Skyrmionium - high velocity without the skyrmion Hall effect

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Above-room-temperature chiral skyrmion lattice and Dzyaloshinskii-Moriya interaction in a van der Waals ferromagnet Fe3-xGaTe2

Skyrmions in existing 2D van der Waals (vdW) materials have primarily been limited to cryogenic temperatures, and the underlying physical mechanism of the Dzyaloshinskii-Moriya interaction (DMI), a crucial ingredient for stabilizing chiral skyrmions, remains inadequately explored. Here, we report the observation of Néel-type skyrmions in a vdW ferromagnet Fe3-xGaTe2 above room temperature. Contrary to previous assumptions of centrosymmetry in Fe3-xGaTe2, the atomic-resolution scanning transmission electron microscopy reveals that the off-centered FeΙΙ atoms break the spatial inversion symmetry, rendering it a polar metal. First-principles calculations further elucidate that the DMI primarily stems from the Te sublayers through the Fert-Lévy mechanism. Remarkably, the chiral skyrmion lattice in Fe3-xGaTe2 can persist up to 330 K at zero magnetic field, demonstrating superior thermal stability compared to other known skyrmion vdW magnets. This work provides valuable insights into skyrmionics and presents promising prospects for 2D material-based skyrmion devices operating beyond room temperature.

Stable skyrmion bundles at room temperature and zero magnetic field in a chiral magnet

Topological spin textures are characterized by magnetic topological charges, Q, which govern their electromagnetic properties. Recent studies have achieved skyrmion bundles with arbitrary integer values of Q, opening possibilities for exploring topological spintronics based on Q. However, the realization of stable skyrmion bundles in chiral magnets at room temperature and zero magnetic field - the prerequisite for realistic device applications - has remained elusive. Here, through the combination of pulsed currents and reversed magnetic fields, we experimentally achieve skyrmion bundles with different integer Q values - reaching a maximum of 24 at above room temperature and zero magnetic field - in the chiral magnet Co8Zn10Mn2. We demonstrate the field-driven annihilation of high-Q bundles and present a phase diagram as a function of temperature and field. Our experimental findings are consistently corroborated by micromagnetic simulations, which reveal the nature of the skyrmion bundle as that of skyrmion tubes encircled by a fractional Hopfion.

Optimizing skyrmionium movement and stability via stray magnetic fields in trilayer nanowire constructs

Skyrmioniums, known for their unique transport and regulatory properties, are emerging as potential cornerstones for future data storage systems. However, the stability of skyrmionium movement faces considerable challenges due to the skyrmion Hall effect, which is induced by deformation. In response, our research introduces an innovative solution: we utilized micro-magnetic simulations to create a sandwiched trilayer nanowire structure augmented with a stray magnetic field. This combination effectively guides the skyrmionium within the ferromagnetic (FM) layer. Our empirical investigations reveal that the use of a stray magnetic field not only reduces the size of the skyrmionium but also amplifies its stability. This dual-effect proficiently mitigates the deformation of skyrmionium movement and boosts their thermal stability. We find these positive outcomes are most pronounced at a particular intensity of the stray magnetic field. Importantly, the required stray magnetic field can be generated using a heavy metal (HM1) layer of suitable thickness, rendering the practical application of this approach plausible in real-world experiments. Additionally, we analyze the functioning mechanism based on the Landau-Lifshitz-Gilbert (LLG) equation and energy variation. We also develop a deep spiking neural network (DSNN), which achieves a remarkable recognition accuracy of 97%. This achievement is realized through supervised learning via the spike timing dependent plasticity rule (STDP), considering the nanostructure as an artificial synapse device that corresponds to the electrical properties of the nanostructure. In conclusion, our study provides invaluable insights for the design of innovative information storage devices utilizing skyrmionium technology. By tackling the issues presented by the skyrmion Hall effect, we outline a feasible route for the practical application of this advanced technology. Our research, therefore, serves as a robust platform for continued investigations in this field.

Magnetic Bimerons in Cylindrical Nanotubes

This work presents the analysis of the stability of magnetic bimerons in a cylindrical nanotube. Through micromagnetic simulations, we study the influence of magnetic and geometrical parameters on the bimeron existence and size. The obtained results allow us to present diagram states showing the stability region of a bimeron as a function of the nanotube's height and radius for different anisotropy and Dzyaloshinskii-Moriya interaction strengths. We also obtain two other magnetic states in the range of parameters where the bimeron is not stable: helicoidal and saturated states.

