Skyrmion Structure Research Articles

Optical polarization skyrmionic fields in free space

We construct optical beams in free space with robust skyrmionic structures in their polarization fields, both in the electric spin vector for near-circular fields and in the polarization direction for near-linear fields, and for both Bloch (spiral) and Néel (hedgehog) textures. These structures are made possible by the spin–orbit coupling of tightly-focused nonparaxial optics as applied to higher-order Full-Poincaré beams, as well as by standing-wave configurations comprising forwards- and backwards-propagating waves. Our constructions show near-uniform circular and linear polarizations, providing a high degree of topological protection in the absence of nonlinear interactions.

Energy-efficient polarity reversal of a target skyrmion driven by spin-transfer effect

We investigated the current-induced polarity reversal for a ground-state target skyrmion in a spin-valve nanopillar structure, demonstrating two reversal modes distinguished by current density. In view of the considerable write energy consumption (ΔE) caused by Joule heating effect, we proposed a multivariate optimization method considering the coupling of the current density, the applied area and the effective excitation time. This optimization can significantly improve the system stability and reduce ΔE to about 30% without sacrificing reversal efficiency. Our results explain the physical origin of polarity reversal of target skyrmion and overcome a major difficulty for the practical application of skyrmionic spin structures as high-density elements in memory devices.

In‐Plane Magnetic Field‐Driven Creation and Annihilation of Magnetic Skyrmion Strings in Nanostructures

AbstractIn bulk chiral crystals, 3D structures of magnetic skyrmions form topologically protected skyrmion strings (SkS) that have shown potential as magnonic nano‐waveguides for information transfer. Although SkS stability is expected to be enhanced in nanostructures of skyrmion‐hosting materials, experimental observation and detection of SkS in nanostructures under an applied in‐plane magnetic field is difficult. Here, temperature‐dependent magnetic field‐driven creation and annihilation of SkS in B20 FeGe nanostructures (nanowires and nanoplates) under in‐plane magnetic field (H||) are shown and the mechanisms behind these transformations are explained. Unusual asymmetric and hysteretic magnetoresistance (MR) features are observed but previously unexplained during magnetic phase transitions within the SkS stability regime when H|| is along the nanostructure's long edge, which increase the sensitivity of MR detection. Lorentz transmission electron microscopy of the SkS and other magnetic textures under H|| in corroboration with the analysis of the anisotropic MR responses elucidates the field‐driven creation and annihilation processes of SkS responsible for such hysteretic MR features and reveals an unexplored stability regime in nanostructures.

Depth profiling of 3D skyrmion lattices in a chiral magnet—A story with a twist

From the perspective of surface science, only the topmost atomic layers usually exhibit physical properties that are different to those of the bulk material, whereas the deeper layers are assumed to be bulk-like and remain largely unexplored. Going beyond conventional diffraction and imaging techniques, we have determined the depth dependence of the full 3D spin structure of magnetic skyrmions below the surface of a bulk Cu2OSeO3 sample using the polarization dependence of resonant elastic x-ray scattering (REXS). While the bulk spin configuration showed the anticipated Bloch type structure, it was found that the skyrmion lattice changes to a Néel twisting (i.e., with a different helicity angle) at the surface within a distance of several hundred nm. The exact surface helicity angle and penetration length of this twist have been determined, revealing the detailed internal structure of the skyrmion tube. It was found that the experimental penetration length of the Néel twisting is 7× longer than the theoretical value given by the ratio of J/D. This indicates that apart from the considered spin interactions, i.e., the Heisenberg exchange interaction J and the Dzyaloshinskii-Moriya interaction D, as well as the Zeeman interaction, other effects must play an important role. The findings suggest that the surface reconstruction of the skyrmion lattice is a universal phenomenon, stemming from the breaking of translational symmetry at the interface.

Focused ion beam irradiation for generation of skyrmionic bubble like structures

Skyrmions provide high potential for low power magnetic computing. However, we are lacking methods for the controlled nucleation of skyrmions in magnetic thin films. We present a procedure for a controlled generation of skyrmionic bubble like structures (SBSs) at well-defined spots by focused ion beam (FIB) irradiation of magnetic multilayers. Series of Pt/Co/Ir and Pt/Co/W multilayers with interfacial Dzyaloshinskii-Moriya interaction (iDMI) were sputtered and optimized with respect to the domain structure and development under magnetic field. Applying an external magnetic field pulse of specific strength to a sample in both the demagnetized domain state and the uniform ferromagnetic state results in the condensation and nucleation of bubbles, respectively. In multilayer films, SBSs form randomly across the sample. To control the bubble nucleation, we irradiate the multilayer stacks with 50kVGa+ ions to alter the magnetic properties along a hexagonal grid. We observe nucleation and geometric confinement of bubbles within the center of the hexagons. The lowered anisotropy in irradiated regions forms potential barriers which stabilizes the bubbles at room temperature and zero field. FIB tuned magnetic thin films give an exciting platform to investigate the behavior of SBSs in a confined state and to study the possibilities of controlled field- and current-driven motion.

