Bound States of Skyrmions and Merons near the Lifshitz Point

Homochiral antiferromagnetic merons, antimerons and bimerons realized in synthetic antiferromagnets

The ever-growing demand for device miniaturization and energy efficiency in data storage and computing technology has prompted a shift towards antiferromagnetic topological spin textures as information carriers. This shift is primarily owing to their negligible stray fields, leading to higher possible device density and potentially ultrafast dynamics. We realize in this work such chiral in-plane topological antiferromagnetic spin textures namely merons, antimerons, and bimerons in synthetic antiferromagnets by concurrently engineering the effective perpendicular magnetic anisotropy, the interlayer exchange coupling, and the magnetic compensation ratio. We demonstrate multimodal vector imaging of the three-dimensional Néel order parameter, revealing the topology of those spin textures and a globally well-defined chirality, which is a crucial requirement for controlled current-induced dynamics. Our analysis reveals that the interplay between interlayer exchange and interlayer magnetic dipolar interactions plays a key role to significantly reduce the critical strength of the Dzyaloshinskii-Moriya interaction required to stabilize topological spin textures, such as antiferromagnetic merons, in synthetic antiferromagnets, making them a promising platform for next-generation spintronics applications.

Skyrmion Fluid and Bimeron Glass Protected by a Chiral Spin Liquid on a Kagome Lattice

Skyrmions are of interest both from a fundamental and technological point of view, due to their potential to act as information carriers. But one challenge concerns their manipulation, especially at high temperature where thermal fluctuations eventually disintegrate them. Here we study the competition between skyrmions and a chiral spin liquid, using the latter as an entropic buffer to impose a quasivacuum of skyrmions. As a result, the temperature becomes a knob to tune the skyrmion density from a dense liquid to a diluted gas, protecting the integrity of each skyrmion from paramagnetic disintegration. With this additional knob in hand, we find at high field a topological spin glass made of zero- and one-dimensional topological defects (respectively skyrmions and bimerons).

Metastability of photonic spin meron lattices in the presence of perturbed spin-orbit coupling

Photonic skyrmions and merons are topological quasiparticles characterized by nontrivial electromagnetic textures, which have received increasing research attention recently, providing novel degree of freedom to manipulate light-matter interactions and exhibiting excellent potential in deep-subwavelength imaging and nanometrology. Here, the topological stability of photonic spin meron lattices, which indicates the invariance of skyrmion number and robustness of spin texture under a continuous deformation of the field configuration, is demonstrated by inducing a perturbation to break the C₄ symmetry in the presence spin-orbit coupling in an optical field. We revealed that amplitude perturbation would result in an amplitude-dependent shift of spin center, while phase perturbation leads to the deformation of domain walls, manifesting the metastability of photonic meron. Such spin topology is verified through the interference of plasmonic vortices with a broken rotational symmetry. The results provide new insights on optical topological quasiparticles, which may pave the way towards applications in topological photonics, optical information storage and transfer.

Multiple Topological Magnetism in van der Waals Heterostructure of MnTe2/ZrS2

Topological magnetism in low-dimensional systems is of fundamental and practical importance in condensed-matter physics and material science. Here, using first-principles and Monte Carlo simulations, we present that multiple topological magnetism (i.e., skyrmion and bimeron) can survive in van der Waals heterostructure MnTe₂/ZrS₂. Arising from interlayer coupling, MnTe₂/ZrS₂ can harbor a large Dzyaloshinskii-Moriya interaction. This, combined with exchange interaction, yields an intriguing skyrmion phase under a tiny magnetic field of 75 mT. Meanwhile, upon harnessing a small electric field, magnetic bimeron can be observed in MnTe₂/ZrS₂, suggesting the existence of multiple topological magnetism. Through interlayer sliding, both topological magnetisms can be switched on-off. In addition, the impacts of d_∥ and K_eff on these spin textures are revealed, and a dimensionless parameter κ is utilized to describe their joint effect. These explored phenomena and insights not only are useful for fundamental research in topological magnetism but also enable novel applications in nanodevices.

