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

In-Situ Monitoring the Magnetotransport Signature of Topological Transitions in a Chiral Magnet

Emerging magnetic fields related to the presence of topologically protected spin textures such as skyrmions are expected to give rise to additional, topology-related contributions to the Hall effect. In order to doubtlessly identify this so-called topological Hall effect, it is crucial to disentangle such contributions from the anomalous Hall effect. This necessitates a direct correlation of the transversal Hall voltage with the underlying magnetic textures. A novel measurement platform is developed that allows to acquire high-resolution Lorentz transmission electron microscopy images of magnetic textures as a function of an external magnetic field and to concurrently measure the (anomalous) Hall voltage in-situ in the microscope on one and the same specimen. This approach is used to investigate the transport signatures of the chiral soliton lattice and antiskyrmions in Mn1.4PtSn. Notably, the observed textures allow to fully understand the measured Hall voltage without the need of any additional contributions due to a topological Hall effect, and the field-controlled formation and annihilation of anstiskyrmions are found to have no effect on the measured Hall voltage.

Magnetic domain wall and skyrmion manipulation by static and dynamic strain profiles

Magnetic domain walls and skyrmions in thin film micro- and nanostructures have been of interest to a growing number of researchers since the turn of the millennium, motivated by the rich interplay of materials, interface and spin physics as well as by the potential for applications in data storage, sensing and computing. This review focuses on the manipulation of magnetic domain walls and skyrmions by piezoelectric strain, which has received increasing attention recently. Static strain profiles generated, for example, by voltage applied to a piezoelectric-ferromagnetic heterostructure, and dynamic strain profiles produced by surface acoustic waves, are reviewed here. As demonstrated by the success of magnetic random access memory, thin magnetic films have been successfully incorporated into complementary metal-oxide-semiconductor back-end of line device fabrication. The purpose of this review is therefore not only to highlight promising piezoelectric and magnetic materials and their properties when combined, but also to galvanise interest in the spin textures in these heterostructures for a variety of spin- and straintronic devices.

Fundamental theory of current-induced motion of magnetic skyrmions

Magnetic skyrmions are topological spin textures that appear in magnets with broken spatial inversion symmetry as a consequence of competition between the (anti)ferromagnetic exchange interactions and the Dzyaloshinskii-Moriya interactions in a magnetic field. In the research of spintronics, the current-driven dynamics of skyrmions has been extensively studied aiming at their applications to next-generation spintronic devices. However, current-induced skyrmion motion exhibits diverse behaviors depending on various factors and conditions such as the type of skyrmion, driving mechanism, system geometry, direction of applied current, and type of the magnet. While this variety attracts enormous research interest of fundamental science and enriches their possibilities of technical applications, it is, at the same time, a source of difficulty and complexity that hinders their comprehensive understandings. In this article, we discuss fundamental and systematic theoretical descriptions of current-induced motion of skyrmions driven by the spin-transfer torque and the spin-orbit torque. Specifically, we theoretically describe the behaviors of current-driven skyrmions depending on the factors and conditions mentioned above by means of analyses using the Thiele equation. Furthermore, the results of the analytical theory are visually demonstrated and quantitatively confirmed by micromagnetic simulations using the Landau-Lifshitz-Gilbert-Slonczewski equation. In particular, we discuss dependence of the direction and velocity of motion on the type of skyrmion (Bloch type and Néel type) and its helicity, the system geometry (thin plate and nanotrack), the direction of applied current (length and width direction of the nanotrack) and its spin-polarization orientation, and the type of magnet (ferromagnet and antiferromagnet). The comprehensive theory provided by this article is expected to contribute significantly to research on the manipulation and control of magnetic skyrmions by electric currents for future spintronics applications.

Visualization of Skyrmion-Superconducting Vortex Pairs in a Chiral-Magnet-Superconductor Heterostructure

Magnetic skyrmions, the topological states possessing chiral magnetic structure with nontrivial topology, have been widely investigated as a promising candidate for spintronic devices. They can also couple with superconducting vortices to form skyrmion-vortex pairs, hosting Majorana zero mode, which is a potential candidate for topological quantum computing. Many theoretical proposals have been put forward on constructing skyrmion-vortex pairs in heterostructures of chiral magnets and superconductors. Nevertheless, how to generate skyrmion-vortex pairs in a controllable way experimentally remains a significant challenge. We have designed a heterostructure of a chiral magnet and superconductor [Ta/Ir/CoFeB/MgO]_{7}/Nb in which zero field Néel-type skyrmions can be stabilized and the superconducting vortices can couple with the skyrmions when Nb is in the superconducting state. We have directly observed the formation of skyrmion-superconducting vortex pairs that is dependent on the direction of the applied magnetic field. Our results provide an effective method to manipulate the quantum states of skyrmions with the help of superconducting vortices, which can be used to explore new routines to control the skyrmions for spintronics devices.

All-Optical Control of Bubble and Skyrmion Breathing

Controlling the dynamics of topologically protected spin objects by all-optical means promises enormous potential for future spintronic applications. Excitation of bubbles and skyrmions in ferrimagnetic [Fe(0.35  nm)/Gd(0.40  nm)]_{160} multilayers by ultrashort laser pulses leads to a periodic modulation of the core diameter of these spin objects, the so-called breathing mode. We demonstrate versatile amplitude and phase control of this breathing using a double excitation scheme, where the observed dynamics is controlled by the excitation delay. We gain insight into both the timescale on which the breathing mode is launched and the role of the spin object size on the dynamics. Our results demonstrate that ultrafast optical excitation allows for precise tuning of the spin dynamics of trivial and nontrivial spin objects, showing a possible control strategy in device applications.

