Direct Observation of Room-Temperature Magnetic Skyrmion Motion Driven by Ultra-Low Current Density in Van Der Waals Ferromagnets

The recent discovery of room-temperature ferromagnetism in 2D van der Waals (vdW) materials, such as Fe3 GaTe2 (FGaT), has garnered significant interest in offering a robust platform for 2D spintronic applications. Various fundamental operations essential for the realization of 2D spintronics devices are experimentally confirmed using these materials at room temperature, such as current-induced magnetization switching or tunneling magnetoresistance. Nevertheless, the potential applications of magnetic skyrmions in FGaT systems at room temperature remain unexplored. In this work, the current-induced generation of magnetic skyrmions in FGaT flakes employing high-resolution magnetic transmission soft X-ray microscopy is introduced, supported by a feasible mechanism based on thermal effects. Furthermore, direct observation of the current-induced magnetic skyrmion motion at room temperature in FGaT flakes is presented with ultra-low threshold current density. This work highlights the potential of FGaT as a foundation for room-temperature-operating 2D skyrmion device applications.

Skyrmion motion under temperature gradient and application in logic devices

Under the presence of temperature gradient (TG) on a nanotrack, it is necessary to investigate the skyrmion dynamics in various magnetic systems under the combined effect of forces due to magnonic spin transfer torque(μSTT),thermal STT (τSTT), entropic difference(dS),as well as thermal induced dipolar field (DF). Hence, in this work, the dynamics of skyrmions in ferromagnets (FM), synthetic antiferromagnets (SAF), and antiferromagnets (AFM) have been studied under different TGs and damping constants (αG). It is observed thatαGplays a major role in deciding the direction of skyrmion motion either towards the hotter or colder side in different magnetic structures. Later, FM skyrmion based logic device is proposed that consists of a cross-coupled nanotrack, where the skyrmions on horizontal and vertical nanotrack are controlled by exploiting TG and electrical STT (eSTT), respectively by taking the advantages of thermal induced skyrmion Hall effect (SkHE). The proposed device performs AND and OR logic functionalities simultaneously, when the applied current density is2×1011Am-2.Moreover, the proposed device is also able to exhibit the half adder functionality by tuning the applied current density to3×1011Am-2.The total energy consumption for AND and OR logic operation and half adder are 33.63 fJ and 25.06 fJ, respectively. This paves the way for the development of energy-efficient logic devices with ultra-high storage density.

Nontraditional Movement Behavior of Skyrmion in a Circular-Ring Nanotrack

Magnetic skyrmions are considered promising candidates for use as information carriers in future spintronic devices. To achieve the development of skyrmion-based spintronic devices, a reasonable and feasible nanotrack is essential. In this paper, we conducted a study on the current-driven skyrmion movement in a circular-ring-shaped nanotrack. Our results suggest that the asymmetry of the inside and outside boundary of the circular ring changed the stable position of the skyrmion, causing it to move like the skyrmion Hall effect when driven by currents. Moreover, the asymmetric boundaries have advantages in enhancing or weakening the skyrmion Hall effect. Additionally, we also compared the skyrmion Hall effect from the asymmetric boundary of circular-ring nanotracks with that from the inhomogeneous Dzyaloshinskii-Moriya interaction. It was found that the skyrmion Hall effect in the circular ring is significantly greater than that caused by the inhomogeneous Dzyaloshinskii-Moriya interaction. These results contribute to our understanding of the skyrmion dynamics in confined geometries and offer an alternative method for controlling the skyrmion Hall effect of skyrmion-based devices.

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.

