Skyrmion Structure Research Articles

Enhancing the Thermal Stability of Skyrmion in Magnetic Nanowires for Nanoscale Data Storage.

Magnetic skyrmion random switching and structural stability are critical limitations for storage data applications. Enhancing skyrmions' magnetic properties could improve their thermal structural stability. Hence, micromagnetic calculation was carried out to explore the thermal nucleation and stability of skyrmions in magnetic nanodevices. Different magnetic properties such as uniaxial magnetic anisotropy energy (Ku), saturation magnetization (Ms) and Dzyaloshinskii-Moriya interaction (DMI) were used to assess the thermal stability of skyrmions in magnetic nanowires. For some values of Ms and Ku, the results verified that the skyrmion structure is stable at temperatures above 800 K, which is higher than room temperature. Additionally, manipulating the nanowire geometry was found to have a substantial effect on the thermal structural stability of the skyrmion in storage nanodevices. Increasing the nanowire dimensions, such as length or width, enhanced skyrmions' structural stability against temperature fluctuations in nanodevices. Furthermore, the random nucleation of the skyrmions due to the device temperature was examined. It was shown that random skyrmion nucleation occurs at temperature values greater than 700 K. These findings make skyrmion devices suitable for storage applications.

Ultrafast manipulations of nanoscale skyrmioniums

The advancement of next-generation magnetic devices depends on fast manipulating magnetic microstructures at the nanoscale. A universal method is presented for rapid and reliable generating, controlling, and driving nano-scale skyrmioniums, through high-throughput micromagnetic simulations. Ultrafast switches are realized between skyrmionium and skyrmion states and rapidly change their polarities in monolayer magnetic nanodisks by perpendicular magnetic fields. The transition mechanism by alternating magnetic fields differs from that under steady magnetic fields. New skyrmionic textures, such as flower-like and windmill-like skyrmions, are discovered. Moreover, this nanoscale skyrmionium can move rapidly and stably in nanoribbons using weaker spin-polarized currents. Explicit discussions are held regarding the physical mechanisms involved in ultrafast manipulations of skyrmioniums. This work provides further physical insights into the manipulation and application of topological skyrmionic structures for developing low-power consumption and nanostorage devices.

Optical skyrmion and its "zipper-like" topological behavior in an energy flux field.

The optical skyrmion and its topological behavior are analyzed in an energy flux field constructed by an X-type vortex in a high numerical aperture system. The conditions for the formation of a skyrmion structure in this field are discussed, showing that the vortex pattern of the transverse energy flow and the inverse energy flow are crucial for the skyrmions and also are controlled by the phase gradient of the X-type vortex. Notably, the "zipper-like" topological reaction, which is the first, to our knowledge, found in ferromagnetic materials, is observed, and the physical mechanism is also explained by the relation of orbital angular momentum density and Poynting vectors. The results will reach the topological theory and may have applications in optical traps and data storage.

Achiral hard bananas assemble double-twist skyrmions and blue phases.

Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.

Molecular shape, elastic constants and spontaneous twist in chiral and achiral nematics: insights from a generalised Maier–Saupe framework

ABSTRACT Ordinary nematic liquid crystals have a uniform director field as ground state. However, there are relevant examples of spontaneously twisted nematic states, not only in chiral, but also in achiral materials. Different twist configurations can be found, with the director modulation along the twist axis, as in the cholesteric and in the twist-bend nematic phase, or perpendicular to it, as in blue phases and in skyrmion structures. Here, we develop a generalised Maier–Saupe theory to calculate the thermodynamic and elastic properties, included saddle-splay, of nematics made of particles whose shape can be described as a distorted rod. This turns out to be a powerful approach for screening the relation between the molecular shape and the formation of modulated nematic phases. Application to the paradigmatic models of banana-shaped and helical particles allows us to identify the role of distinct shape features, such as curvature and chirality, and the distinct mechanisms by which these promote twisted configurations.

Thickness- and Field-Dependent Magnetic Domain Evolution in van der Waals Fe3GaTe2.