Real-Space Topology-Engineering of Skyrmionic Spin Textures in a van der Waals Ferromagnet Fe3GaTe2

Realizing magnetic skyrmions in two-dimensional (2D) van der Waals (vdW) ferromagnets offers unparalleled prospects for future spintronic applications. The room-temperature ferromagnet Fe3GaTe2 provides an ideal platform for tailoring these magnetic solitons. Here, skyrmions of distinct topological charges are artificially introduced and engineered by using magnetic force microscopy (MFM). The skyrmion lattice is realized by a specific field-cooling process and can be further erased and painted via delicate manipulation of the tip stray field. The skyrmion lattice with opposite topological charges (S = ±1) can be tailored at the target regions to form topological skyrmion junctions (TSJs) with specific configurations. The delicate interplay of TSJs and spin-polarized device current were finally investigated via the in situ transport measurements, alongside the topological stability of TSJs. Our results demonstrate that Fe3GaTe2 not only serves as a potential building block for skyrmion-based spintronic devices, but also presents prospects for Fe3GaTe2-based heterostructures with the engineered topological spin textures.

Eliminating Skyrmion Hall Effect in Ferromagnetic Skyrmions

Skyrmion Hall effect (SkHE) remains an obstacle for the application of magnetic skyrmions. While methods have been established to cancel or compensate SkHE in artificial antiferromagnets and ferrimagnets, eliminating intrinsic SkHE in ferromagnets is still a big challenge. Here, we propose a strategy to eliminate SkHE by intercalating nonmagnetic elements into van der Waals bilayer ferromagnets featuring in-plane ferromagnetism. The in-plane magnetism, along with a delicate balance among exchange interactions, Dzyaloshinskii-Moriya interactions (DMI), and magnetocrystalline anisotropy, creates interlayer bimerons/quadmerons, whose polarity can be controlled by DMI. Opposite DMI in the upper and lower layers results in opposite polarity and topological charge number Q-locking of topological spin texture, therefore, eliminating the SkHE. By intercalating Sr (Ba) in bilayer VSe2, we identify ten topological magnetic structures with zero topological charge number. Furthermore, we present a phase diagram illustrating diverse magnetic configurations achievable within the bimagnetic atomic layer, offering valuable guidance for future investigations.

Zero-field magnetic skyrmions in exchange-biased ferromagnetic-antiferromagnetic bilayers

We report on the stabilization of ferromagnetic skyrmions in zero external magnetic fields, in exchange-biased systems composed of ferromagnetic-antiferromagnetic (FM-AFM) bilayers. By performing atomistic spin dynamics simulations, we study cases of compensated, uncompensated, and partly uncompensated FM-AFM interfaces, and investigate the impact of important parameters such as temperature, inter-plane exchange interaction, Dzyaloshinskii-Moriya interaction, and magnetic anisotropy on the skyrmions appearance and stability. The model with an uncompensated FM-AFM interface leads to the stabilization of individual skyrmions and skyrmion lattices in the FM layer, caused by the effective field from the AFM instead of an external magnetic field. Similarly, in the case of a fully compensated FM-AFM interface, we show that FM skyrmions can be stabilized. We also demonstrate that accounting for interface roughness leads to stabilization of skyrmions both in compensated and uncompensated interface. Moreover, in bilayers with a rough interface, skyrmions in the FM layer are observed for a wide range of exchange interaction values through the FM-AFM interface, and the chirality of the skyrmions depends critically on the exchange interaction.

Macroscopic tunneling probe of Moiré spin textures in twisted CrI3

Various noncollinear spin textures and magnetic phases have been predicted in twisted two-dimensional CrI3 due to competing ferromagnetic (FM) and antiferromagnetic (AFM) interlayer exchange from moiré stacking-with potential spintronic applications even when the underlying material possesses a negligible Dzyaloshinskii-Moriya or dipole-dipole interaction. Recent measurements have shown evidence of coexisting FM and AFM layer order in small-twist-angle CrI3 bilayers and double bilayers. Yet, the nature of the magnetic textures remains unresolved and possibilities for their manipulation and electrical readout are unexplored. Here, we use tunneling magnetoresistance to investigate the collective spin states of twisted double-bilayer CrI3 under both out-of-plane and in-plane magnetic fields together with detailed micromagnetic simulations of domain dynamics based on magnetic circular dichroism. Our results capture hysteretic and anisotropic field evolutions of the magnetic states and we further uncover two distinct non-volatile spin textures (out-of-plane and in-plane domains) at ≈1° twist angle, with a different global tunneling resistance that can be switched by magnetic field.

Spontaneous Atomic-Scale Polar Skyrmions and Merons on a SrTiO3 (001) Surface: Defect Engineering for Emerging Topological Orders

The emergence of nontrivial topological order in condensed matter has been attracting a great deal of attention owing to its promising technological applications in novel functional nanodevices. In ferroelectrics, the realization of polar topological order at an ultimately small scale is extremely challenging due to the lack of chiral interaction and the critical size of the ferroelectricity. Here, we break through these limitations and demonstrate that the ultimate atomic-scale polar skyrmion and meron (∼2 nm) can be induced by engineering oxygen vacancies on the SrTiO3 (001) surface based on first-principles calculations. The paraelectric-to-antiferrodistortive phase transition leads to a novel topological transition from skyrmion to meron, indicating phase-topology correlations. We also discuss accumulating and driving polar skyrmions based on the oxygen divacancy model; these results and the recent discovery of defect engineering techniques suggest the possibility of arithmetic operations on topological numbers through the natural self-organization and diffusion features of oxygen vacancies.