Reversible Transformation between Isolated Skyrmions and Bimerons

Skyrmions and bimerons are versatile topological spin textures that can be used as information bits for both classical and quantum computing. The transformation between isolated skyrmions and bimerons is an essential operation for computing architecture based on multiple different topological bits. Here we report the creation of isolated skyrmions and their subsequent transformation to bimerons by harnessing the electric current-induced Oersted field and temperature-induced perpendicular magnetic anisotropy variation. The transformation between skyrmions and bimerons is reversible, which is controlled by the current amplitude and scanning direction. Both skyrmions and bimerons can be created in the same system through the skyrmion-bimeron transformation and magnetization switching. Deformed skyrmion bubbles and chiral labyrinth domains are found as nontrivial intermediate transition states. Our results may provide a unique way for building advanced information-processing devices using different types of topological spin textures in the same system.

Skyrmion Echo in a System of Interacting Skyrmions

We consider helical rotation of skyrmions confined in the potentials formed by nanodisks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Because of the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g., by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice versa), and this restores the initial signal (which is the essence of skyrmion echo).

Low-Energy Excitations of Skyrmion Crystals in a Centrosymmetric Kondo-Lattice Magnet: Decoupled Spin-Charge Excitations and Nonreciprocity

We theoretically study spin and charge excitations of skyrmion crystals stabilized by conduction-electron-mediated magnetic interactions via spin-charge coupling in a centrosymmetric Kondo-lattice model by large-scale spin-dynamics simulations combined with the kernel polynomial method. We reveal clear segregation of spin and charge excitation channels and nonreciprocal nature of the spin excitations governed by the Fermi-surface geometry, which are unique to the skyrmion crystals in centrosymmetric itinerant hosts and can be a source of novel physical phenomena.

Magnetoelectric Classification of Skyrmions

We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and antiskyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show that the nonzero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity, and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures.

Topology dependence of skyrmion Seebeck and skyrmion Nernst effect

We explore the dynamics of skyrmions with various topological charges induced by a temperature gradient in an ultra-thin insulating magnetic film. Combining atomistic spin simulations and analytical calculations we find a topology-dependent skyrmion Seebeck effect: while skyrmions and antiskyrmions move to the hot regime, a topologically trivial localized spin structure moves to the cold regime. We further reveal the emergence of a skyrmion Nernst effect, i.e. finite, topology-dependent velocities transverse to the direction of the temperature gradient. These findings are in agreement with accompanying simulations of skyrmionic motion induced by monochromatic magnon currents, allowing us to demonstrate that the magnonic spin Seebeck effect is responsible for both, skyrmion Seebeck and Nernst effect. Furthermore we employ scattering theory together with Thiele's equation to identify linear momentum transfer from the magnons to the skyrmion as the dominant contribution and to demonstrate that the direction of motion depends on the topological magnon Hall effect and the topological charge of the skyrmion.

Spontaneous magnetic merons in a half-metallic Mn2I3Br3 monolayer with easy-plane anisotropy

Spontaneous magnetic merons are found to exist in a wide magnetic field range (0–6 T) stabilized by the large in-plane magnetic anisotropy and strong Dzyaloshinskii–Moriya interaction in a half-metallic Mn2I3Br3 monolayer.

Photonic Spin Lattices: Symmetry Constraints for Skyrmion and Meron Topologies

Symmetry and topology govern many electronic, magnetic, and photonic phenomena in condensed matter physics and optics, resulting in counterintuitive skyrmion, meron, and other phenomena important for modern technologies. Here we demonstrate photonic spin lattices as a new topological construct governed by the spin-orbit coupling in an optical field. The symmetry of the electromagnetic field in the presence of the spin-orbit interaction may result in only two types of photonic spin lattices: either hexagonal spin-skyrmion or square spin-meron lattices. We show that these spin structures correspond to the lowest energy of the electromagnetic field configuration, therefore, energetically stable. We further show that in the absence of spin-orbit coupling these spin topologies are degenerated in dynamic field skyrmions, unifying the description of electromagnetic field topologies. The results provide a new understanding of electromagnetic field topology and its transformations as well as new opportunities for applications in quantum technologies, spin optics, and topological photonics.

Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets

Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.

Interplay between Single-Ion and Two-Ion Anisotropies in Frustrated 2D Semiconductors and Tuning of Magnetic Structures Topology

The effects of competing magnetic interactions in stabilizing different spin configurations are drawing renewed attention in order to unveil emerging topological spin textures and to highlight microscopic mechanisms leading to their stabilization. The possible key role of the two-site exchange anisotropy in selecting specific helicity and vorticity of skyrmionic lattices has only recently been proposed. In this work, we explore the phase diagram of a frustrated localized magnet characterized by a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy and the single-ion anisotropy. The effects of an external magnetic field applied perpendicularly to the magnetic layer, are also investigated. By means of Monte Carlo simulations, we find an abundance of different spin configurations, going from trivial to high-order Q skyrmionic and meronic lattices. In closer detail, we find that a dominant role is played by the two-ion over the single-ion anisotropy in determining the planar spin texture; the strength and the sign of single ion anisotropy, together with the magnitude of the magnetic field, tune the perpendicular spin components, mostly affecting the polarity (and, in turn, the topology) of the spin texture. Our analysis confirms the crucial role of the anisotropic symmetric exchange in systems with dominant short-range interactions; at the same time, we predict a rich variety of complex magnetic textures, which may arise from a fine tuning of competing anisotropic mechanisms.

Skyrmion ratchet propagation: utilizing the skyrmion Hall effect in AC racetrack storage devices

Magnetic skyrmions are whirl-like nano-objects with topological protection. When driven by direct currents, skyrmions move but experience a transverse deflection. This so-called skyrmion Hall effect is often regarded a drawback for memory applications. Herein, we show that this unique effect can also be favorable for spintronic applications: We show that in a racetrack with a broken inversion symmetry, the skyrmion Hall effect allows to translate an alternating current into a directed motion along the track, like in a ratchet. We analyze several modes of the ratchet mechanism and show that it is unique for topological magnetic whirls. We elaborate on the fundamental differences compared to the motion of topologically trivial magnetic objects, as well as classical particles driven by periodic forces. Depending on the exact racetrack geometry, the ratchet mechanism can be soft or strict. In the latter case, the skyrmion propagates close to the efficiency maximum.

Antiferromagnetic half-skyrmions and bimerons at room temperature

In the quest for post-CMOS (complementary metal-oxide-semiconductor) technologies, driven by the need for improved efficiency and performance, topologically protected ferromagnetic 'whirls' such as skyrmions^1-8 and their anti-particles have shown great promise as solitonic information carriers in racetrack memory-in-logic or neuromorphic devices^1,9-11. However, the presence of dipolar fields in ferromagnets, which restricts the formation of ultrasmall topological textures^3,6,8,9,12, and the deleterious skyrmion Hall effect, when skyrmions are driven by spin torques^9,10,12, have thus far inhibited their practical implementation. Antiferromagnetic analogues, which are predicted to demonstrate relativistic dynamics, fast deflection-free motion and size scaling, have recently become the subject of intense focus^9,13-19, but they have yet to be experimentally demonstrated in natural antiferromagnetic systems. Here we realize a family of topological antiferromagnetic spin textures in α-Fe₂O₃-an Earth-abundant oxide insulator-capped with a platinum overlayer. By exploiting a first-order analogue of the Kibble-Zurek mechanism^20,21, we stabilize exotic merons and antimerons (half-skyrmions)⁸ and their pairs (bimerons)^16,22, which can be erased by magnetic fields and regenerated by temperature cycling. These structures have characteristic sizes of the order of 100 nanometres and can be chemically controlled via precise tuning of the exchange and anisotropy, with pathways through which further scaling may be achieved. Driven by current-based spin torques from the heavy-metal overlayer, some of these antiferromagnetic textures could emerge as prime candidates for low-energy antiferromagnetic spintronics at room temperature^1,9-11,23.