A magnetic skyrmion diode based on potential well inducting effect

Magnetic skyrmions have great potential in the application of spintronic devices due to their stable topologically protected spin configuration. To meet the needs of spintronic device design, it is necessary to manipulate the movement of the magnetic skyrmions. Here we propose a skyrmion diode based on potential well induced skyrmion motion through theoretical calculations. The potential well is generated by the voltage-controlled magnetic anisotropy (VCMA) gradient. By utilizing the induction of the potential well as well as the skyrmion Hall effect (SkHE), the velocity and trajectory of the skyrmions can be controlled and the forward pass and reverse cutoff functions of diode-like devices have been realized. Furthermore, we report the dynamics of current-driven skyrmions in a racetrack with locally applied VCMA. Under the influence of the SkHE, the difference in dynamic behavior between forward and reverse motion of the skyrmions is obvious, and the potential well can produce different pinning, depinning and annihilating effects on forward and reverse moving skyrmions. O ur results can be beneficial for the design and development of magnetic skyrmion diodes.&#xD.

Topological skyrmion phases of matter

We introduce topological phases of matter defined by skyrmions in the ground state spin---or pseudospin---expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are protected by a symmetry present in centrosymmetric superconductors. We consider a tight-binding model for spin-triplet superconductivity in transition metal oxides and find it realizes each of these topological skyrmion phases. The chiral phase is furthermore realized for a parameter set characterizing Sr2RuO4 with spin-triplet superconductivity. We also find two types of topological phase transitions by which the skyrmion number can change. The second type occurs without the closing of energy gaps in a system described by a quadratic Hamiltonian without breaking the protecting symmetries when atomic spin-orbit coupling is non-negligible and there is a suitable additional degree of freedom. This contradicts the ``flat band'' limit assumption important in use of entanglement spectrum and Wilson loops, and in construction of the ten-fold way classification scheme of topological phases of matter. We furthermore predict two kinds of bulk-boundary correspondence signatures---one for measurements which execute a partial trace over degrees of freedom other than spin, which yields quantized transport signatures---and a second resulting from skyrmions trapping defects with their own non-trivial topology that is discussed in a second work, which yields generalizations of unpaired Majorana zero-modes.

Mechanism of Skyrmion Attraction in Chiral Magnets near the Ordering Temperatures

Isolated chiral skyrmions are investigated within the phenomenological Dzyaloshinskii model near the ordering temperatures of quasi-two-dimensional chiral magnets with Cnv symmetry and three-dimensional cubic helimagnets. In the former case, isolated skyrmions (IS) perfectly blend into the homogeneously magnetized state. The interaction between these particle-like states, being repulsive in a broad low-temperature (LT) range, is found to switch into attraction at high temperatures (HT). This leads to a remarkable confinement effect: near the ordering temperature, skyrmions exist only as bound states. This is a consequence of the coupling between the magnitude and the angular part of the order parameter, which becomes pronounced at HT. The nascent conical state in bulk cubic helimagnets, on the contrary, is shown to shape skyrmion internal structure and to substantiate the attraction between them. Although the attracting skyrmion interaction in this case is explained by the reduction of the total pair energy due to the overlap of skyrmion shells, which are circular domain boundaries with the positive energy density formed with respect to the surrounding host phase, additional magnetization "ripples" at the skyrmion outskirt may lead to attraction also at larger length scales. The present work provides fundamental insights into the mechanism for complex mesophase formation near the ordering temperatures and constitutes a first step to explain the phenomenon of multifarious precursor effects in that temperature region.

Influence of magnetic structure on the performance of twisted skyrmion-based nano-oscillator

The spin torque nano-oscillator (STNO), a nanosize microwave signal generator, have caught the attention of a number of researchers due to its obvious advantages. Recently a chiral bulk material with twisted skyrmion has been discovered in studies with different helicity degrees. In this work, we design a new STNO based on twisted skyrmion existing in free layers of magnetic tunnel junction structure. We first investigate the effect of the magnetic moment of fixed layer on the twisted skyrmion and frequency of STNO. Although the magnetic moment of fixed layer does not affect the state of the twisted skyrmion but affects the precession frequency of STNO. Later, the current, external magnetic field and Dzyaloshinskii-Moriya interaction strength are changed to regulate the oscillation frequency of STNO. Our result may be favorable for the design of new twisted skyrmion-based STNO.

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.