The discovery of room-temperature ferromagnetism in van der Waals (vdW) materials opens new avenues for exploring low-dimensional magnetism and its applications in spintronics. Recently, the observation of the room-temperature topological Hall effect in the vdW ferromagnet Fe3GaTe2 suggests the possible existence of room-temperature skyrmions, yet skyrmions have not been directly observed. In this study, real-space imaging was employed to investigate the domain evolution of the labyrinth and skyrmion structure. First, Néel-type skyrmions can be created at room temperature. In addition, the influence of flake thickness and external magnetic field (during field cooling) on both labyrinth domains and the skyrmion lattice is unveiled. Due to the competition between magnetic anisotropy and dipole interactions, the specimen thickness significantly influences the density of skyrmions. These findings demonstrate that Fe3GaTe2 can host room-temperature skyrmions of various sizes, opening up avenues for further study of magnetic topological textures at room temperature.

Exploring approximate analytical expression for magnetic skyrmion structure based on symbolic regression method

Magnetic skyrmion is a kind of nontrivial topological magnetic structure, which can exist stably in chiral magnet with Dzyaloshinskii-Moriya (DM) interaction, and its static and dynamic properties are closely related to its structural characteristics. However, there are no general analytical expressions for skyrmion profiles. Therefore, many researchers have provided approximate solutions. In this paper, a new approach to exploring magnetic skyrmion structures is introduced by using a symbolic regression approach. Considering the influence of DM interaction and external magnetic field on magnetic skyrmion structure, two suitable approximate expressions are obtained through symbolic regression algorithms. The applicability of these expressions depends on the dominant interaction. The research results in this work validate the powerful capability of symbolic regression algorithms in exploring the magnetic skyrmion profiles. So, the present study provides a new method for finding the analytical expressions for magnetic structure.

Realization of Wilson fermions in topolectrical circuits

The Wilson fermion (WF) is a fundamental particle in the theory of quantum chromodynamics. Theoretical calculations have shown that the WF with a half skyrmion profile represents a quantum anomalous semimetal phase supporting a chiral edge current, but the experimental evidence is still lacking. In this work, we report a direct observation of the WF in circuit systems. We find that WFs manifest as topological spin textures analogous to the half skyrmion, half-skyrmion pair, and Néel skyrmion structures, depending on their mass. Transformations of different WF states are realized by tuning the electric elements. We further experimentally observe the propagation of chiral edge current along the domain-wall separating two circuits with contrast fractional Chern numbers. Our work provides experimental evidence for WFs in topolectrical circuits. The nontrivial analogy between the WF state and the skyrmionic structure builds an intimate connection between the two burgeoning fields.

Magnetic Response of Nematic Superconductors: Skyrmion Stripes and Their Signatures in Muon Spin Relaxation Experiments.

We investigate the magnetic response of nematic superconductors, presenting a new approach to find vortex and skyrmion structures beyond symmetry-constraining Ansätze. Using this approach we show that nematic superconductors form distinctive skyrmion stripes. Our approach lends itself to accurate determination of the field distribution for muon spin rotation probes. We use this to show that the skyrmion structure manifests as a double peak in the field distribution, markedly different from the signal of standard vortex lattices.

Field-driven collapsing dynamics of skyrmions in magnetic multilayers

Magnetic skyrmions are fascinating topological particle-like textures promoted by a trade-off among interfacial properties (perpendicular anisotropy and Dzyaloshinskii-Moriya interaction (DMI)) and dipolar interactions. Depending on the dominant interaction, complex spin textures, including pure N\'eel and hybrid skyrmions have been observed in multilayer heterostructures. A quantification of these different spin textures typically requires a depth-reoslved magnetic imaging or scattering techniques. In the present work, we will show qualitatively different collapsing dynamics for pure N\'eel and hybrid skyrmions induced by a perpendicular magnetic field in two representative systems, [Pt/Co/Ir]15 and [Ta/CoFeB/MgO]15 multilayers. Skyrmions in the former stack undergo two morphological transitions, upon reversing the perpendicular field direction. Skyrmions in [Ta/CoFeB/MgO]15 multilayers exhibit a continuous transition, which is mainly linked to a reversible change of the skyrmion size. A full micromagnetic phase diagram is presented to identify these two collapsing mechanisms as a function of material parameters. Since the two distinct collapsing dynamics rely on the detailed layer-dependent spin structures of skyrmions, they could be used as potential fingerprints for identifying the skyrmion type in magnetic multilayers. Our work suggests the employment of pure and hybrid skyrmions for specific applications, due to the strong correlation between the skyrmion dynamics and 3-dimentional spin profiles.