Stabilization and adiabatic control of antiferromagnetically coupled skyrmions without the topological Hall effect

Synthetic antiferromagnetically coupled (SAF) multilayers provide different physics of stabilizing skyrmions while eliminating the topological Hall effect (THE), enabling efficient and stable control. The effects of material parameters, external current drive, and a magnetic field on the skyrmion equilibrium and propagation characteristics are largely unresolved. Here, we present a computational and theoretical demonstration of the large window of material parameters that stabilize SAF skyrmions determined by saturation magnetization, uniaxial anisotropy, and Dzyaloshinskii-Moriya interaction. Current-driven SAF skyrmion velocities reach ∼200 m s-1 without the THE. The SAF velocities are about 3-10 times greater than the typical ferromagnetic skyrmion velocities. The current densities needed for driving SAF skyrmions could be reduced to 108 A m-2, while 1011 A m-2 or above is needed for ferromagnetic skyrmions. By reducing the SAF skyrmion drive current by 3 orders, Joule heating is reduced by 6 orders of magnitude. These results pave the way for new SAF interfaces with improved equilibrium, dynamics, and power savings in THE-free skyrmionics.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.

Reversible conversion between skyrmions and skyrmioniums

Skyrmions and skyrmioniums are topologically non-trivial spin textures found in chiral magnetic systems. Understanding the dynamics of these particle-like excitations is crucial for leveraging their diverse functionalities in spintronic devices. This study investigates the dynamics and evolution of chiral spin textures in [Pt/Co]₃/Ru/[Co/Pt]₃ multilayers with ferromagnetic interlayer exchange coupling. By precisely controlling the excitation and relaxation processes through combined magnetic field and electric current manipulation, reversible conversion between skyrmions and skyrmioniums is achieved. Additionally, we observe the topological conversion from a skyrmionium to a skyrmion, characterized by the sudden emergence of the skyrmion Hall effect. The experimental realization of reversible conversion between distinct magnetic topological spin textures represents a significant development that promises to expedite the advancement of the next generation of spintronic devices.

Realization and Current-Driven Dynamics of Fractional Hopfions and Their Ensembles in a Helimagnet FeGe

3D topological spin textures-hopfions-are predicted in helimagnetic systems but are not experimentally confirmed thus far. By utilizing an external magnetic field and electric current in the present study, 3D topological spin textures are realized, including fractional hopfions with nonzero topological index, in a skyrmion-hosting helimagnet FeGe. Microsecond current pulses are employed to control the dynamics of the expansion and contraction of a bundle composed of a skyrmion and a fractional hopfion, as well as its current-driven Hall motion. This research approach has demonstrated the novel electromagnetic properties of fractional hopfions and their ensembles in helimagnetic systems.

Seeding and Emergence of Composite Skyrmions in a van der Waals Magnet

Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, more exotic states with varying topology, such as antiskyrmions, merons, or bimerons and 3D states such as skyrmion strings, chiral bobbers, and hopfions, have been experimentally reported. Along these lines, the realization of states with higher-order topology has the potential to open new avenues of research in topological magnetism and its spintronic applications. Here, real-space imaging of such spin textures, including skyrmion, skyrmionium, skyrmion bag, and skyrmion sack states, observed in exfoliated flakes of the van der Waals magnet Fe_3-x GeTe₂ (FGT) is reported. These composite skyrmions may emerge from seeded, loop-like states condensed into the stripe domain structure, demonstrating the possibility to realize spin textures with arbitrary integer topological charge within exfoliated flakes of 2D magnets. The general nature of the formation mechanism motivates the search for composite skyrmion states in both well-known and new magnetic materials, which may yet reveal an even richer spectrum of higher-order topological objects.

Squishing Skyrmions: Symmetry-Guided Dynamic Transformation of Polar Topologies Under Compression

Mechanical controllability of recently discovered topological defects (e.g., skyrmions) in ferroelectric materials is of interest for the development of ultralow-power mechano-electronics that are protected against thermal noise. However, fundamental understanding is hindered by the "multiscale quantum challenge" to describe topological switching encompassing large spatiotemporal scales with quantum mechanical accuracy. Here, we overcome this challenge by developing a machine-learning-based multiscale simulation framework─a hybrid neural network quantum molecular dynamics (NNQMD) and molecular mechanics (MM) method. For nanostructures composed of SrTiO₃ and PbTiO₃, we find how the symmetry of mechanical loading essentially controls polar topological switching. We find under symmetry-breaking uniaxial compression a squishing-to-annihilation pathway versus formation of a topological composite named skyrmionium under symmetry-preserving isotropic compression. The distinct pathways are explained in terms of the underlying materials' elasticity and symmetry, as well as the Landau-Lifshitz-Kittel scaling law. Such rational control of ferroelectric topologies will likely facilitate exploration of the rich ferroelectric "topotronics" design space.