Gradient-Induced Dzyaloshinskii-Moriya Interaction

The Dzyaloshinskii-Moriya interaction (DMI) that arises in the magnetic systems with broken inversion symmetry plays an essential role in topological spintronics. Here, by means of atomistic spin calculations, we study an intriguing type of DMI (g-DMI) that emerges in the films with composition gradient. We show that both the strength and chirality of g-DMI can be controlled by the composition gradient even in the disordered system. The layer-resolved analysis of g-DMI unveils its additive nature inside the bulk layers and clarifies the linear thickness dependence of g-DMI observed in experiments. Furthermore, we demonstrate the g-DMI-induced chiral magnetic structures, such as spin spirals and skyrmions, and the g-DMI driven field-free spin-orbit torque (SOT) switching, both of which are crucial toward practical device application. These results elucidate the underlying mechanisms of g-DMI and open up a new way to engineer the topological magnetic textures.

Topological electrostatics

We present a theory of optimal topological textures in nonlinear sigma-models with degrees of freedom living in the GrassmannianGr(M,N)manifold. These textures describe skyrmion lattices ofN-component fermions in a quantising magnetic field, relevant to the physics of graphene, bilayer and other multicomponent quantum Hall systems near integer filling factorsν > 1. We derive analytically the optimality condition, minimizing topological charge density fluctuations, for a general Grassmannian sigma modelGr(M,N)on a sphere and a torus, together with counting arguments which show that for any filling factor and number of components there is a critical value of topological chargedcabove which there are no optimal textures. Belowdca solution of the optimality condition on a torus is unique, while in the case of a sphere one has, in general, a continuum of solutions corresponding to new non-Goldstone zero modes, whose degeneracy is not lifted (via a order from disorder mechanism) by any fermion interactions depending only on the distance on a sphere. We supplement our general theoretical considerations with the exact analytical results for the case ofGr(2,4), appropriate for recent experiments in graphene.

Optimization strategies and artifacts of time-involved small-angle neutron scattering experiments

Kinetic small-angle neutron scattering provides access to the microscopic properties of mesoscale systems under slow, periodic perturbations. By interlocking the phases of neutron pulse, sample modulation and detector signal, time-involved small-angle neutron scattering experiments (TISANE) allow one to exploit the neutron velocity spread and record data without major sacrifice in intensity at timescales down to microseconds. This article reviews the optimization strategies of TISANE that arise from specific aspects of the process of data acquisition and data analysis starting from the basic principles of operation. Typical artifacts of data recorded in TISANE due to the choice of time binning and neutron chopper pulse width are illustrated by virtue of the response of the skyrmion lattice in MnSi under periodic changes of the direction of the stabilizing magnetic field.

Current-Induced Magnetic Skyrmions with Controllable Polarities in the Helical Phase

We report the current-induced creation of magnetic skyrmions in a chiral magnet FeGe nanostructure by using in situ Lorentz transmission electron microscopy. We show that magnetic skyrmions with controllable polarity can be transferred from the helical ground state simply by controlling the direction of the current flow at zero magnetic fields. The force analysis and symmetry consideration, backed up by micromagnetic simulations, well explain the experimental results, where magnetic skyrmions are created because of the edge instability of the helical state in the presence of spin-transfer torque. The on-demand generation of skyrmions and control of their polarity by electric current without the need for a magnetic field will enable novel purely electric-controlled skyrmion devices.

Magnetic Field Magnitudes Needed for Skyrmion Generation in a General Perpendicularly Magnetized Film

Due to its topological protection, the magnetic skyrmion has been intensively studied for both fundamental aspects and spintronics applications. However, despite recent advancements in skyrmion research, the deterministic creation of isolated skyrmions in a generic perpendicularly magnetized film is still one of the most essential and challenging techniques. Here, we present a method to create magnetic skyrmions in typical perpendicular magnetic anisotropy (PMA) films by applying a magnetic field pulse and a method to determine the magnitude of the required external magnetic fields. Furthermore, to demonstrate the usefulness of this result for future skyrmion research, we also experimentally study the PMA dependence on the minimum size of skyrmions. Although field-driven skyrmion generation is unsuitable for device application, this result can provide an easier approach for obtaining isolated skyrmions, making skyrmion-based research more accessible.