Electrical Detection and Nucleation of a Magnetic Skyrmion in a Magnetic Tunnel Junction Observed via Operando Magnetic Microscopy

Magnetic skyrmions are topological spin textures which are envisioned as nanometer scale information carriers in magnetic memory and logic devices. The recent demonstrations of room temperature skyrmions and their current induced manipulation in ultrathin films were first steps toward the realization of such devices. However, important challenges remain regarding the electrical detection and the low-power nucleation of skyrmions, which are required for the read and write operations. Here, we demonstrate, using operando magnetic microscopy experiments, the electrical detection of a single magnetic skyrmion in a magnetic tunnel junction (MTJ) and its nucleation and annihilation by gate voltage via voltage control of magnetic anisotropy. The nucleated skyrmion can be manipulated by both gate voltages and external magnetic fields, leading to tunable intermediate resistance states. Our results unambiguously demonstrate the readout and voltage controlled write operations in a single MTJ device, which is a major milestone for low power skyrmion based technologies.

Quantification of Hybrid Topological Spin Textures and Their Nanoscale Fluctuations in Ferrimagnets

Noncolinear spin textures, including chiral stripes and skyrmions, have shown great potential in spintronics. Basic configurations of spin textures are either Bloch or Néel types, and the intermediate hybrid type has rarely been reported. A major challenge in identifying hybrid spin textures is to quantitatively determine the hybrid angle, especially in ferrimagnets with weak net magnetization. Here, we develop an approach to quantify magnetic parameters, including chirality, saturation magnetization, domain wall width, and hybrid angle with sub-5 nm spatial resolution, based on Lorentz four-dimensional scanning transmission electron microscopy (Lorentz 4D-STEM). We find strong nanometer-scale variations in the hybrid angle and domain wall width within structurally and chemically homogeneous FeGd ferrimagnetic films. These variations fluctuate during different magnetization circles, revealing intrinsic local magnetization inhomogeneities. Furthermore, hybrid skyrmions can also be nucleated in FeGd films. These analyses demonstrate that the Lorentz 4D-STEM is a quantitative tool for exploring complex spin textures.

Chiral Skyrmions Interacting with Chiral Flowers

The chiral nature of active matter plays an important role in the dynamics of active matter interacting with chiral structures. Skyrmions are chiral objects, and their interactions with chiral nanostructures can lead to intriguing phenomena. Here, we explore the random-walk dynamics of a thermally activated chiral skyrmion interacting with a chiral flower-like obstacle in a ferromagnetic layer, which could create topology-dependent outcomes. It is a spontaneous mesoscopic order-from-disorder phenomenon driven by the thermal fluctuations and topological nature of skyrmions that exists only in ferromagnetic and ferrimagnetic systems. The interactions between the skyrmions and chiral flowers at finite temperatures can be utilized to control the skyrmion position and distribution without applying any external driving force or temperature gradient. The phenomenon that thermally activated skyrmions are dynamically coupled to chiral flowers may provide a new way to design topological sorting devices.

Releasing antiferromagnetic skyrmions from local magnetic-anisotropy defects

Lattice defects may work as a kind of apparatus for catching topological excitations, preventing their escape. So, the problem of removing skyrmions from eventual local defects in magnetic materials must be closely related to new technologies such as skyrmionic. Here, we examine the conditions for drawing a skyrmion from a magnetic impurity in a two-dimensional antiferromagnetic system by applying spin-polarized currents (SPC). Two types of impurities are investigated (local easy-axis and easy-plane anisotropy defects). Also, two methods to release the skyrmion with SPC are explored. In principle, our results could be qualitatively relevant to any other type of lattice defect.

Enhanced thermally-activated skyrmion diffusion with tunable effective gyrotropic force

Magnetic skyrmions, topologically-stabilized spin textures that emerge in magnetic systems, have garnered considerable interest due to a variety of electromagnetic responses that are governed by the topology. The topology that creates a microscopic gyrotropic force also causes detrimental effects, such as the skyrmion Hall effect, which is a well-studied phenomenon highlighting the influence of topology on the deterministic dynamics and drift motion. Furthermore, the gyrotropic force is anticipated to have a substantial impact on stochastic diffusive motion; however, the predicted repercussions have yet to be demonstrated, even qualitatively. Here we demonstrate enhanced thermally-activated diffusive motion of skyrmions in a specifically designed synthetic antiferromagnet. Suppressing the effective gyrotropic force by tuning the angular momentum compensation leads to a more than 10 times enhanced diffusion coefficient compared to that of ferromagnetic skyrmions. Consequently, our findings not only demonstrate the gyro-force dependence of the diffusion coefficient but also enable ultimately energy-efficient unconventional stochastic computing.

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.

