role in future spintronic devices. While the magnetic skyrmion with a unit topological charge Q has been extensively studied, spin textures with other integer valued have not been verified well so far. Here, we report the real-space image, creation, and manipulation of a type of multi Q three-dimensional skyrmionic texture, where a circular spin spiral ties a bunch of skyrmion tubes. We define these objects as skyrmion bundles, and show they have arbitrarily integer values Q fro…
Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
Nankai University（南开大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Chinese Academy of Sciences（中国科学院）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Zhejiang University（浙江大学）
Magnetic skyrmions are topologically-protected spin textures with attractive properties suitable for high-density and low-power spintronic device applications. Much effort has been dedicated to understanding the dynamical behaviours of the magnetic skyrmions. However, experimental observation of the ultrafast dynamics of this chiral magnetic texture in real space, which is the hallmark of its quasiparticle nature, has so far remained elusive. Here, we report nanosecond-dynamics of a 100 nm-size magnetic skyrmion during a current pulse application, using a time-resolved pump-probe soft X-ray im…
Magnetic domain structure and spin-dependent reflectivity measurements on cobalt thin films intercalated at the graphene / Ir(111) interface are investigated using spin-polarised low-energy electron microscopy. We find that graphene-covered cobalt films have surprising magnetic properties. Vectorial imaging of magnetic domains reveals an unusually gradual thickness-dependent spin reorientation transition, in which magnetisation rotates from out-of-the-film plane to the in-plane direction by less than 10$^\circ$ per cobalt monolayer. During this transition, cobalt films have a meandering spin t…