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.

A skyrmion content-addressable cell for skyrmion magnetic memories

Content-addressable memories (CAMs) allow searching a pattern, processing in parallel all the data stored. Beyond-CMOS technologies can provide new opportunities to improve CAM memories implementations both at the device and architectural level. In this article, we propose a ternary content-addressable memory cell based on skyrmion technology. The proposed memory cell is based on skyrmion racetrack memory. The cell is able to signal if the bit contained in the cell in form of skyrmion corresponds to an electrical input, the target of the search operation. The proposed design, verified by means of micromagnetic simulations, has an area of 0.054μm²and can perform a search operation in 3.3 ns with an energy of 10.5 fJ. The operation performed is non-destructive and does not require conversion between the magnetic and the electronic domains. For this reason, the designed cell has the potential to be used as a basic block for non-volatile CAM memories. Here, we propose also a layout structure to implement a CAM memory employing the proposed cell. This structure allows to achieve memory density comparable to traditional racetrack memories and execute at the same time CAM operations.

Skyrmions-based logic gates in one single nanotrack completely reconstructed via chirality barrier

Logic gates based on magnetic elements are promising candidates for logic-in-memory applications with non-volatile data retention, near-zero leakage and scalability. In such spin-based logic devices, however, the multi-strip structure and fewer functions are obstacles to improving integration and reducing energy consumption. Here we propose a skyrmions-based single-nanotrack logic family including AND, OR, NOT, NAND, NOR, XOR and XNOR that can be implemented and reconstructed by building and switching the Dzyaloshinskii-Moriya interaction (DMI) chirality barrier on a racetrack memory. Besides the pinning effect of the DMI chirality barrier on skyrmions, the annihilation, fusion and shunting of two skyrmions with opposite chirality are also achieved and demonstrated via local reversal of the DMI, which are necessary for the design of an engineer programmable logic nanotrack, transistor and complementary racetrack memory.

Soft-Magnetic Skyrmions Induced by Surface-State Coupling in an Intrinsic Ferromagnetic Topological Insulator Sandwich Structure

A magnetic skyrmion induced on a ferromagnetic topological insulator (TI) is a real-space manifestation of the chiral spin texture in the momentum space and can be a carrier for information processing by manipulating it in tailored structures. Here, a sandwich structure containing two layers of a self-assembled ferromagnetic septuple-layer TI, Mn(Bi_1-xSb_x)₂Te₄ (MnBST), separated by quintuple layers of TI, (Bi_1-xSb_x)₂Te₃ (BST), is fabricated and skyrmions are observed through the topological Hall effect in an intrinsic magnetic topological insulator for the first time. The thickness of BST spacer layer is crucial in controlling the coupling between the gapped topological surface states in the two MnBST layers to stabilize the skyrmion formation. The homogeneous, highly ordered arrangement of the Mn atoms in the septuple-layer MnBST leads to a strong exchange interaction therein, which makes the skyrmions "soft magnetic". This would open an avenue toward a topologically robust rewritable magnetic memory.

Dynamics of flowing 2D skyrmions

We investigate, numerically, the effects of externally imposed material flows on the structure and temporal evolution of liquid crystal (LC) skyrmions. The dynamics of a 2D system of skyrmions is modeled using the Ericksen-Leslie theory, which is based on two coupled equations, one for material flow and the other for the director field. As the time scales of the velocity and director fields differ by several orders of magnitude for realistic values of the system parameters, we have simplified the calculations by assuming that the velocity relaxes instantaneously when compared to the relaxation of the director field. Thus, we have used a finite-differences method known as artificial compressibility with adaptive time step to solve the velocity field and a fourth-order Runge-Kutta method for the director field. We characterized the skyrmion shape or configuration as a function of the time and the average velocity of the flow field. We found that for velocities above a certain threshold, the skyrmions stretch in the direction perpendicular to the flow, by contrast to the regime of weak flows where the skyrmions stretch along the streamlines of the flow field. These two regimes are separated by an abrupt (first-order) dynamical transition, which is robust with respect to e.g., the LC elastic anisotropy. Additionally, we have found how the presence of a second skyrmion affects the evolution of the shape of the skyrmions, by comparing the evolution of pairs of skyrmions to the evolution of a single-skyrmion.

