Skyrmion Structure Research Articles

Structure and Field Evolution of Magnetic Skyrmions in Co/Pt-Based Multilayers by In-Situ Electron Holography

Structure and Field Evolution of Magnetic Skyrmions in Co/Pt-Based Multilayers by In-Situ Electron Holography

Topological Charge Control of Skyrmion Structure in Frustrated Magnets by Circularly Polarized Light

The classical Heisenberg model with the ${J}_{1}$-${J}_{2}$-${J}_{3}$ interaction forms a skyrmion structure, which is characterized by quantized topological charge. Due to the symmetric interaction, the generated topological charges are randomly distributed in the system, and not controllable intrinsically. Here we show theoretically that manipulation of topological charge can be carried out by applying circularly polarized light, as a result of the mechanism of the topological inverse Faraday effect arising from the coupling of light helicity and topological charge. The effect is expected to be useful for control of the topological charge bit in a skyrmion-based racetrack memory.

Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice

Stimulated by the recent progress in engineering topological band structures in cold atomic gases, we study the dynamic topological phenomena for atoms loaded in a periodically driven optical lattice. When the frequency of the periodic modulation is low, the time-dependent Hamiltonian can be mapped to a two-dimensional topological insulator, with the discretized frequency components playing the role of an additional, synthetic dimension. In the high-frequency limit, we derive the effective Floquet Hamiltonian of the system, and reveal the occurrence of Floquet dynamic quantum phase transitions---an emergent topological phenomenon in the micromotion of the Floquet dynamics. Addressing the relation between the topology of the effective Floquet Hamiltonian and the presence of dynamic topological phenomena, we demonstrate that the topologically nontrivial nature of the Floquet Hamiltonian is a sufficient but not necessary condition for the onset of the Floquet dynamic quantum phase transition. We further discuss the relation of the topology of the Floquet Hamiltonian with the existence of dynamic skyrmion structures in the emergent momentum-time manifold of the micromotion, as well as the fate of these dynamic topological phenomena when the modulation frequency decreases away from the high-frequency limit. Finally, making use of the rich level structures of $^{171}\mathrm{Yb}$ atoms, we show that the system under study can be implemented in a one-dimensional Raman lattice where states in the ${}^{1}{S}_{0}$ ground-state manifold are coupled by Raman beams with periodically modulated amplitudes.

Mutual Interaction between Superconductors and Ferromagnetic Skyrmionic Structures in Confined Geometries

The mutual interaction between a chiral ferromagnetic disk with confined skyrmionic structures and a superconducting disk is studied. The interaction is accounted for by solving simultaneously the Brown and London equations. We find that for a superconductor under an applied uniform field, the stray field of the shielding currents can trigger switching between different skyrmionic states in the ferromagnet that is not possible without the superconductor. We discuss the effect of the different parameters on the results and some possible applications such as multivalued logic, storage, and skyrmionic metamaterials.

Manipulation of Skyrmion Motion Dynamics for Logical Device Application Mediated by Inhomogeneous Magnetic Anisotropy.

Magnetic skyrmions are promising potential information carriers for future spintronic devices owing to their nanoscale size, non-volatility and high mobility. In this work, we demonstrate the controlled manipulation of skyrmion motion and its implementation in a new concept of racetrack logical device by introducing an inhomogeneous perpendicular magnetic anisotropy (PMA) via micromagnetic simulation. Here, the inhomogeneous PMA can be introduced by a capping nano-island that serves as a tunable potential barriers/well which can effectively modulate the size and shape of isolated skyrmion. Using the inhomogeneous PMA in skyrmion-based racetrack enables the manipulation of skyrmion motion behaviors, for instance, blocking, trapping or allowing passing the injected skyrmion. In addition, the skyrmion trapping operation can be further exploited in developing special designed racetrack devices with logic AND and NOT, wherein a set of logic AND operations can be realized via skyrmion–skyrmion repulsion between two skyrmions. These results indicate an effective method for tailoring the skyrmion structures and motion behaviors by using inhomogeneous PMA, which further provide a new pathway to all-electric skyrmion-based memory and logic devices.