Three-dimensional structure of hybrid magnetic skyrmions determined by neutron scattering

Magnetic skyrmions are topologically protected chiral spin textures which present opportunities for next-generation magnetic data storage and logic information technologies. The topology of these structures originates in the geometric configuration of the magnetic spins - more generally described as the structure. While the skyrmion structure is most often depicted using a 2D projection of the three-dimensional structure, recent works have emphasized the role of all three dimensions in determining the topology and their response to external stimuli. In this work, grazing-incidence small-angle neutron scattering and polarized neutron reflectometry are used to determine the three-dimensional structure of hybrid skyrmions. The structure of the hybrid skyrmions, which includes a combination of N\'eel-like and Bloch-like components along their length, is expected to significantly contribute to their notable stability, which includes ambient conditions. To interpret the neutron scattering data, micromagnetic simulations of the hybrid skyrmions were performed, and the corresponding diffraction patterns were determined using a Born approximation transformation. The converged magnetic profile reveals the magnetic structure along with the skyrmion depth profile, including the thickness of the Bloch and N\'eel segments and the diameter of the core.

Skyrmions in blue phases of chiral liquid crystals

ABSTRACTUsing high-resolution microscope observations, we show that both the static cubic (BPI) and the dynamic amorphous (BPIII) blue phases consist of fractional skyrmion filaments that transform into the same quasi two-dimensional structure of ‘baby’ half-skyrmions upon confinement to ultra-thin layers. We confirm this using numerical simulations of BPIII skyrmion structures in confinement combined with optical simulations, which reproduce experimental images, shown to originate at the glass-sample boundaries. Chiral nature of skyrmion filaments is demonstrated through experimental observations and optical simulations using circularly polarised light of opposite handedness producing images that vary strongly in comparative optical contrast. Direct observations and light scattering measurements of BPIII dynamics in bulk reveal that it is a highly dynamic phase, distinguished by two well-separated dynamic regimes, the slower of which can be observed even with a naked eye. We show that the slow dynamics corresponds to the thermally driven collective reshaping of the amorphous structure, while the fast mode is due to the director fluctuations within the filaments. Chirality of the relaxation modes in the bulk isotropic phase is also demonstrated and discussed. We show the dynamics in thinnest layers still show a two phase behaviour, with overall dynamics of half-skyrmions dramatically slowed down.

Stacking-dependent nonreciprocal transport in magnetic skyrmions

I theoretically propose an emergence of nonlinear nonreciprocal transport in centrosymmetric magnets with topological spin textures. By focusing on the stacking degree of freedom of the skyrmion crystals on a layered triangular lattice, I find that the ABC-stacking structure of the skyrmion crystals gives rise to out-of-plane nonreciprocal transport without the relativistic spin–orbit coupling. I show that such nonreciprocal transport is caused by an asymmetric band modulation due to the stacking structure, where the scalar chirality across the layers is a key ingredient. I also show an effective spin model to stabilize the ABC-stacking skyrmion structure. The present results indicate that the stacking structure of the skyrmion crystal becomes a source of further intriguing transport properties.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering.

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Three-dimensional structure of magnetic skyrmions

Magnetic skyrmions (skyrmions hereafter) are magnetization configurations, whose topological robustness and nanoscale size have led to speculation that they could find use as a next-generation information carrier. Skyrmions have been observed in magnetic multilayer materials that are thin compared to the radius of a skyrmion, and chiral cubic single crystals that can be far larger than any characteristic skyrmion scale. In these single crystals, one would expect that skyrmions could exhibit interesting three-dimensional (3D) characteristics. Here, the symmetry of the micromagnetic free energy is investigated. This symmetry permits a complex 3D modulation of a skyrmion string, which we show to be a requirement of a skyrmion coexisting with the conical state. We discuss the implications of this modulation with respect to Thiele's equation and interskyrmion interactions. Further to this internal modulation, we study theoretically and show experimentally that the strings themselves must contort towards the surfaces of their confining crystals.

Magnetic reversal stability of spin textures in synthetic antiferromagnetic nanodots

In this work, we demonstrate the nucleation and stability of spin textures in synthetic antiferromagnetic (SAF) nanodot-shaped systems. By employing micromagnetic simulations at 300 K and zero-field, we obtain phase diagrams distinguishing antiferromagnetic (AFM) single domain, skyrmion and skyrmionium states, among other relevant spin textures, depending on the magnetic and geometric parameters of the circular disk. Furthermore, we investigate the magnetization reversal stability under out-of-plane magnetic fields, revealing that, only under specific conditions, AFM skyrmionic textures are preserved in the absence of magnetic fields. The conservation of the skyrmionic structures along the hysteresis cycle is directly linked with an energy barrier reduction for the nucleation of the spin textures. Our findings demonstrate a very promising route in stabilizing AFM chiral skyrmionic structures in nanodots, at ambient conditions, which is a step towards their use in future antiferromagnetic devices.