Stabilization and racetrack application of asymmetric Néel skyrmions in hybrid nanostructures

Magnetic skyrmions, topological quasiparticles, are small stable magnetic textures that possess intriguing properties and potential for data storage applications. Hybrid nanostructures comprised of skyrmions and soft magnetic material can offer additional advantages for developing skyrmion-based spintronic and magnonic devices. We show that a Néel-type skyrmion confined within a nanodot placed on top of a ferromagnetic in-plane magnetized stripe produces a unique and compelling platform for exploring the mutual coupling between magnetization textures. The skyrmion induces an imprint upon the stripe, which, in turn, asymmetrically squeezes the skyrmion in the dot, increasing their size and the range of skyrmion stability at small values of Dzyaloshinskii-Moriya interaction, as well as introducing skyrmion bi-stability. Finally, by exploiting the properties of the skyrmion in a hybrid system, we demonstrate unlimited skyrmion transport along a racetrack, free of the skyrmion Hall effect.

Instability of Magnetic Skyrmion Strings Induced by Longitudinal Spin Currents

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices, suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a nonequilibrium phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning.

Encoding and Multiplexing Information Signals in Magnetic Multilayers with Fractional Skyrmion Tubes

Tailored magnetic multilayers (MMLs) provide skyrmions with enhanced thermal stability, leading to the possibility of skyrmion-based devices for room-temperature applications. At the same time, the search for additional stable topological spin textures has been under intense research focus. Besides their fundamental importance, such textures may expand the information encoding capability of spintronic devices. However, fractional spin texture states within MMLs in the vertical dimension are yet to be investigated. In this work, we demonstrate numerically fractional skyrmion tubes (FSTs) in a tailored MML system. We subsequently propose to encode sequences of information signals with FSTs as information bits in a tailored MML device. Micromagnetic simulations and theoretical calculations are used to verify the feasibility of hosting distinct FST states within a single device, and their thermal stability is investigated. A multilayer multiplexing device is proposed, where multiple sequences of the information signals can be encoded and transmitted based on the nucleation and propagation of packets of FSTs. Finally, pipelined information transmission and automatic demultiplexing are demonstrated by exploiting the skyrmion Hall effect and introducing voltage-controlled synchronizers and width-based track selectors. The findings indicate that FSTs can be potential candidates as information carriers for future spintronic applications.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

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.

Systematic Control of Ferrimagnetic Skyrmions via Composition Modulation in Pt/Fe1-xTbx/Ta Multilayers

Magnetic skyrmions are topological spin textures that can be used as memory and logic components for advancing the next generation spintronics. In this regard, control of nanoscale skyrmions, including their sizes and densities, is of particular importance for enhancing the storage capacity of skyrmionic devices. Here, we propose a viable route for engineering ferrimagnetic skyrmions via tuning the magnetic properties of the involved ferrimagnets Fe_1-xTb_x. Via tuning the composition of Fe_1-xTb_x that alters the magnetic anisotropy and the saturation magnetization, the size of the ferrimagnetic skyrmion (d_s) and the average density (η_s) can be effectively tailored in [Pt/Fe_1-xTb_x/Ta]₁₀ multilayers. In particular, a stabilization of sub-50 nm skyrmions with a high density is demonstrated at room temperature. Our work provides an effective approach for designing ferrimagnetic skyrmions with the desired size and density, which could be useful for enabling high-density ferrimagnetic skyrmionics.

Universal Quantum Computation Based on Nanoscale Skyrmion Helicity Qubits in Frustrated Magnets

We propose a skyrmion-based universal quantum computer. Skyrmions have the helicity degree of freedom in frustrated magnets, where twofold degenerated Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction. We construct a qubit based on them. A skyrmion must become a quantum-mechanical object when its size is of the order of nanometers. It is shown that the universal quantum computation is possible based on nanoscale skyrmions in a magnetic bilayer system. The one-qubit quantum gates are materialized by controlling the electric field and the spin current. The two-qubit gate is materialized with the use of the Ising-type exchange coupling. The merit of the present mechanism is that external magnetic field is not necessary. Our results may open a possible way toward universal quantum computation based on nanoscale topological spin textures.

Small-angle neutron scattering of long-wavelength magnetic modulations in reduced sample dimensions

Magnetic small-angle neutron scattering (SANS) is ideally suited to providing direct reciprocal-space information on long-wavelength magnetic modulations, such as helicoids, solitons, merons or skyrmions. SANS of such structures in thin films or micro-structured bulk materials is strongly limited by the tiny scattering volume vis a vis the prohibitively high background scattering by the substrate and support structures. Considering near-surface scattering just above the critical angle of reflection, where unwanted signal contributions due to substrate or support structures become very small, it is established that the scattering patterns of the helical, conical, skyrmion lattice and fluctuation-disordered phases in a polished bulk sample of MnSi are equivalent for conventional transmission and near-surface SANS geometries. This motivates the prediction of a complete repository of scattering patterns expected for thin films in the near-surface SANS geometry for each orientation of the magnetic order with respect to the scattering plane.