Interpolation and extrapolation between the magnetic chiral states using autoencoder

Autoencoder, an artificial neural network, was adopted to generate spin structures that interpolate and extrapolate between two distinct magnetic chiral states, the labyrinth structure and the skyrmion structure. We trained the autoencoder using two distinct magnetic chiral structures. Each input data is encoded through a deep learning process into a latent code, a new representation of the information in a reduced dimensional space. We investigated the latent space to acquire information on the structure of the latent code distribution. With the acquired information, we successfully produced various magnetic structures that exhibit plausible properties under various external fields not provided in the training data. The latent codes were modified by two algorithms. The first algorithm utilizes inversion and translation operation in the latent space and the second algorithm uses recursive flow with a modification bias. The first produced structures preserving the chiral structure of original data and the second produced statistically plausible states.

Unraveling Dissipation-Related Features in Magnetic Imaging by Bimodal Magnetic Force Microscopy

Magnetic Force Microscopy (MFM) is the principal characterization technique for the study of low-dimensional magnetic materials. Nonetheless, during years, the samples under study was limited to samples in the field of data storage, such as longitudinal hard disk, thin films, or patterned nanostructures. Nowadays, thanks to the advances and developments in the MFM modes and instrumentation, other fields are emerging like skyrmionic structures, 2D materials or biological samples. However, in these experiments artifacts in the magnetic images can have strong impact and need to be carefully verified for a correct interpretation of the results. For that reason, in this paper we will explore new ideas combining the multifrequency modes with the information obtained from the experimental dissipation of energy associated to tip-sample interactions.

Spontaneous formation of skyrmion structure in a hard magnetic film with low coercivity

Magnetic skyrmions have attracted enormous research interest since the discovery a decade ago. In this experiment, the spontaneous formation of skyrmions was not observed in common soft-magnetic but in low coercivity hard-magnetic thin films. In this work, Ta (50 nm)/Nd-Fe-B (100 nm)/Ta (2 nm)/Ce-Fe-B (100 nm)/Ta (2 nm)/Nd-Fe-B (100 nm)/Ta (40 nm) multilayer film was prepared by magnetron sputtering. Skyrmion-like bubbles which correspond to vortex structure appeared in the annealed film. Through the OOMMF simulation, We got the formation conditions of the spontaneous vortex. The results of the simulation were consistent with the test results, and the formation mechanism of a skyrmion was pointed out. On the other hand, it could be inferred that skyrmions can be regulated by adjusting or controlling technology for heating processing since it appears spontaneously in annealed hard magnetic films.

Generalized model of MnSi-like spiral magnets

A general, symmetry-allowed model of nearest-neighbour interactions for MnSi-like magnets is presented. A left-handed helical magnet phase occurs within a large parameter space of the model, which is explored via numerical simulation. The relations between microscopic features of the spiral structure and various model parameters, including an external magnetic field, are determined and show good agreement with predictions from free energy considerations. A skyrmion structure is stabilized near the boundary.

Skyrmion based magnonic crystals

Magnonics is now an attractive field which focuses on the dynamic characteristics of magnons, a kind of quasiparticles in magnetic media, and attempts to apply magnons for functional devices. In order to construct magnon-based devices, it is necessary to fabricate materials with specific and tunable magnon bands and bandgaps. Skyrmion-based magnonic crystal is one of the most suitable materials which possess periodical skyrmion structure and show applicative magnon bands and bandgaps. In this review, we provide an overview over recent theoretical and experimental research on skyrmion-based magnonic crystals. We will first provide an introduction of magnonic crystals and magnetic skyrmion. Then, we will show the theoretical and experimental progress on skyrmion-based magnonic crystals and their magnon band characteristics. At the end, we will give an outlook and perspectives of new fascinating fields on topological nontrivial magnon modes, as well as hybrid and quantum magnonic phenomena of skyrmion-based magnonic crystals.