Nucleation and manipulation of single skyrmions using spin-polarized currents in antiferromagnetic skyrmion-based racetrack memories

In this work, an ultrafast nucleation of an isolated anti-ferromagnetic (AFM) skyrmion was reported in an AFM layer with DMi strengths of 0.47\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document}-0.32 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{mJ}/{\mathrm{m}}^{2}$$\end{document}mJ/m2 using spin-transfer torque by locally injecting pure spin currents into magnetic tracks. Besides, we revealed the key advantages of AFM skyrmion-based racetrack memories by comparing the motion of AFM and FM skyrmions driven by spin–orbit torques (SOTs) for different skyrmion sizes along racetrack memories with various notch sizes. Our results indicate that for AFM skyrmion, the skyrmion Hall effect does not exist during the skyrmion motion, therefore at small skyrmion sizes, we succeeded to overcome the repulsive forces developed in the notch area for low and large SOTs. The obtained findings were carefully analyzed by computing the variation of energy barriers associated with the notch for different skyrmion sizes using minimum energy path (MEP) calculations. We showed that the larger the skyrmion size, the harder it is to shrink the skyrmion in the notch which produces a high energy barrier (E_b) for large skyrmion sizes. Moreover, as the notch size increases, the skyrmion size shrinks further, and hence E_b increases proportionally. Nevertheless, we proved that AFM skyrmions are more efficient and flexible than FM skyrmions against boundary forces.

The skyrmion bags in an anisotropy gradient

Skyrmion bags as spin textures with arbitrary topological charge are expected to be the carriers in racetrack memory. Here, we theoretically and numerically investigated the dynamics of skyrmion bags in an anisotropy gradient. It is found that, without the boundary potential, the dynamics of skyrmion bags are dependent on the spin textures, and the velocity of skyrmionium withQ = 0 is faster than other skyrmion bags. However, when the skyrmion bags move along the boundary, the velocities of all skyrmion bags with differentQare same. In addition, we theoretically derived the dynamics of skyrmion bags in the two cases using the Thiele approach and discussed the scope of Thiele equation. Within a certain range, the simulation results are in good agreement with the analytically calculated results. Our findings provide an alternative way to manipulate the racetrack memory based on the skyrmion bags.

Voltage-Controlled Skyrmionic Interconnect with Multiple Magnetic Information Carriers

Magnetic skyrmions have been in the spotlight since they were observed in technologically relevant systems at room temperature. More recently, there has been increasing interest in additional quasiparticles that may exist as stable/metastable spin textures in magnets, such as the skyrmionium and the antiskyrmionite (i.e., a skyrmion bag with two skyrmions inside) that have distinct topological characteristics. The next challenge and opportunity, at the same time, is to investigate the use of multiple magnetic quasiparticles as information carriers in a single device for next-generation nanocomputing. In this paper, we propose a spintronic interconnect device where multiple sequences of information signals are encoded and transmitted simultaneously by skyrmions, skyrmioniums, and antiskyrmionites. The proposed spintronic interconnect device can be pipelined via voltage-controlled magnetic anisotropy (VCMA) gated synchronizers that behave as intermediate registers. We demonstrate theoretically that the interconnect throughput and transmission energy can be effectively tuned by the VCMA gate voltage and appropriate electric current pulses. By carefully adjusting the device structure characteristics, our spintronic interconnect device exhibits comparable energy efficiency with copper interconnects in mainstream CMOS technologies. This study provides fresh insight into the possibilities of skyrmionic devices in future spintronic applications.

XMCD and ab initio study of interface-engineered ultrathin Ru/Co/W/Ru films with perpendicular magnetic anisotropy and strong Dzyaloshinskii-Moriya interaction

Understanding the nature of recently discovered spin-orbital induced phenomena and a definition of a general approach for "ferromagnet/heavy-metal" layered systems to enhance and manipulate spin-orbit coupling, spin-orbit torque, and the Dzyaloshinskii-Moriya interaction (DMI) assisted by atomic-scale interface engineering are essential for developing spintronics and spin-orbitronics. Here, we exploit X-ray magnetic circular dichroism (XMCD) spectroscopy at the L_2,3-edges of 5d and 4d non-magnetic heavy metals (W and Ru, respectively) in ultrathin Ru/Co/W/Ru films to determine their induced magnetic moments due to the proximity to the ferromagnetic layer of Co. The deduced orbital and spin magnetic moments agree well with the theoretically predicted values, highlighting the drastic effect of constituting layers on the system's magnetic properties and the strong interfacial DMI in Ru/Co/W/Ru films. As a result, we demonstrate the ability to simultaneously control the strength of magnetic anisotropy and intermixing-enhanced DMI through the interface engineered inversion asymmetry in thin-film chiral ferromagnets, which are a potential host for stable magnetic skyrmions.