Control of the Half‐Skyrmion Hall Effect and Its Application to Adder–Subtractor

AbstractSkyrmions have attracted a great attention in spintronics because of their potential use as robust information carriers with distinctive protection. Though the realization of skyrmion‐based devices requires flexible control of a skyrmion motion, achieving such a skyrmion motion has been hampered by the skyrmion Hall effect (SkHE), which refers to the presence of a finite angle between a current and the skyrmion trajectory. Here, new insight for the precise control of half‐skyrmion motion is presented, including complete suppression of the SkHE by deforming the internal structure of skyrmions, which is experimentally achieved by external magnetic field to steer current‐driven half‐skyrmions in the desired direction. Furthermore, based on the unique advantages in half‐skyrmions, the potential of half‐skyrmions application beyond skyrmion‐based electronics is also demonstrated by presenting simple half‐skyrmion‐based addition/subtraction operation. The findings of controllability of 2D half‐skyrmion motion will provide new perspectives on utilization of topological solitons for device applications.

Mixed topology ring states for Hall effect and orbital magnetism in skyrmions of Weyl semimetals

Skyrmion lattices as a novel type of chiral spin states are attracting increasing attention, owing to their peculiar properties stemming from real-space topological properties. At the same time, the properties of magnetic Weyl semimetals with complex $k$-space topology are moving into the focus of research in spintronics. We consider the Hall transport properties and orbital magnetism of skyrmion lattices imprinted in topological semimetals, by employing a minimal model of a 2D mixed Weyl semimetal which, as a function of the magnetization direction, exhibits two Chern insulator phases separated by a Weyl state for an an in-plane magnetization direction. We find that while the orbital magnetization is topologically robust and Hall transport properties are very sensitive to the details of the spin distribution in accordance to the behavior expected from the recently discovered chiral Hall effect[1], their behavior in the region of the Chern insulator gap is largely determined by the properties of the so-called mixed topology ring states, emerging in domain walls that separate the skyrmion core from the ferromagnetic background. In particular, we show that these localized ring states possess a given orbital chirality which reverses sign as a function of the skyrmion radius, thereby mediating a smooth switching dynamics of the orbital magnetization of the skyrmion lattice. We speculate that while the emergent ring states can possibly play a role in the physics of Majorana states, probing their properties experimentally can provide insights into the details of skyrmionic spin structures.

High-resolution tunneling spin transport characteristics of topologically distinct magnetic skyrmionic textures from theoretical calculations

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 (Pt0.95Ir0.05)/Fe/Pd(111) ultrathin magnetic film are considered. Using an out-of-plane magnetized SP-STM tip it is found that the maps of the LSC vectors acting on the spins of the magnetic textures and all STT vector components exhibit the same topology as the skyrmionic objects. In contrast, an in-plane magnetized tip generally does not result in spin transport vector maps that are topologically equivalent to the underlying spin structure, except for the LSC vectors acting on the spins of the skyrmionic textures at a specific relation between the spin polarizations of the sample and the tip. The magnitudes of the spin transport vector quantities exhibit close relations to charge current SP-STM images irrespectively of the skyrmionic topologies. Moreover, we find that the STT efficiency (torque/current ratio) acting on the spins of the skyrmions can reach large values up to ~25 meV/μA (~0.97 h/e) above the rim of the magnetic objects, but it considerably varies between large and small values depending on the lateral position of the SP-STM tip above the topological spin textures. A simple expression for the STT efficiency is introduced to explain its variation. Our calculated spin transport vectors can be used for the investigation of spin-polarized tunneling-current-induced spin dynamics of topologically distinct surface magnetic skyrmionic textures.

Численное моделирование двумерных магнитных скирмионных структур

Численное моделирование двумерных магнитных скирмионных структур

Skyrmion spin transfer torque due to current confined in a nanowire

In this work we compute the torque field present in a ferromagnet in contact with a metallic nanowire when a skyrmion is present. If the nanowire is narrow enough the current is carried by a single conduction band. In this regime the classical torque model breaks down and we show that a skyrmion driven by spin transfer torque moves in a different direction than predicted by the classical model. However, the amount of charge current required to move a skyrmion with a certain velocity in the single band regime is similar to a classical model of torque where it is implicitly assumed current transport by many conduction bands. The single band regime is more efficient creating spin current from charge current because of the perfect polarization of the single band but is less efficient creating torque from spin current. Nevertheless, it is possible to take profit of the single band regime to move skyrmions even with no net charge or spin current flowing between the device contacts. We have also been able to recover the classical limit considering an ensemble of only a few electronic states. In this limit we have discovered that electron diffusion needs to be considered even in ballistic nanowires due the effect of the skyrmion structure on the electron current.