The lifetime of micron scale topological chiral magnetic states with atomic resolution

A new method for the numerical computation of the lifetimes of magnetic states within harmonic transition state theory (HTST) has been developed. In the simplest case, the system is described by a Heisenberg-like Hamiltonian with short-range interaction. Calculations are performed in Cartesian coordinates. Constraints on the values of magnetic moments are taken into account using Lagrange multipliers. The pre-exponential factor in the Arrhenius law in HTST is written in terms of the determinants of the Hessian of energy at the minima and saddle points on the multidimensional energy surface. An algorithm for calculating these determinants without searching for eigenvalues of the Hessian but using recursive relations is proposed. The method allows calculating determinants for systems containing millions of magnetic moments. This makes it possible to calculate the pre-exponential factor and estimate the lifetimes of micron-scale topological structures with atomic resolution, which until now has been impossible using standard approaches. The accuracy of the method is demonstrated by calculating 2D and 3D skyrmionic structures.

Stripe skyrmions and skyrmion crystals

Skyrmions are important in quantum field theory and information technology for being topological solitons and for their attractive applications. Magnetic skyrmions are believed to be circular and stripy spin textures accompanied skyrmion crystals (SkXs) termed spiral/helical/cycloid orders have zero skyrmion number. Here we show that those stripy spin textures are skyrmions, siblings of circular skyrmions in SkXs and cousins of isolated circular skyrmions. Various irregular morphologies are the nature structures of skyrmions in the ground states. At the extreme of one skyrmion in the whole sample, the skyrmion is a ramified stripe. As the skyrmion number density increases, skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to circular objects. At a high skyrmion number density, SkXs are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open an avenue for manipulating skyrmions.

Topological Euler insulators and their electric circuit realization

The Euler number is a new topological number recently debuted in the topological physics. Unlike the Chern number defined for a band, it is defined for interbands. We propose a simple model realizing the topological Euler insulator for the first time. We utilize the fact that the Euler number in a three-band model in two dimensions is reduced to the Pontryagin number. A skyrmion structure appears in momentum phase, yielding a nontrivial Euler number. Topological edge states emerge when the Euler number is nonzero. We discuss how to realize this model in electric circuits. We show that topological edge states are well signaled by impedance resonances.

Skyrmion devices for memory and logic applications

Skyrmions have received considerable attention in various studies since the experimental observation in magnetic materials in 2009. Skyrmions, which are topological, particle-like localized structures, show significant fundamental research value in the field of physics and materials and are also regarded as novel information carriers that have the potential for use in developing high-density, low-power, and multi-functional spintronic devices. In this Perspective, we first overview the development, structure, and materials of skyrmions. Subsequently, we focus on the recent progress in skyrmion devices for memory and logic applications and discuss their challenges and prospects.

Non-Bloch quench dynamics

We study the quench dynamics of non-Hermitian topological models with non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentum-time domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians. The skyrmion structures anchor on the fixed points of dynamics whose existence are conditional on the coincidence of generalized Brillouin zones of the pre- and post-quench Hamiltonians. Global signatures of dynamic skyrmions, however, persist well beyond such a condition, thus offering a general dynamic detection scheme for non-Bloch topology in the presence of non-Hermitian skin effects. Applying our theory to an experimentally relevant, non-unitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics.

Magnetic skyrmion binning

When spin polarised electrons flow through a magnetic texture a transfer torque is generated. We examine the effect of this torque on skyrmions and skyrmion bags, skyrmionic structures of arbitrary integer topological degree, in thin ferromagnetic films. Using micromagnetic simulations and analysis from the well known Thiele equation we explore the potential for sorting or binning skyrmions of varying degrees mechanically. We investigate the applicability of the Thiele equation to problems of this nature and derive a theory of skyrmion deflection ordered by topological degree.