Lorentz electron ptychography for imaging magnetic textures beyond the diffraction limit.

Nanoscale spin textures, especially magnetic skyrmions, have attracted intense interest as candidate high-density and power-efficient information carriers for spintronic devices1,2. Facilitating a deeper understanding of sub-hundred-nanometre to atomic-scale spin textures requires more advanced magnetic imaging techniques3-5. Here we demonstrate a Lorentz electron ptychography method that can enable high-resolution, high-sensitivity magnetic field imaging for widely available electron microscopes. The resolution of Lorentz electron ptychography is not limited by the usual diffraction limit of lens optics, but instead is determined by the maximum scattering angle at which a statistically meaningful dose can still be recorded-this can be an improvement of up to 2-6 times depending on the allowable dose. Using FeGe as the model system, we realize a more accurate magnetic field measurement of skyrmions with an improved spatial resolution and sensitivity by also correcting the probe-damping effect from the imaging optics via Lorentz electron ptychography. This allows us to directly resolve subtle internal structures of magnetic skyrmions near the skyrmion cores, boundaries and dislocations in an FeGe single crystal. Our study establishes a quantitative, high-resolution magnetic microscopy technique that can reveal nanoscale spin textures, especially magnetization discontinuities and topological defects in nanomagnets6. The technique's high-dose efficiency should also make it well suited for the exploration of magnetic textures in electron radiation-sensitive materials such as organic or molecular magnets7.

Skyrmionic spin structures in layered Fe5GeTe2 up to room temperature

The role of the crystal lattice, temperature and magnetic field for the spin structure formation in the 2D van der Waals magnet Fe5GeTe2 with magnetic ordering up to room temperature 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 centrosymmetry. These skyrmions can be observed even in the absence of external fields. To understand the complex magnetic order in Fe5GeTe2, we compare macroscopic magnetometry characterization results with microscopic density functional theory and spin-model calculations. Our results show that even up to room temperature, topological spin structures can be stabilized in centrosymmetric van der Waals magnets.

Exponential Temperature Effects on Skyrmion-Skyrmion Interaction

Understanding the dynamic behaviors of magnetic skyrmions has great potential in the application of spintronics. This is especially the case for the interaction between two skyrmions. In the literature, the attractive and repulsive skyrmion-skyrmion interactions are demonstrated as strongly related to the distance of two skyrmions and external magnetic fields. However, as a natural property, the temperature effect on skyrmion-skyrmion interactions is unclear, which lacks understanding from thermodynamics, and accordingly its driving force equation is absent. Here, we employ a temperature-related phase-field simulation and demonstrate that the skyrmion-skyrmion interaction is dramatically changed by temperature (e.g., a temperature change of only a few kelvins results in an eightfold higher interaction), which can lead to critical temperature behavior of skyrmion phase. Detailed analysis shows the interaction potential decreases exponentially with an increase of temperature, and this pronounced temperature dependence originates from the temperature-related skyrmion structure. Then, an equation is proposed to describe the skyrmion interaction at finite temperatures. Therefore, this study provides a deeper understanding of the skyrmion kinetic behavior and explores the temperature control of skyrmion interactions coupled with other sources of interaction, which is a guidance for future study of skyrmions and their applications.

Bessel vortices in spin-orbit-coupled binary Bose–Einstein condensates with Zeeman splitting

We present an analysis of stationary solutions for two-dimensional (2D) Bose–Einstein condensates (BECs) with the Rashba spin–orbit (SO) coupling and Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system can be solved exactly. The solutions are semi-vortices of the Bessel-vortex (BV) and modified Bessel-vortex (MBV) types, in the presence of the weak and strong Zeeman splitting, respectively. The ground states (GSs) of the full nonlinear system are constructed with the help of a specially designed neural network (NN). The GS of the mixed-mode type appears as cross-attraction interaction increases. The spin texture of the GS is produced in detail. It exhibits the Néel skyrmion structure for the semi-vortex GS of the BV type, and the respective skyrmion number is found in an analytical form. On the other hand, GSs of the MBV and mixed-mode types do not form skyrmions.