Room-Temperature Magnetic Skyrmions and Large Topological Hall Effect in Chromium Telluride Engineered by Self-Intercalation

Room-temperature magnetic skyrmion materials exhibiting robust topological Hall effect (THE) are crucial for novel nano-spintronic devices. However, such skyrmion-hosting materials are rare in nature. In this study, a self-intercalated transition metal dichalcogenide Cr_{1+ x} Te₂ with a layered crystal structure that hosts room-temperature skyrmions and exhibits large THE is reported. By tuning the self-intercalate concentration, a monotonic control of Curie temperature from 169 to 333 K and a magnetic anisotropy transition from out-of-plane to the in-plane configuration are achieved. Based on the intercalation engineering, room-temperature skyrmions are successfully created in Cr_1.53 Te₂ with a Curie temperature of 295 K and a relatively weak perpendicular magnetic anisotropy. Remarkably, a skyrmion-induced topological Hall resistivity as large as ≈106 nΩ cm is observed at 290 K. Moreover, a sign reversal of THE is also found at low temperatures, which can be ascribed to other topological spin textures having an opposite topological charge to that of the skyrmions. Therefore, chromium telluride can be a new paradigm of the skyrmion material family with promising prospects for future device applications.

Disorder-Induced Topological State Transition in the Optical Skyrmion Family

Skyrmions endowed with topological protection have been extensively investigated in various platforms including magnetics, ferroelectrics, and liquid crystals, stimulating applications such as memories, logic devices, and neuromorphic computing. While the optical counterpart has been proposed and realized recently, the study of optical skyrmions is still in its infancy. Among the unexplored questions, the investigation of the topology induced robustness against disorder is of substantial importance on both fundamental and practical sides but remains elusive. In this Letter, we manage to generate optical skyrmions numerically in real space with different topological features at will, providing a unique platform to investigate the robustness of various optical skyrmions. A disorder-induced topological state transition is observed for the first time in a family of optical skyrmions composed of six classes with different skyrmion numbers. Intriguingly, the optical skyrmions produced from a vectorial hologram are exceptionally robust against scattering from a random medium, shedding light on topological photonic devices for the generation and manipulation of robust states for applications including imaging and communication.

Single Skyrmion Generation via a Vertical Nanocontact in a 2D Magnet-Based Heterostructure

Skyrmions have been well studied in chiral magnets and magnetic thin films due to their potential application in practical devices. Recently, monochiral skyrmions have been observed in two-dimensional van der Waals magnets. Their atomically flat surfaces and capability to be stacked into heterostructures offer new prospects for skyrmion applications. However, the controlled local nucleation of skyrmions within these materials has yet to be realized. Here, we utilize real-space X-ray microscopy to investigate a heterostructure composed of the 2D ferromagnet Fe₃GeTe₂ (FGT), an insulating hexagonal boron nitride layer, and a graphite top electrode. Upon a stepwise increase of the voltage applied between the graphite and FGT, a vertically conducting pathway can be formed. This nanocontact allows the tunable creation of individual skyrmions via single nanosecond pulses of low current density. Furthermore, time-resolved magnetic imaging highlights the stability of the nanocontact, while our micromagnetic simulations reproduce the observed skyrmion nucleation process.

Experimental Realization of a Skyrmion Circulator

Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.

Skyrmion-skyrmion interaction induced by itinerant electrons in a ferromagnetic strip

Magnetic skyrmions are promising spin textures for building next-generation magnetic memories and spintronic devices. Nevertheless, one of the major challenges in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures in different geometries. Here we numerically study the skyrmion-skyrmion interaction potential that arises due to the dynamics of itinerant electrons coupled to the magnetic texture in a ferromagnetic background with racetrack geometry. We consider different topological textures (ferromagnetic (FM) and antiferromagnetic (AFM)), namely: skyrmions, antiskyrmions and biskyrmions. We show that at low electron filling, for sufficiently short separation, the skyrmions strongly couple each other yielding a bound-state bound by electronic dynamics. However, when the filling is increased, the interaction potential energy presents local minima at specific values of the skyrmion-skyrmion distance. Each of these local minima corresponds to energetically stable positions of skyrmions which are 'protected' by well-defined energy barriers. By inspecting the local charge density, we find that in the case of AFM skyrmions, the local antiferromagnetic nature prevents electronic penetration into the core, allowing the AFM skyrmions to be seen as infinite potential barriers for electrons.

Structural Chirality of Polar Skyrmions Probed by Resonant Elastic X-Ray Scattering

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Emergence of zero-field non-synthetic single and interchained antiferromagnetic skyrmions in thin films

Antiferromagnetic (AFM) skyrmions are envisioned as ideal localized topological magnetic bits in future information technologies. In contrast to ferromagnetic (FM) skyrmions, they are immune to the skyrmion Hall effect, might offer potential terahertz dynamics while being insensitive to external magnetic fields and dipolar interactions. Although observed in synthetic AFM structures and as complex meronic textures in intrinsic AFM bulk materials, their realization in non-synthetic AFM films, of crucial importance in racetrack concepts, has been elusive. Here, we unveil their presence in a row-wise AFM Cr film deposited on PdFe bilayer grown on fcc Ir(111) surface. Using first principles, we demonstrate the emergence of single and strikingly interpenetrating chains of AFM skyrmions, which can co-exist with the rich inhomogeneous exchange field, including that of FM skyrmions, hosted by PdFe. Besides the identification of an ideal platform of materials for intrinsic AFM skyrmions, we anticipate the uncovered knotted solitons to be promising building blocks in AFM spintronics.

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.