Plasmonic Skyrmion Lattice Based on the Magnetoelectric Effect

The physical mechanism of the plasmonic skyrmion lattice formation in a magnetic layer deposited on a metallic substrate is studied theoretically. The optical lattice is the essence of the standing interference pattern of the surface plasmon polaritons created through coherent or incoherent laser sources. The nodal points of the interference pattern play the role of lattice sites where skyrmions are confined. The confinement appears as a result of the magnetoelectric effect and the electric field associated with the plasmon waves. The proposed model is applicable to yttrium iron garnet and single-phase multiferroics and combines plasmonics and skyrmionics.

Controlling bimerons as skyrmion analogues by ferroelectric polarization in 2D van der Waals multiferroic heterostructures

Atom-thick van der Waals heterostructures with nontrivial physical properties tunable via the magnetoelectric coupling effect are highly desirable for the future advance of multiferroic devices. In this work on LaCl/In₂Se₃ heterostructure consisting of a 2D ferromagnetic layer and a 2D ferroelectric layer, reversible switch of the easy axis and the Curie temperature of the magnetic LaCl layer has been enabled by switching of ferroelectric polarization in In₂Se₃. More importantly, magnetic skyrmions in the bimerons form have been discovered in the LaCl/In₂Se₃ heterostructure and can be driven by an electric current. The creation and annihilation of bimerons in LaCl magnetic nanodisks were achieved by polarization switching. It thus proves to be a feasible approach to achieve purely electric control of skyrmions in 2D van der Waals heterostructures. Such nonvolatile and tunable magnetic skyrmions are promising candidates for information carriers in future data storage and logic devices operated under small electrical currents.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Current-Induced Dynamics and Chaos of Antiferromagnetic Bimerons

A magnetic bimeron is a topologically nontrivial spin texture carrying an integer topological charge, which can be regarded as the counterpart of the skyrmion in easy-plane magnets. The controllable creation and manipulation of bimerons are crucial for practical applications based on topological spin textures. Here, we analytically and numerically study the dynamics of an antiferromagnetic bimeron driven by a spin current. Numerical simulations demonstrate that the spin current can create an isolated bimeron in the antiferromagnetic thin film via the dampinglike spin torque. The spin current can also effectively drive the antiferromagnetic bimeron without a transverse drift. The steady motion of an antiferromagnetic bimeron is analytically derived and is in good agreement with the simulation results. Also, we find that the alternating-current-induced motion of the antiferromagnetic bimeron can be described by the Duffing equation due to the presence of the nonlinear boundary-induced force. The associated chaotic behavior of the bimeron is analyzed in terms of the Lyapunov exponents. Our results demonstrate the inertial dynamics of an antiferromagnetic bimeron, and may provide useful guidelines for building future bimeron-based spintronic devices.

Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions

Current-induced motion of non-axisymmetric skyrmions within tilted ferromagnetic phases of polar helimagnets with the easy plane anisotropy is studied by micromagnetic simulations. Such non-axisymmetric skyrmions consist of a circular core and a crescent-shaped domain-wall region formed with respect to the tilted surrounding state. Current-driven motion of non-axisymmetric skyrmions exhibits two distinct time regimes: initially the skyrmions rotate towards the current flow direction and subsequently move along the current with the skyrmionic crescent first. According to the Thiele equation, the asymmetric distribution of the topological charge and the dissipative force tensor play an important role for giving the different velocities for the circular and the crescent-shaped constituent parts of the skyrmion what underlies such a shuttlecock-like movement. Moreover, the current-velocity relation depends on the angle of the tilted ferromagnetic phase what makes in particular the transverse velocity of skyrmions sensitive to their field-driven configurational transformation. We also argue the possibility of magnetic racetrack waveguides based on complex interplay of robust asymmetric skyrmions with multiple twisted edge states.