Defect-Induced Magnetic Skyrmion in a Two-Dimensional Chromium Triiodide Monolayer

Chromium iodide monolayers, which have different magnetic properties in comparison to the bulk chromium iodide, have been shown to form skyrmionic states in applied electromagnetic fields or in Janus-layer devices. In this work, we demonstrate that spin-canted solutions can be induced into monolayer chromium iodide by select substitution of iodide atoms with isovalent impurities. Several concentrations and spatial configurations of halide substitutional defects are selected to probe the coupling between the local defect-induced geometric distortions and orientation of chromium magnetic moments. This work provides atomic-level insight into how atomically precise chemical doping can be used to create and control complex magnetic patterns in chromium iodide layers and lays out the foundation for investigating the field- and geometric-dependent magnetic properties in similar two-dimensional materials.

Characterization of a Disordered above Room Temperature Skyrmion Material Co8Zn8Mn4

Topologically nontrivial spin textures host great promise for future spintronic applications. Skyrmions in particular are of burgeoning interest owing to their nanometric size, topological protection, and high mobility via ultra-low current densities. It has been previously reported through magnetic susceptibility, microscopy, and scattering techniques that Co8Zn8Mn4 forms an above room temperature triangular skyrmion lattice. Here, we report the synthesis procedure and characterization of a polycrystalline Co8Zn8Mn4 disordered bulk sample. We employ powder X-ray diffraction and backscatter Laue diffraction as characterization tools of the crystallinity of the samples, while magnetic susceptibility and Small Angle Neutron Scattering (SANS) measurements are performed to study the skyrmion phase. Magnetic susceptibility measurements show a dip anomaly in the magnetization curves, which persists over a range of approximately 305 K-315 K. SANS measurements reveal a rotationally disordered polydomain skyrmion lattice. Applying a symmetry-breaking magnetic field sequence, we were able to orient and order the previously jammed state to yield the prototypical hexagonal diffraction patterns with secondary diffraction rings. This emergence of the skyrmion order serves as a unique demonstration of the fundamental interplay of structural disorder and anisotropy in stabilizing the thermal equilibrium phase.

Two-dimensional characterization of three-dimensional magnetic bubbles in Fe3Sn2 nanostructures

We report differential phase contrast scanning transmission electron microscopy (TEM) of nanoscale magnetic objects in Kagome ferromagnet Fe3Sn2 nanostructures. This technique can directly detect the deflection angle of a focused electron beam, thus allowing clear identification of the real magnetic structures of two magnetic objects including three-ring and complex arch-shaped vortices in Fe3Sn2 by Lorentz-TEM imaging. Numerical calculations based on real material-specific parameters well reproduced the experimental results, showing that the magnetic objects can be attributed to integral magnetizations of two types of complex three-dimensional (3D) magnetic bubbles with depth-modulated spin twisting. Magnetic configurations obtained using the high-resolution TEM are generally considered as two-dimensional (2D) magnetic objects previously. Our results imply the importance of the integral magnetizations of underestimated 3D magnetic structures in 2D TEM magnetic characterizations.

Confinement and Protection of Skyrmions by Patterns of Modified Magnetic Properties

Magnetic skyrmions are versatile topological excitations that can be used as nonvolatile information carriers. The confinement of skyrmions in channels is fundamental for any application based on the accumulation and transport of skyrmions. Here, we report a method that allows effective position control of skyrmions in designed channels by engineered energy barriers and wells, which is realized in a magnetic multilayer film by harnessing the boundaries of patterns with modified magnetic properties. We experimentally and computationally demonstrate that skyrmions can be attracted or repelled by the boundaries of areas with modified perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. By fabricating square and stripe patterns with modified magnetic properties, we show the possibility of building reliable channels for confinement, accumulation, and transport of skyrmions, which effectively protect skyrmions from being destroyed at the device edges. Our results are useful for the design of spintronic applications using either static or dynamic skyrmions.

