Types Of Skyrmions Research Articles

The electron resistance of a single skyrmion within ballistic approach

An alternative way of skyrmion quasi-particle detection is simulated at low voltage bias. The point contact (PC), attached to the strip with a Néel-type skyrmion, can detect it with a higher efficiency than a magnetic tunnel junction. The method is based on detecting the skyrmion via the ballistic magnetoresistance ratio (BRR). PC's resistance with skyrmion significantly differs from the one without it. BRR is estimated in the framework of the point contact model for two directions of spin-polarized current: perpendicular to the transport direction (case 1) and along one (case 2). Skyrmion's size is assumed to be around 3.6 nm in diameter—smaller, or comparable, to the mean free path of electrons, allowing it to utilize the ballistic transport approach. As a result, resistance values for the considered Néel type skyrmion within the related size are estimated as 157 Ω for case 1 and 452.2 Ω for case 2 with optimistic BRR 101.3% and 291.7%, respectively. BRR for case 2 is higher due to the spin-filtering effect. The method also has the potential to detect the skyrmion type, or other magnetic nano structures such as bimeron, domain wall (DW), etc.

Multiferroic quantum material Ba2Cu1−xMnxGe2O7 (0 ≤ x ≤ 1) as a potential candidate for frustrated Heisenberg antiferromagnet

Multiferroic Ba2CuGe2O7 was anticipated as a potential member of the exciting group of materials hosting a skyrmion or vortex lattice because of its profound Dzyaloshinskii–Moriya interaction (DMI) and the absence of single ion anisotropy (SIA). This phase, however, could not be evidenced and instead, it exhibits a complex incommensurate antiferromagnetic (AFM) cycloidal structure. Its sister compound Ba2MnGe2O7, in contrast, is characterized by a relatively strong in-plane exchange interaction that competes with a non-vanishing SIA and the weak DMI, resulting in a quasi-two-dimensional commensurate AFM structure. Considering this versatility in the magnetic interactions, a mixed solid solution of Cu and Mn in Ba2Cu1−xMnxGe2O7 can hold an interesting playground for its interactive DMI and SIA depending on the mixed spin states of the transition metal ions towards the skyrmion physics. Here, we present a detailed study of the micro- and macroscopic spin structure of the Ba2Cu1−xMnxGe2O7 solid solution series using high-resolution neutron powder diffraction techniques. We have developed a remarkably rich magnetic phase diagram as a function of the applied magnetic field and x, which consists of two end-line phases separated by a potentially quantum-critical phase at x = 0.57. An AFM conical structure at zero magnetic field is demonstrated to persist up to x = 0.50. Our results provide crucial information on the spin structure and magnetic properties, which are necessary for the general understanding and theoretical developments on multiferroicity in the frame of skyrmion type or frustrated AFM lattice where DMI and SIA play an important role.

Evolution of magnetization textures in Mn1.4PtSn under magnetic field

We have used Lorentz transmission electron microscopy (LTEM) and the transport of intensity equation (TIE) method to investigate the spin structures in the Mn1.4PtSn magnet, which exhibits D2d symmetry. The evolution of the spin structures under the external magnetic field was observed. In particular, a perpendicular field is able to modulate the striped domain widths and to induce the formation of anti-skyrmions and bubbles. While an in-plane magnetic field can control the state of these structures, the coexistence of different types of skyrmions suggests that the hysteresis properties of the magnet may affect the effectiveness of the field control.

Dynamic control of optical skyrmions in cylindrical waveguide

In recent times, the optical skyrmions have received an increasing amount of interest owing to its applications in optical manipulation, super-resolution imaging and microscopy, quantum technologies. However, few studies are focused on the dynamic control of optical skyrmions. It is found that Neel-type photonic skyrmions were discovered in evanescent electromagnetic waves. Here, we find the Bloch-type skyrmions in a three-dimensional cylindrical waveguide. By modulating the amplitude ratio of two incident vortex beams, the new types of skyrmions such as Twisted-type skyrmions and Planar-type skyrmions can be found. Further more, we have also achieved arbitrary modulation ratios of internal spin components. It is believed that our findings greatly enrich the types of photonic skyrmions and provide a method to freely control the photonic skyrmions.

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.