Distinguishing the Two-Component Anomalous Hall Effect from the Topological Hall Effect

In transport, the topological Hall effect (THE) presents itself as nonmonotonic features (or humps and dips) in the Hall signal and is widely interpreted as a sign of chiral spin textures, like magnetic skyrmions. However, when the anomalous Hall effect (AHE) is also present, the coexistence of two AHEs could give rise to similar artifacts, making it difficult to distinguish between genuine THE with AHE and two-component AHE. Here, we confirm genuine THE with AHE by means of transport and magneto-optical Kerr effect (MOKE) microscopy, in which magnetic skyrmions are directly observed, and find that genuine THE occurs in the transition region of the AHE. In sharp contrast, the artifact "THE" or two-component AHE occurs well beyond the saturation of the "AHE component" (under the false assumption of THE + AHE). Furthermore, we distinguish artifact "THE" from genuine THE by three methods: (1) minor loops, (2) temperature dependence, and (3) gate dependence. Minor loops of genuine THE with AHE are always within the full loop, while minor loops of the artifact "THE" may reveal a single loop that cannot fit into the "AHE component". In addition, the temperature or gate dependence of the artifact "THE" may also be accompanied by a polarity change of the "AHE component", as the nonmonotonic features vanish, while the temperature dependence of genuine THE with AHE reveals no such change. Our work may help future researchers to exercise caution and use these methods for careful examination in order to ascertain the genuine THE.

Magnetic-Field-Assisted Diffusion Motion of Magnetic Skyrmions

Studies of the diffusion dynamics of magnetic skyrmions have generated widespread interest in both fundamental physics and spintronics applications. Here we report the magnetic-field-assisted diffusion motion of skyrmions in a microstructured chiral FeGe magnet. We demonstrate the enhancement of diffusion motion of magnetic skyrmions that is manipulated and driven by an oscillatory magnetic field. Further, the directed diffusion of skyrmions is observed when an in-plane field was introduced to break the symmetry of the system. Finally, we demonstrate the application of a magnetic field can induce an arrangements transition of skyrmions assemble in microstructure, that is, from a stiff hexagonal lattice to a weak interactional isotropic state. By using a step-ascended magnetic field we finished the observation of a particle-like diffusive motion for magnetic skyrmions that transport from high-concentration regions to low-concentration regions and the diffusion flux is proportional to the concentration gradient followed Fick's law.

Magnetic Skyrmions with Unconventional Helicity Polarization in a Van Der Waals Ferromagnet

Skyrmion helicity, which defines the spin swirling direction, is a fundamental parameter that may be utilized to encode data bits in future memory devices. Generally, in centrosymmetric ferromagnets, dipole skyrmions with helicity of -π/2 and π/2 are degenerate in energy, leading to equal populations of both helicities. On the other hand, in chiral materials where the Dzyaloshinskii-Moriya interaction (DMI) prevails and the dipolar interaction is negligible, only a preferred helicity is selected by the type of DMI. However, whether there is a rigid boundary between these two regimes remains an open question. Herein, the observation of dipole skyrmions with unconventional helicity polarization in a van der Waals ferromagnet, Fe_{5- δ} GeTe₂ , is reported. Combining magnetometry, Lorentz transmission electron microscopy, electrical transport measurements, and micromagnetic simulations, the short-range superstructures in Fe_{5- δ} GeTe₂ resulting in a localized DMI contribution, which breaks the degeneracy of the opposite helicities and leads to the helicity polarization, is demonstrated. Therefore, the helicity feature in Fe_{5- δ} GeTe₂ is controlled by both the dipolar interaction and DMI that the former leads to Bloch-type skyrmions with helicity of ±π/2 whereas the latter breaks the helicity degeneracy. This work provides new insights into the skyrmion topology in van der Waals materials.

Gate-controlled skyrmion and domain wall chirality

Magnetic skyrmions are localized chiral spin textures, which offer great promise to store and process information at the nanoscale. In the presence of asymmetric exchange interactions, their chirality, which governs their dynamics, is generally considered as an intrinsic parameter set during the sample deposition. In this work, we experimentally demonstrate that a gate voltage can control this key parameter. We probe the chirality of skyrmions and chiral domain walls by observing the direction of their current-induced motion and show that a gate voltage can reverse it. This local and dynamical reversal of the chirality is due to a sign inversion of the interfacial Dzyaloshinskii-Moriya interaction that we attribute to ionic migration of oxygen under gate voltage. Micromagnetic simulations show that the chirality reversal is a continuous transformation, in which the skyrmion is conserved. This control of chirality with 2-3 V gate voltage can be used for skyrmion-based logic devices, yielding new functionalities.

A micromagnetic theory of skyrmion lifetime in ultrathin ferromagnetic films

We use the continuum micromagnetic framework to derive the formulas for compact skyrmion lifetime due to thermal noise in ultrathin ferromagnetic films with relatively weak interfacial Dzyaloshinskii-Moriya interaction. In the absence of a saddle point connecting the skyrmion solution to the ferromagnetic state, we interpret the skyrmion collapse event as "capture by an absorber" at microscale. This yields an explicit Arrhenius collapse rate with both the barrier height and the prefactor as functions of all the material parameters, as well as the dynamical paths to collapse.

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.

Skyrmion pinning energetics in thin film systems

A key issue for skyrmion dynamics and devices are pinning effects present in real systems. While posing a challenge for the realization of conventional skyrmionics devices, exploiting pinning effects can enable non-conventional computing approaches if the details of the pinning in real samples are quantified and understood. We demonstrate that using thermal skyrmion dynamics, we can characterize the pinning of a sample and we ascertain the spatially resolved energy landscape. To understand the mechanism of the pinning, we probe the strong skyrmion size and shape dependence of the pinning. Magnetic microscopy imaging demonstrates that in contrast to findings in previous investigations, for large skyrmions the pinning originates at the skyrmion boundary and not at its core. The boundary pinning is strongly influenced by the very complex pinning energy landscape that goes beyond the conventional effective rigid quasi-particle description. This gives rise to complex skyrmion shape distortions and allows for dynamic switching of pinning sites and flexible tuning of the pinning.