STABILITY OF SKYRMIONS IN THE FRUSTRATED ANTIFERROMAGNETIC/FERROELECTRIC BILAYERS WITH THE TRIANGULAR LATTICE

The formation and conditions of stability of a skyrmions at the interface between a ferroelectric layer and antiferromagnetic layer with triangilar lattice and its phase transition are studied. All interactions between spins and polarizations are limited to nearest neighbors (NN). The antiferromagnetic exchange interaction among the spins inside antiferromagnetic layer will compete with the perpendicular interface interaction between adjacent layers. The ground state spin configuration at zero temperature is calculated by using the numerical high performance steepest descent method. The resulting configuration is non-collinear. Small values of external field yields small values of angles between spins in the plane so that the ground state configurations have antiferromagnetic and non collinear domains. We observe the creation of single spin vortices. We noted that for zero applied magnetic field the skyrmions in the antiferromagnetic/ferroelectric bilayers with triangular lattice can be created in the region of interface magnetoelectric interaction value between 0.85 and 1.95. The strong external magnetic field applied perpendicular to the interface with non-collinear Dzyaloshinskiy-Morya-like magnetoelectric interaction at the interface leads to remove the skyrmion phase and magnetic phase transitions. With increasing the interface magnetoelectric coupling, the skyrmion lattice disappear. We found the formation perfect skyrmion structure at non-zero external magnetic field and moderate values of magnetoelectric interaction. The skyrmions structure is stable in a large region of the interface magnetoelectric interaction between antiferromagnetic and ferroelectric films. The results of Monte Carlo simulations that we carried out confirm that observed skyrmions are stable up to a finite temperature.

Triple helix versus skyrmion lattice in two-dimensional noncentrosymmetric magnets

It is commonly assumed that a lattice of skyrmions, emerging in two-dimensional non-centrosymmetric magnets in external magnetic fields, can be represented as a sum of three magnetic helices. In order to test this assumption we compare two approaches to a description of regular skyrmion structure. We construct (i) a lattice of Belavin-Polyakov-like skyrmions within the stereographic projection method, and (ii) a deformed triple helix defined with the use of elliptic functions. The estimates for the energy density and magnetic profiles show that these two ansatzes are nearly identical at zero temperature for intermediate magnetic fields. However at higher magnetic fields, near the transition to topologically trivial uniform phase, the stereographic projection method is preferable, particularly, for the description of disordered skyrmion liquid phase. We suggest to explore the intensities of the secondary Bragg peaks to obtain the additional information about the magnetic profile of individual skyrmions. We estimate these intensities to be several percents of the main Bragg peak at high magnetic fields.

Direct Observation of Cycloidal Spin Modulation and Field-induced Transition in Néel-type Skyrmion-hosting VOSe2O5

We investigate the spin rotational structure of magnetic skyrmions in a tetragonal polar magnet VOSe2O5 via polarized small-angle neutron scattering (SANS). Spin polarization analysis of the scattered neutrons provides consistent evidence for the cycloidal spin modulation in all the incommensurate phases at zero and non-zero magnetic field along the c axis, including the triangular skyrmion-lattice phase. In the vicinity of the skyrmion phase, we performed extensive SANS measurements to unravel a field-induced incommensurate phase (IC-2 state). We discuss the possibility of anisotropic double-q state as an alternative spin structure to provisional square skyrmion-lattice state.

Geometrically Constrained Skyrmions

Skyrmions are chiral swirling magnetization structures with nanoscale size. These structures have attracted considerable attention due to their topological stability and promising applicability in nanodevices, since they can be displaced with spin-polarized currents. However, for the comprehensive implementation of skyrmions in devices, it is imperative to also attain control over their geometrical position. Here we show that, through thickness modulations introduced in the host material, it is possible to constrain three-dimensional skyrmions to desired regions. We investigate skyrmion structures in rectangular FeGe platelets with micromagnetic finite element simulations. First, we establish a phase diagram of the minimum-energy magnetic state as a function of the external magnetic field strength and the film thickness. Using this understanding, we generate preferential sites for skyrmions in the material by introducing dot-like “pockets” of reduced film thickness. We show that these pockets can serve as pinning centers for the skyrmions, thus making it possible to obtain a geometric control of the skyrmion position. This control allows for stabilization of skyrmions at positions and in configurations that they would otherwise not attain. Our findings may have implications for technological applications in which skyrmions are used as units of information that are displaced along racetrack-type shift register devices.