Tunable spin texture transformation with field-free biskyrmion over a broad temperature range in rare-earth ferrimagnets

Exploring and discovering various types of skyrmions has enriched the fundamental study and the active skyrmionics aiming at using skyrmions in spintronics due to the advantages of global stability as high-density magnetic information bit. The unique capability to introduce abundant spin structures, physical phenomena, and dynamics due to the interactions of 4f and 3d electrons push the rare-earth–transition metal (RE–TM) magnets into the research frontier again. Herein, the exotic magnetic domain configurations are discovered in traditional ThMn12-type RE–TM magnets. It is clearly demonstrated that the magnetic anisotropy alteration and magnetic coupling between the respective RE and TM sublattices are responsible for the abundant magnetic domain evolution. In particular, the field-free biskyrmions at room temperature and tunable spin texture transformation are successfully obtained via manipulating the in-plane magnetic anisotropy, which has broadened the physical mechanism and application exploration of manipulating ferrimagnetic order to generate topological spin structures in strategic rare-earth magnets.

Synthetic spin dynamics with Bessel-Gaussian optical skyrmions.

Skyrmions are topologically stable fields that cannot be smoothly deformed into any other field configuration that differs topologically, that is, one that possesses a different integer topological invariant called the Skyrme number. They have been studied as 3-dimensional and 2-dimensional skyrmions in both magnetic and, more recently, optical systems. Here, we introduce an optical analogy to magnetic skyrmions and demonstrate their dynamics within a magnetic field. Our optical skyrmions and synthetic magnetic field are both engineered using superpositions of Bessel-Gaussian beams, with time dynamics observed over the propagation distance. We show that the skyrmionic form changes during propagation, exhibiting controllable periodic precession over a well defined range, analogous to time varying spin precession in homogeneous magnetic fields. This local precession manifests as the global beating between skyrmion types, while still maintaining the invariance of the Skyrme number, which we monitor through a full Stokes analysis of the optical field. Finally, we outline, through numerical simulation, how this approach could be extended to create time varying magnetic fields, offering free-space optical control as a powerful analogue to solid state systems.

Spin thermoelectric effects of skyrmions in ferromagnetic topological insulators

The thermoelectric effects of ferromagnetic topological insulators with either two-dimensional circular or one-dimensional domain wall skyrmions are studied theoretically. It is found that the topological spin-textures play a significant role in the manipulation of spin-dependent thermoelectric properties. In the vicinity of the charge neutrality point, spin Seebeck coefficients possess finite values whose sign and magnitude can be tuned by temperature in spite of vanishing charge Seebeck coefficients. The majority of the effects of circular skyrmions occurs in the edge-state transport regime by generating Fano antiresonances. While the domain wall skyrmion primarily influences the thermoelectric behaviors near the boundary between the edge-state and bulk-state transport regimes with the resonant tunneling mechanism. Both types of skyrmions which function effectively in distinct transport regimes have potential applications in thermoelectrics.

Tuning the Coexistence Regime of Incomplete and Tubular Skyrmions in Ferromagnetic/Ferrimagnetic/Ferromagnetic Trilayers.

The development of skyrmionic devices requires a suitable tuning of material parameters to stabilize skyrmions and control their density. It has been demonstrated recently that different skyrmion types can be simultaneously stabilized at room temperature in heterostructures involving ferromagnets, ferrimagnets, and heavy metals, offering a new platform of coding binary information in the type of skyrmion instead of the presence/absence of skyrmions. Here, we tune the energy landscape of the two skyrmion types in such heterostructures by engineering the geometrical and material parameters of the individual layers. We find that a fine adjustment of the ferromagnetic layer thickness, and thus its magnetic anisotropy, allows the trilayer system to support either one of the skyrmion types or the coexistence of both and with varying densities.

Skyrmion pinning by disk-shaped defects

High precision skyrmion pinning by an intentionally created magnetic structure is important in skyrmion manipulation. Here, we consider skyrmion pinning by various types of disks. Among other findings, we clarify that, in terms of pinning position and pinning potential landscape, one needs to distinguish thin-wall skyrmions from thick-wall skyrmions because of fundamental differences. A skyrmion wall prefers areas with a weaker exchange stiffness, a larger DMI constant, or a smaller magnetic anisotropy while a skyrmion core experiences only the magnetic anisotropy, not exchange stiffness and DMI. Depending on disk type, skyrmion type, and the relative size of the disk (to skyrmion), a skyrmion can be pinned at the symmetric (center) or asymmetric (off-center) point of a disk. In case a skyrmion is pinned by a local energy minimum, thermal agitation can depin the skyrmion, and the pinning lifetime follows an Arrhenius law. Interestingly, when the disk size is comparable to the skyrmion size, the skyrmion deforms greatly such that the skyrmion will shrink or expand to fill the whole disk. These findings should be important for skyrmion manipulations.