Magnon-drag thermoelectric transport with skyrmion structure

Thermoelectric effects driven by magnetization dynamics under a temperature gradient are studied for ferromagnets with and without a skyrmion structure. We calculate charge currents in a four-terminal geometry using the adiabatic pumping formula with full account of magnetization dynamics based on the stochastic Landau–Lifshitz–Gilbert equation. The longitudinal current (Seebeck effect) is induced from the thermally driven spin waves via the spin-transfer and momentum-transfer processes, and these two processes contribute constructively (destructively) in ferromagnets having a negative (positive) s-d exchange interaction. The transverse currents (anomalous Nernst effect) arise in proportion to the number of skyrmions, whose mechanism is identified as the thermal topological Hall effect of magnons followed by the momentum-transfer drag process.

Tunable terahertz oscillation arising from Bloch-point dynamics in chiral magnets

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 transient creation and propagation of topological singularities (magnetic monopole-like Bloch points). Critically, during the winding/unwinding of skyrmionic textures, our results predict that the Bloch-point propagation will give rise to an emergent electric field in a terahertz frequency range and with substantial amplitude. We also demonstrate ways for controlling Bloch-point dynamics, which directly enable the tuneability on both frequency and amplitude of this signal. Our studies provide a concept of directly exploiting topological singularities for terahertz skyrmion-based electronic devices.

The internal dynamic modes of an antiskyrmion in ultrathin ferromagnetic nanodisks

We report a numerical study on the internal resonant modes of an antiskyrmion structure in thin-film ferromagnetic nanodisks by using micromagnetic simulations. As the samples are excited by an oscillating magnetic field along different directions, we are able to resolve several sets of resonant eigenmodes: gyrotropic mode and azimuthal and radial spin wave modes. At the in-plane field excitation, the gyrotropic mode at the low frequency behaves consistently with Thiele’s analytic theory, while a pair of twin azimuthal spin wave modes at higher frequencies demonstrate that their splitting is strongly relevant to the coexistent gyrotropic mode. At the out-of-plane field excitation, several breathing-like radial spin wave modes have been found. In addition, we carry out a brief comparison between these modes and their counterpart modes of an isolated skyrmion structure. We also quantitatively investigate the dependence of the eigenfrequencies of these modes on the different parameter sets of the sample size and internal interactions, which exhibit complex relationships between the internal dynamic modes of an antiskrymion and the geometry and material of the sample.

SU(3) Topology of Magnon-Phonon Hybridization in 2D Antiferromagnets.

Magnon-phonon hybrid excitations are studied theoretically in a two-dimensional antiferromagnet with an easy axis normal to the plane. We show that two magnon bands and one phonon band are intertwined by the magnetoelastic coupling through a nontrivial SU(3) topology, which can be intuitively perceived by identifying a skyrmion structure in the momentum space. Our results are insensitive to lattice details and generally applicable to two-dimensional antiferromagnets. We show this by developing a continuum theory as the long-wavelength approximation to the tight-binding model. The theoretical results can be probed by measuring the thermal Hall conductance as a function of the temperature and the magnetic field. We envision that the magnetoelastic coupling in antiferromagnets can be a promising venue in search of various topological excitations, which cannot be found in magnetic or elastic models alone.

Direct Demonstration of Topological Stability of Magnetic Skyrmions via Topology Manipulation.

Topological protection precludes a continuous deformation between topologically inequivalent configurations in a continuum. Motivated by this concept, magnetic skyrmions, topologically nontrivial spin textures, are expected to exhibit topological stability, thereby offering a prospect as a nanometer-scale nonvolatile information carrier. In real materials, however, atomic spins are configured as not continuous but discrete distributions, which raises a fundamental question if the topological stability is indeed preserved for real magnetic skyrmions. Answering this question necessitates a direct comparison between topologically nontrivial and trivial spin textures, but the direct comparison in one sample under the same magnetic fields has been challenging. Here we report how to selectively achieve either a skyrmion state or a topologically trivial bubble state in a single specimen and thereby experimentally show how robust the skyrmion structure is in comparison with the bubbles. We demonstrate that topologically nontrivial magnetic skyrmions show longer lifetimes than trivial bubble structures, evidencing the topological stability in a real discrete system. Our work corroborates the physical importance of the topology in the magnetic materials, which has hitherto been suggested by mathematical arguments, providing an important step toward ever-dense and more-stable magnetic devices.