Asymmetry in the propagation of vortex domain wall artificial skyrmion composite system

We studied the propagation of an artificial skyrmion coupled to the vortex domain wall (VDW). We discovered the following effect: depending on the propagation's direction, the dynamics of the coupled skyrmion VDW can be faster than the isolated VDW's velocity. The reason for such behavior is the structural distortion that occurs in the coupled system. We interpret the numerical results in terms of the modified Thiele's equation. In particular, increasing the Thiele's equation counteractive coefficient leads to the perfect fitting with the micromagnetic simulation results.

Skyrmions near defects

We study the impact of an exchange-reducing defect on a skyrmion in a thin film of finite thickness. Attraction of the skyrmion to a defect is demonstrated in a lattice model by computing the micromagnetic energy accounting for the exchange, Dzyaloshinskii-Moriya interaction, magnetic anisotropy, and dipole-dipole coupling. The spiraling dynamics of the skyrmion toward the defect is illustrated by solving numerically the full Landau-Lifshitz-Gilbert equations on a lattice and, independently, by solving the Thiele equation, with the two methods in agreement with each other. Depinning of the skyrmion by the current is investigated. We find that the skyrmion deforms when it is close to the defect. Deformation is small in the parameter space far from the phase boundary that determines stability of skyrmions. It increases dramatically near the phase boundary, leading to the transformation of the skyrmion by the defect into a snake-like magnetic domain.

Skyrmion driven by rotary magnetic field on the surface of magnetic nanotube: a Monte Carlo study

We report a Monte-Carlo simulation of the formation of skyrmions under a rotary magnetic field on a nanotube. The zero-field magnetic state is characterized as helical stripe domains swirling on the nanotube, with one to three periods depending on the ratio of Dzyaloshinskii-Moriya to ferromagnetic interaction and tubular size. Under a rotary magnetic field, the formation of skyrmions is in pair and the skyrmion number can be tuned. The movement of skyrmions is neither synchronous along with the rotary field, nor along a helical trajectory perpendicular to the rotary field. It is ascribed to that within a skyrmion pair, on one hand, the coupling between skyrmions is nonnegligible; on the other hand, different skyrmion pairs side by side are decoupled. This work predicts a way of nanotube-based skyrmion manipulation, and might develop the rotary information storage on energy- and space-saving modes or an edgeless racetrack memory.

Antiferromagnetic skyrmion repulsion based artificial neuron device

Magnetic skyrmions are potential candidates for neuromorphic computing due to their inherent topologically stable particle-like behavior, low driving current density, and nanoscale size. Antiferromagnetic skyrmions are favored as they can be driven parallel to in-plane electrical currents as opposed to ferromagnetic skyrmions which exhibit the skyrmion Hall effect and eventually cause their annihilation at the edge of nanotracks. In this paper, an antiferromagnetic skyrmion based artificial neuron device consisting of a magnetic anisotropy barrier on a nanotrack is proposed. It exploits inter-skyrmion repulsion, mimicking the integrate-fire (IF) functionality of a biological neuron. The device threshold represented by the maximum number of skyrmions that can be pinned by the barrier can be tuned based on the particular current density employed on the nanotrack. The corresponding neuron spiking event occurs when a skyrmion overcomes the barrier. By raising the device threshold, lowering the barrier width and height, the operating current density of the device can be decreased to further enhance its energy efficiency. The proposed device paves the way for developing energy-efficient neuromorphic computing in antiferromagnetic spintronics.