Skyrmions, topological spin textures, can be pinned by defects present in the material that hosts them, influencing their motion. Here, Gruber et al show that the skyrmions are pinned at their boundary where the finite size of the skyrmions governs their pinning, and they demonstrate that certain pinning sites can switched on and off in-situ.

Deterministic Generation and Guided Motion of Magnetic Skyrmions by Focused He+-Ion Irradiation

Magnetic skyrmions are quasiparticles with nontrivial topology, envisioned to play a key role in next-generation data technology while simultaneously attracting fundamental research interest due to their emerging topological charge. In chiral magnetic multilayers, current-generated spin-orbit torques or ultrafast laser excitation can be used to nucleate isolated skyrmions on a picosecond time scale. Both methods, however, produce randomly arranged skyrmions, which inherently limits the precision on the location at which the skyrmions are nucleated. Here, we show that nanopatterning of the anisotropy landscape with a He⁺-ion beam creates well-defined skyrmion nucleation sites, thereby transforming the skyrmion localization into a deterministic process. This approach allows control of individual skyrmion nucleation as well as guided skyrmion motion with nanometer-scale precision, which is pivotal for both future fundamental studies of skyrmion dynamics and applications.

Interplay between quantum anomalous Hall effect and magnetic skyrmions

Quantum anomalous Hall effect (QAHE) and magnetic skyrmion (SK), as two typical topological states in momentum (K) and real (R) spaces, attract much interest in condensed matter physics. However, the interplay between these two states remains to be explored. We propose that the interplay between QAHE and SK may generate an RK joint topological skyrmion (RK-SK), characterized by the SK surrounded by nontrivial chiral boundary states (CBSs). Furthermore, the emerging external field–tunable CBS in RK-SK could create additional degrees of freedom for SK manipulations, beyond the traditional SK. Meanwhile, external field can realize a rare topological phase transition between K and R spaces. Our work opens avenues for exploring unconventional quantum states and topological phase transitions in different spaces.

Quantum anomalous Hall effect (QAHE) and magnetic skyrmion (SK) represent two typical topological states in momentum (K) and real (R) spaces, respectively. However, little is known about the interplay between these two states. Here, we propose that the coexistence of QAHE and SK may generate a previously unknown SK state, named the RK joint topological skyrmion (RK-SK), which is characterized by the SK surrounded by nontrivial chiral boundary states (CBSs). Interestingly, beyond the traditional SK state that can solely be used via creation or annihilation, the number and chirality of CBS in RK-SK can be tunable under external fields as demonstrated in Janus monolayer (ML) MnBi₂X₂Te₂ (X= S, Se), creating additional degrees of freedom for SK-state manipulations. Moreover, it is also found that external fields can induce a continuous topology phase transition from K-space QAHE to R-space SK in ML MnBi₂X₂Te₂, providing an ideal platform to understand the cross-over phenomena of multiple-space topologies.

Topological Hall effect in SrRuO3thin films and heterostructures

Transition metal oxides hold a wide spectrum of fascinating properties endowed by the strong electron correlations. In 4dand 5doxides, exotic phases can be realized with the involvement of strong spin-orbit coupling (SOC), such as unconventional magnetism and topological superconductivity. Recently, topological Hall effects (THEs) and magnetic skyrmions have been uncovered in SrRuO₃thin films and heterostructures, where the presence of SOC and inversion symmetry breaking at the interface are believed to play a key role. Realization of magnetic skyrmions in oxides not only offers a platform to study topological physics with correlated electrons, but also opens up new possibilities for magnetic oxides using in the low-power spintronic devices. In this review, we discuss recent observations of THE and skyrmions in the SRO film interfaced with various materials, with a focus on the electric tuning of THE. We conclude with a discussion on the directions of future research in this field.

Observation of Magnetic Helicoidal Dichroism with Extreme Ultraviolet Light Vortices

We report on the experimental evidence of magnetic helicoidal dichroism, observed in the interaction of an extreme ultraviolet vortex beam carrying orbital angular momentum with a magnetic vortex. Numerical simulations based on classical electromagnetic theory show that this dichroism is based on the interference of light modes with different orbital angular momenta, which are populated after the interaction between light and the magnetic topology. This observation gives insight into the interplay between orbital angular momentum and magnetism and sets the framework for the development of new analytical tools to investigate ultrafast magnetization dynamics.

Realizing Quantum Technologies in Nanomaterials and Nanoscience

A brief overview of quantum materials and their prospects for applications, in the near, mid, and far-term in the areas of quantum information science, spintronics, valleytronics, and twistronics and those involving topology are covered in this perspective. The material and processing challenges that will modulate the realism of the applications will be discussed as well.