Scattering of Dirac electrons from a skyrmion: Emergence of robust skew scattering

We study electron scattering from a closed magnetic structure embedded in the top surface of a topological insulator (TI). Outside the structure there is a uniform layer of ferromagnetic insulator (FMI), leading to a positive effective mass for the Dirac electrons. The mass inside can be engineered to be negative, leading to a skyrmion structure. The geometric shape of the structure can be circular or deformed, leading to integrable or chaotic dynamics, respectively, in the classical limit. For a circular structure, the relativistic quantum scattering characteristics can be calculated analytically. For a deformed structure, we develop an efficient numerical method, the multiple multipole method, to solve the scattering wavefunctions. We find that anomalous Hall effect as characterized by strong skew scattering can arise, which is robust against structural deformation due to the resonant modes. In the short (long) wavelength regime, the resonant modes manifest themselves as confined vortices (excited edge states). The origin of the resonant states is the spin phase factor of massive Dirac electrons at the skyrmion boundary. Further, in the short wavelength regime, for a circular skyrmion, a large number of angular momentum channels contribute to the resonant modes. In this regime, in principle, classical dynamics are relevant, but we find that geometric deformations, even those as severe as leading to fully developed chaos, have little effect on the resonant modes. The vortex structure of the resonant states makes it possible to electrically ``charge'' the skyrmion, rendering feasible to manipulate its motion electrically. In the long wavelength regime, only the lowest angular momentum channels contribute to the resonant modes, making the skew scattering sharply directional. These phenomena may find applications for information storage and in Hall devices based on dynamic skyrmion.

Localized structures in magnetic systems without the center of inversion

The main theoretical and experimental results of the study of magnetic skyrmions in films of isotropic chiral magnets are considered. A significant part of the paper presents new results that were not included in previous monographs and reviews. Skyrmions are formations characterized by a quantized topological number. They attract considerable attention of researchers due to their dynamics in external fields, which has promising features in terms of applications in spintronics. Special attention is given to the structure and interaction of 3D skyrmions, and a new magnetic structure — the chiral bobber — is considered.

Shear banding, intermittency, jamming, and dynamic phases for skyrmions in inhomogeneous pinning arrays

We examine driven skyrmion dynamics in systems with inhomogeneous pinning where a strip of strong pinning coexists with a region containing no pinning. For driving parallel to the strip, we find that the initial skyrmion motion is confined to the unpinned region and the skyrmion Hall angle is zero. At larger drives, a transition occurs to a phase in which motion also appears within the pinned region, creating a shear band in the skyrmion velocity, while the skyrmion Hall angle is still zero. As the drive increases further, the flow becomes disordered and the skyrmion Hall angle increases with drive until saturating at the highest drives when the system transitions into a moving crystal phase. The different dynamic phases are associated with velocity and density gradients across the pinning boundaries. We map out the dynamic phases as a function of pinning strength, skyrmion density, and Magnus force strength, and correlate the phase boundaries with features in the velocity-force curves and changes in the local and global ordering of the skyrmion structure. For large Magnus forces, the shear banding instability is replaced by large scale intermittent flow in the pinned region accompanied by simultaneous motion perpendicular to the direction of the drive, which appears as oscillations in the transport curves. We also examine the case of a drive applied perpendicular to the strip, where we find a jamming effect in which the skyrmion flow is blocked by skyrmion-skyrmion interactions until the drive is large enough to induce plastic flow.

Spin waves in skyrmionic structures with various topological charges

Equilibrium properties and localized magnon excitations are investigated in topologically distinct skyrmionic textures. The observed shape of the structures and their orientation on the lattice is explained based on their vorticities and the symmetry of the crystal. The transformation between different textures and their annihilation as a function of magnetic field is understood based on the energy differences between them. The angular momentum spin-wave eigenmodes characteristic of cylindrically symmetric structures are combined in the distorted spin configurations, leading to avoided crossings in the magnon spectrum. The susceptibility of the skyrmionic textures to homogeneous external fields is calculated, revealing that a high number of modes become detectable due to the hybridization between the angular momentum eigenmodes. These findings should contribute to the observation of spin waves in distorted skyrmionic structures via experiments and numerical simulations, widening the range of their possible applications in magnonic devices.

Analysis on Structure and Response of Magnetic Skyrmions by Transmission Electron Microscope

Analysis on Structure and Response of Magnetic Skyrmions by Transmission Electron Microscope