Isotropic Nature of the Metallic Kagome Ferromagnet Fe3Sn2 at High Temperatures

Anisotropy and competing exchange interactions have emerged as two central ingredients needed for centrosymmetric materials to exhibit topological spin textures. Fe3Sn2 is thought to have these ingredients as well, as it has recently been discovered to host room temperature skyrmionic bubbles with an accompanying topological Hall effect. We present small-angle inelastic neutron scattering measurements that unambiguously show that Fe3Sn2 is an isotropic ferromagnet below T C ≈ 660     K to at least 480 K - the lower temperature threshold of our experimental configuration. Fe3Sn2 is known to have competing magnetic exchange interactions, correlated electron behavior, weak magnetocrystalline anisotropy, and lattice anisotropy; all of these features are thought to play a role in stabilizing skyrmions in centrosymmetric systems. Our results reveal that at elevated temperatures, there is an absence of magnetocrystalline anisotropy and that the system behaves as a typical exchange ferromagnet with a spin stiffness D T = 0   K = 271 ± 9   meV     Å 2 .

Magnetic Direct-Write Skyrmion Nanolithography

Magnetic skyrmions are stable spin textures with quasi-particle behavior and attract significant interest in fundamental and applied physics. The metastability of magnetic skyrmions at zero magnetic field is particularly important to enable, for instance, a skyrmion racetrack memory. Here, the results of the nucleation of stable skyrmions and formation of ordered skyrmion lattices by magnetic force microscopy in (Pt/CoFeSiB/W)_n multilayers, exploiting the additive effect of the interfacial Dzyaloshinskii-Moriya interaction, are presented. The appropriate conditions under which skyrmion lattices are confined with a dense two-dimensional liquid phase are identified. A crucial parameter to control the skyrmion lattice characteristics and the number of scans resulting in the complete formation of a skyrmion lattice is the distance between two adjacent scanning lines of a magnetic force microscopy probe. The creation of skyrmion patterns with complex geometry is demonstrated, and the physical mechanism of direct magnetic writing of skyrmions is comprehended by micromagnetic simulations. This study shows a potential of a direct-write (maskless) skyrmion (topological) nanolithography with sub-100 nm resolution, where each skyrmion acts as a pixel in the final topological image.

Detection of the Chiral Spin Structure in Ferromagnetic SrRuO3 Thin Film

SrRuO₃ (SRO) thin films and their heterostructure have attracted much attention because of the recently demonstrated fascinating properties, such as topological Hall effect and skyrmions. Critical to the understanding of those SRO properties is the study of the spin configuration. Here, we conduct resonant soft X-ray scattering (RSXS) at the oxygen K edge to investigate the spin configuration of a four-unit-cell SRO film that was grown epitaxially on a single-crystal SrTiO₃. The RSXS signal under a magnetic field (∼0.4 tesla) clearly shows a magnetic dichroism pattern around the specular reflection. Model calculations on the RSXS signal demonstrate that the magnetic dichroism pattern originates from a Néel-type chiral spin structure in this SRO thin film. We believe that the observed spin structure of the SRO system is a critical piece of information for understanding its intriguing magnetic and transport properties.

Realization of Isolated and High-Density Skyrmions at Room Temperature in Uncompensated Synthetic Antiferromagnets

Magnetic skyrmions are vortex-like spin textures with nontrivial spin topology and novel physical properties that show promise as an essential building block for novel spintronic applications. Skyrmions in synthetic antiferromagnets (SAF) have been proposed long-term to have many advantages than those in ferromagnetic materials, which suffer from fundamental limits for size and efficient manipulation. Thus, experimental realization of skyrmions in SAF is intensely pursued. Here we show the observation of zero-field stable magnetic skyrmions at room temperature in SAF [Co/Pd]/Ru/[Co/Pd] multilayers with Lorentz transmission electron microscope, where uncompensated moments of the SAF provide a medium for the skyrmion characterization. Isolated skyrmions and high-density skyrmions via magnetic field and electromagnetic coordinated methods have been observed, respectively. These created high-density skyrmions maintain at zero-field even when both the current and magnetic field are removed. The use of skyrmions in SAF would advance the process toward practical nonvolatile memories based on spin topology.