Topological superconductivity induced by magnetic texture crystals

We present a detailed investigation of the topological phases and Majorana fermion (MF) excitations that arise from the bulk interplay between (un)conventional one/two-band spin-singlet superconductivity and a number of magnetic texture crystals. The latter define inhomogeneous magnetization profiles which consist of a periodically-repeating primitive cell. Here we focus on magnetic texture crystals with a primitive cell of the helix, whirl, and skyrmion types, which feature distinct symmetry properties. We identify a multitude of accessible topological phases which harbor flat, uni- or bi-directional, (quasi-)helical, or chiral MF edge modes. This rich variety originates from the interplay between topological phases with gapped and nodal bulk energy spectra. The types of the emerging topological superconducting phases and the features of the arising MFs are solely determined by the properties and compatibility of the so-called magnetic and pairing point/space groups. Our analysis is general and does not rely on specific parameters of the models employed here to exemplify the topological scenarios which become accessible. Therefore, our results can be extended to systems with multiple bands, are relevant for a wide range of layered materials and hybrid devices, and provide predictions for strong, weak and crystalline topological phases.

Curvature-induced drift and deformation of magnetic skyrmions: Comparison of the ferromagnetic and antiferromagnetic cases

The influence of the geometrical curvature of chiral magnetic films on the static and dynamic properties of hosted skyrmions is studied theoretically. We predict the effects of the curvature-induced drift of skyrmions under the action of the curvature gradients without any external stimuli. The strength of the curvature-induced driving force essentially depends on the skyrmion type, N\'eel or Bloch, while the trajectory of motion is determined by the type of magnetic ordering: ferromagnetic or antiferromagnetic. When moving on the surface, skyrmions undergo deformations that depend on the type of skyrmion. In the small-curvature limit, using the collective-variable approach we show that the driving force acting on a N\'eel skyrmion is linear in the gradient of the mean curvature. The driving acting on a Bloch skyrmion is much smaller: it is proportional to the product of the mean curvature and its gradient. In contrast to the fast N\'eel skyrmions, the dynamics of the slow Bloch skyrmions is essentially affected by the skyrmion profile deformation. For the sake of simplicity, we restrict ourselves to the case of zero Gaussian curvature and consider cylindrical surfaces of general type. Equations of motion for ferromagnetic and antiferromagnetic skyrmions in curved magnetic films are obtained in terms of collective variables. All analytical predictions are confirmed by numerical simulations.

Skyrmion zoo in graphene at charge neutrality in a strong magnetic field

As a consequence of the approximate spin-valley symmetry in graphene, the ground state of electrons in graphene at charge neutrality is a particular SU(4) quantum-Hall ferromagnet to minimize their exchange energy. If only the Coulomb interaction is taken into account, this ferromagnet can appeal either to the spin degree of freedom or equivalently to the valley pseudo-spin degree of freedom. This freedom in choice is then limited by subleading energy scales that explicitly break the SU(4) symmetry, the simplest of which is given by the Zeeman effect that orients the spin in the direction of the magnetic field. In addition, there are also valley symmetry breaking terms that can arise from short-range interactions or electron-phonon couplings. Here, we build upon the phase diagram, which has been obtained by Kharitonov [Phys. Rev. B \textbf{85}, 155439 (2012)], in order to identify the different skyrmions that are compatible with these types of quantum-Hall ferromagnets. Similarly to the ferromagnets, the skyrmions at charge neutrality are described by the $\text{Gr}(2,4)$ Grassmannian at the center, which allows us to construct the skyrmion spinors. The different skyrmion types are then obtained by minimizing their energy within a variational approach, with respect to the remaining free parameters that are not fixed by the requirement that the skyrmion at large distances from their center must be compatible with the ferromagnetic background. We show that the different skyrmion types have a clear signature in the local, sublattice-resolved, spin magnetization, which is in principle accessible in scanning-tunneling microscopy and spectroscopy.

Coexistence of distinct skyrmion phases observed in hybrid ferromagnetic/ferrimagnetic multilayers

Materials hosting magnetic skyrmions at room temperature could enable compact and energetically-efficient storage such as racetrack memories, where information is coded by the presence/absence of skyrmions forming a moving chain through the device. The skyrmion Hall effect leading to their annihilation at the racetrack edges can be suppressed, for example, by antiferromagnetically-coupled skyrmions. However, avoiding modifications of the inter-skyrmion distances remains challenging. As a solution, a chain of bits could also be encoded by two different solitons, such as a skyrmion and a chiral bobber, with the limitation that it has solely been realized in B20-type materials at low temperatures. Here, we demonstrate that a hybrid ferro/ferri/ferromagnetic multilayer system can host two distinct skyrmion phases at room temperature, namely tubular and partial skyrmions. Furthermore, the tubular skyrmion can be converted into a partial skyrmion. Such systems may serve as a platform for designing memory applications using distinct skyrmion types.