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.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Electrical Generation and Deletion of Magnetic Skyrmion-Bubbles via Vertical Current Injection

The magnetic skyrmion is a topologically protected spin texture that has attracted much attention as a promising information carrier because of its distinct features of suitability for high-density storage, low power consumption, and stability. One of the skyrmion devices proposed so far is the skyrmion racetrack memory, which is the skyrmion version of the domain-wall racetrack memory. For application in devices, skyrmion racetrack memory requires electrical generation, deletion, and displacement of isolated skyrmions. Despite the progress in experimental demonstrations of skyrmion generation, deletion, and displacement, these three operations have yet to be realized in one device. Here, a route for generating and deleting isolated skyrmion-bubbles through vertical current injection with an explanation of its microscopic origin is presented. By combining the proposed skyrmion-bubble generation/deletion method with the spin-orbit-torque-driven skyrmion shift, a proof-of-concept experimental demonstration of the skyrmion racetrack memory operation in a three-terminal device structure is provided.

Spin and Orbital Effects on Asymmetric Exchange Interaction in Polar Magnets: M(IO3)2 (M = Cu and Mn)

Magnetic polar materials feature an astonishing range of physical properties, such as magnetoelectric coupling, chiral spin textures, and related new spin topology physics. This is primarily attributable to their lack of space inversion symmetry in conjunction with unpaired electrons, potentially facilitating an asymmetric Dzyaloshinskii-Moriya (DM) exchange interaction supported by spin-orbital and electron-lattice coupling. However, engineering the appropriate ensemble of coupled degrees of freedom necessary for enhanced DM exchange has remained elusive for polar magnets. Here, we study how spin and orbital components influence the capability of promoting the magnetic interaction by studying two magnetic polar materials, α-Cu(IO₃)₂ (²D) and Mn(IO₃)₂ (⁶S), and connecting their electronic and magnetic properties with their structures. The chemically controlled low-temperature synthesis of these complexes resulted in pure polycrystalline samples, providing a viable pathway to prepare bulk forms of transition-metal iodates. Rietveld refinements of the powder synchrotron X-ray diffraction data reveal that these materials exhibit different crystal structures but crystallize in the same polar and chiral P2₁ space group, giving rise to an electric polarization along the b-axis direction. The presence and absence of an evident phase transition to a possible topologically distinct state observed in α-Cu(IO₃)₂ and Mn(IO₃)₂, respectively, imply the important role of spin-orbit coupling. Neutron diffraction experiments reveal helpful insights into the magnetic ground state of these materials. While the long-wavelength incommensurability of α-Cu(IO₃)₂ is in harmony with sizable asymmetric DM interaction and low dimensionality of the electronic structure, the commensurate stripe AFM ground state of Mn(IO₃)₂ is attributed to negligible DM exchange and isotropic orbital overlapping. The work demonstrates connections between combined spin and orbital effects, magnetic coupling dimensionality, and DM exchange, providing a worthwhile approach for tuning asymmetric interaction, which promotes evolution of topologically distinct spin phases.

Robust skyrmion mediated reversal of ferromagnetic nanodots of 20 nm lateral dimension with high Ms and observable DMI

Implementation of skyrmion based energy efficient and high-density data storage devices requires aggressive scaling of skyrmion size. Ferrimagnetic materials are considered to be a suitable platform for this purpose due to their low saturation magnetization (i.e. smaller stray field). However, this method of lowering the saturation magnetization and scaling the lateral size of skyrmions is only applicable where the skyrmions have a smaller lateral dimension compared to the hosting film. Here, we show by performing rigorous micromagnetic simulation that the size of skyrmions, which have lateral dimension comparable to their hosting nanodot can be scaled by increasing saturation magnetization. Also, when the lateral dimension of nanodot is reduced and thereby the skyrmion confined in it is downscaled, there remains a challenge in forming a stable skyrmion with experimentally observed Dzyaloshinskii–Moriya interaction (DMI) values since this interaction has to facilitate higher canting  per spin to complete a 360° rotation along the diameter. In our study, we found that skyrmions can be formed in 20 nm lateral dimension nanodots with high saturation magnetization (1.30–1.70 MA/m) and DMI values (~ 3 mJ/m²) that have been reported to date. This result could stimulate experiments on implementation of highly dense skyrmion devices. Additionally, using this, we show that voltage controlled magnetic anisotropy based switching mediated by an intermediate skyrmion state can be achieved in the soft layer of a ferromagnetic p-MTJ of lateral dimensions 20 nm with sub 1 fJ/bit energy in the presence of room temperature thermal noise with reasonable DMI ~ 3 mJ/m².

Isolated skyrmion, skyrmion lattice and antiskyrmion lattice creation through magnetization reversal in Co/Pd nanostructure

Skyrmion and antiskyrmion spin textures are axisymmetric inhomogeneous localized objects with distinct chirality in magnetic systems. These spin textures are potential candidates for the next generation energy-efficient spintronic applications due to their unique topological properties. Controlled and effective creation of the spin textures is required to use in conventional and neuromorphic computing applications. Here we show by micromagnetic simulations creating an isolated skyrmion, skyrmion lattice and antiskyrmion lattice through the magnetization reversal in Co/Pd multilayer nanostructure using spin-polarized current. The spin textures' stability depends on the spin-polarized current density, current pulse width, and Dzyaloshinskii-Moriya interaction (DMI). Antiskyrmions are evolved during the formation of a single skyrmion and skyrmion lattice. Skyrmion and antiskyrmion lattices together are observed for lower pulse width, 0.05 ns. Our micromagnetic studies suggest that the two distinct lattice phases' evolution could help to design the topological spin textures-based devices.