Scattering modes of skyrmions in a bilayer system with ferromagnetic coupling

Magnetic skyrmions are quasiparticle-like textures that are topologically different from a single domain magnetization state. Their topological protection, combined with the low current density needed to move them, make these objects relevant to be used as information storage structures. In such a context, the analysis of the interactions between skyrmions is interesting and relevant for future applications. In this work, through micromagnetic simulations and numerical calculations, we studied the interaction between two skyrmions living on different parallel ferromagnetic racetracks connected by an exchange-like interaction. The upper and lower racetracks are separated by a height offset and the interaction between the upper and the lower skyrmion is analyzed in terms of the magnetic and geometrical parameters. Three states are predicted, as a function of these parameters: scattered or free skyrmions, bound skymions, and annihilated skyrmions. Our results, presented in a phase diagram, demonstrate that even in the case here called free skyrmions, there is a small and brief interaction when both are close enough, but the skyrmion in the top layer does not drag the skyrmion in the bottom layer. For bound skyrmions, both keep linked during larger times. In the latter case, there are strong changes in the velocity of the skyrmions induced by the effect of a higher effective mass when both are coupled.

Steering of the Skyrmion Hall Angle by Gate Voltages

Magnetic skyrmions can be driven by an applied spin-polarized electron current that exerts a spin-transfer torque on the localized spins constituting the skyrmion. However, the longitudinal dynamics is plagued by the skyrmion Hall effect, which causes the skyrmions to acquire a transverse velocity component. We show how to use spin-orbit interaction to control the skyrmion Hall angle and how the interplay of spin-transfer and spin-orbit torques can lead to a complete suppression of the transverse motion. Since the spin-orbit torques can be controlled all electronically by a gate voltage, the skyrmion motion can be steered all electronically on a broad racetrack at high speed and conceptually new writing and gating operations can be realized.

Investigation of 2π isolated skyrmion pinning using exchange bias

The 2π isolated chiral skyrmion is a magnetic configuration. Since the total topological charge is zero, the 2π isolated skyrmion driven by a spin-polarized current propagates strictly along the racetrack. The manipulation of 2π-skyrmion, e.g., pinning/depinning at a specific position of the racetrack, is significant. Here, we investigated the 2π-skyrmion pinning in a racetrack using exchange bias. A series of transversal AFM wires were set above the ferromagnetic (FM) racetrack. Spin waves were employed to induce 2π-skyrmion motion to study the dynamics of the 2π-skyrmion pinning. The AFM wires induce exchange bias at the AFM/FM crossing points, which can act as pinning sites. The working window for a 2π-skyrmion in a racetrack was investigated as a function of the exchange bias field, the frequency and amplitude of the oscillating magnetic field for exciting spin waves. The interaction mechanism between the 2π-skyrmion and the exchange bias was also studied. This work may provide guidance for the design of next-generation spintronics.

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.

Artificial Dense Lattices of Magnetic Skyrmions

Multilayer Co/Pt films with perpendicular magnetic anisotropy are irradiated by focused a He⁺ ion beam to locally reduce the anisotropy value. The irradiated spots with the diameters of 100 and 200 nm are arranged in square lattices with the periods of 200 and 300 nm. The formation of nonuniform magnetic states within the spots was observed by magnetic force microscopy methods. We use the concentric distribution of the irradiation fluence within the spot to obtain the radial modulation of the anisotropy constant. This allows us to induce magnetic skyrmions during magnetization reversal of the system. The skyrmions remained stable at zero external magnetic field at room temperature. Magnetization hysteresis loops of the samples were investigated by magnetooptical methods and the results are in good agreement with micromagnetic simulations.

Electrical writing, deleting, reading, and moving of magnetic skyrmioniums in a racetrack device

A magnetic skyrmionium (also called 2π-skyrmion) can be understood as a skyrmion—a topologically nontrivial magnetic whirl—which is situated in the center of a second skyrmion with reversed magnetization. Here, we propose a new optoelectrical writing and deleting mechanism for skyrmioniums in thin films, as well as a reading mechanism based on the topological Hall voltage. Furthermore, we point out advantages for utilizing skyrmioniums as carriers of information in comparison to skyrmions with respect to the current-driven motion. We simulate all four constituents of an operating skyrmionium-based racetrack storage device: creation, motion, detection and deletion of bits. The existence of a skyrmionium is thereby interpreted as a ‘1’ and its absence as a ‘0’ bit.