Controllable skyrmion chirality in ferroelectrics

Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear optics and spintronics to biology and pharmaceuticals. However, chirality is usually an invariable inherent property of a given material that cannot be easily changed at will. Here, we demonstrate that ferroelectric nanodots support skyrmions the chirality of which can be controlled and switched. We devise protocols for realizing control and efficient manipulations of the different types of skyrmions. Our findings open the route for controlled chirality with potential applications in ferroelectric-based information technologies.

Computational Search for Ultrasmall and Fast Skyrmions in the Inverse Heusler Family

Skyrmions are magnetic excitations that are potentially ultrasmall and topologically protected, thus making them interesting for high-density all-electronic ultrafast storage applications. While recent experiments have confirmed the existence of various types of skyrmions, their typical sizes are much larger than traditional domain walls, except at very low temperature. In this article, we explore the optimal material parameters for hosting ultrasmall, fast, and room temperature stable, isolated Neel (hedgehog) skyrmions. As concrete examples, we explore potential candidates from the inverse Heusler family. Using first-principles calculations of structural and magnetic properties, we identify several promising ferrimagnetic inverse Heusler half-metal/near half-metals and analyze their phase space for size and metastability.

Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions

Magnetic skyrmions are promising candidates for future storage devices with a large data density. A great variety of materials have been found that host skyrmions up to the room-temperature regime. Lorentz microscopy, usually performed in a transmission electron microscope (TEM), is one of the most important tools for characterizing skyrmion samples in real space. Using numerical calculations, this work relates the phase contrast in a TEM to the actual magnetization profile of an isolated Néel or Bloch skyrmion, the two most common skyrmion types. Within the framework of the used skyrmion model, the results are independent of skyrmion size and wall width and scale with sample thickness for purely magnetic specimens. Simple rules are provided to extract the actual skyrmion configuration of pure Bloch or Néel skyrmions without the need of simulations. Furthermore, first differential phase contrast (DPC) measurements on Néel skyrmions that meet experimental expectations are presented and showcase the described principles. The work is relevant for material sciences where it enables the engineering of skyrmion profiles via convenient characterization.

Turning a chiral skyrmion inside out

The stability of two-dimensional chiral skyrmions in a tilted magnetic field is studied. It is shown that by changing the direction of the field and its magnitude, one can continuously transform chiral skyrmion into a skyrmion with opposite polarity and vorticity. This turned inside out skyrmion can be considered as an antiparticle for ordinary axisymmetric skyrmion. For any tilt angle of the magnetic field, there is a range of its absolute values where two types of skyrmions may coexist. In a tilted field, the potentials for inter-skyrmion interactions are characterized by the presence of local minima suggesting attractive interaction between the particles. The potentials of inter-particle interactions also have so-called fusion channels allowing either annihilation of two particles or the emergence of a new particle. The presented results are general for a wide class of magnetic crystals with both easy-plane and easy-axis anisotropy.

Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

We report the discovery and direct visualization of skyrmion clusters with mutually-orthogonal orientations of constituent isolated skyrmions in chiral liquid crystals and ferromagnets. We show that the nascent conical state underlies attracting inter-skyrmion potential, whereas an encompassing homogeneous state leads to the repulsive skyrmion-skyrmion interaction. The crossover between different regimes of skyrmion interaction could be identified upon changing layer thickness and/or the surface anchoring. We develop a phenomenological theory describing two types of skyrmions and the underlying mechanisms of their interaction. We show that isolated horizontal skyrmions with the same polarity may approach a vertical isolated skyrmion from both sides and thus constitute two energetically-different configurations which are also observed experimentally. In an extreme regime of mutual attraction, the skyrmions wind around each other forming compact superstructures with undulations. We also indicate that our numerical simulations on skyrmion clusters are valid in a parameter range corresponding to the A-phase region of cubic helimagnets.

Topological transport of vorticity in Heisenberg magnets

We study a robust topological transport carried by vortices in a thin film of an easy-plane ferromagnetic insulator between two metal contacts. A vortex, which is a nonlocal topological spin texture in two-dimensional magnets, exhibits some beneficial features as compared to skyrmions, which are local topological defects. In particular, the total topological charge carried by vorticity is robust against local fluctuations of the spin order-parameter magnitude. We show that an electric current in one of the magnetized metal contacts can pump vortices into the insulating bulk. Diffusion and nonlocal Coulomb-like interaction between these vortices will establish a steady-state vortex flow. Vortices leaving the bulk produce an electromotive force at another contact, which is related to the current-induced vorticity pumping by the Onsager reciprocity. The voltage signal decays algebraically with the separation between two contacts, similarly to a superfluid spin transport. Finally, the vorticity and closely related skyrmion type topological hydrodynamics are generalized to arbitrary dimensions, in terms of nonsingular order-parameter vector fields.