Room-temperature skyrmion phase in bulk Cu2OSeO3 under high pressures

A skyrmion state in a noncentrosymmetric helimagnet displays topologically protected spin textures with profound technological implications for high-density information storage, ultrafast spintronics, and effective microwave devices. Usually, its equilibrium state in a bulk helimagnet occurs only over a very restricted magnetic field-temperature phase space and often in the low-temperature region near the magnetic transition temperature T_c We have expanded and enhanced the skyrmion phase region from the small range of 55 to 58.5 K to 5 to 300 K in single-crystalline Cu₂OSeO₃ by pressures up to 42.1 GPa through a series of phase transitions from the cubic P2₁3, through orthorhombic P2₁2₁2₁ and monoclinic P2₁, and finally to the triclinic P1 phase, using our newly developed ultrasensitive high-pressure magnetization technique. The results are in agreement with our Ginzburg-Landau free energy analyses, showing that pressures tend to stabilize the skyrmion states and at higher temperatures. The observations also indicate that the skyrmion state can be achieved at higher temperatures in various crystal symmetries, suggesting the insensitivity of skyrmions to the underlying crystal lattices and thus the possible more ubiquitous presence of skyrmions in helimagnets.

Determining Surface Terminations and Chirality of Noncentrosymmetric FeGe Thin Films via Scanning Tunneling Microscopy

Scanning tunneling microscopy was used to study the surfaces of 20-100 nm thick FeGe films grown by molecular beam epitaxy. An average surface lattice constant of ∼6.8 Å, in agreement with the bulk value, was observed via scanning tunneling microscopy, low energy electron diffraction, and reflection high energy electron diffraction. Each of the four possible chemical terminations in the FeGe films were identified by comparing atomic-resolution images, showing distinct contrast with simulations from density functional theory calculations. A detailed study of the atomic layering order and registry across step edges allows us to uniquely determine the grain orientation and chirality in these noncentrosymmetric films.

Anatomy of Skyrmionic Textures in Magnetic Multilayers

Room temperature magnetic skyrmions in magnetic multilayers are considered as information carriers for future spintronic applications. Currently, a detailed understanding of the skyrmion stabilization mechanisms is still lacking in these systems. To gain more insight, it is first and foremost essential to determine the full real-space spin configuration. Here, two advanced X-ray techniques are applied, based on magnetic circular dichroism, to investigate the spin textures of skyrmions in [Ta/CoFeB/MgO]_n multilayers. First, by using ptychography, a high-resolution diffraction imaging technique, the 2D out-of-plane spin profile of skyrmions with a spatial resolution of 10 nm is determined. Second, by performing circular dichroism in resonant elastic X-ray scattering, it is demonstrated that the chirality of the magnetic structure undergoes a depth-dependent evolution. This suggests that the skyrmion structure is a complex 3D structure rather than an identical planar texture throughout the layer stack. The analyses of the spin textures confirm the theoretical predictions that the dipole-dipole interactions together with the external magnetic field play an important role in stabilizing sub-100 nm diameter skyrmions and the hybrid structure of the skyrmion domain wall. This combined X-ray-based approach opens the door for in-depth studies of magnetic skyrmion systems, which allows for precise engineering of optimized skyrmion heterostructures.

Emergent electromagnetism in condensed matter

Electrons in solids constitute quantum many-body systems showing a variety of phenomena. It often happens that the eigen states of the Hamiltonian are classified into subgroups separated by energy gaps. Band structures in solids and spin polarization in Mott insulators are two representative examples. The subspace spanned by these wavefunctions belonging to each of this subgroup can be regarded as a manifold in Hilbert space, and concepts concerning differential geometry become relevant. Connection and curvature are two key quantities, which correspond to the vector potential and field strength of electromagnetism, respectively. Therefore, one can construct an effective electromagnetic field from the structure of the Hilbert space, which is called an "emergent electromagnetic field". In this article, we review the physics related to this emergent electromagnetic field in solids, including the gauge theory of strongly correlated electrons, various Hall effects, multiferroics, topological matter, magnetic texture such as skyrmions, and the shift current in noncentrosymmetric materials.

Quenching of Charge and Spin Degrees of Freedom in Condensed Matter

Electrons in condensed matter have internal degrees of freedom, such as charge, spin, and orbital, leading to various forms of ordered states through phase transitions. However, in individual materials, a charge/spin/orbital ordered state of the lowest temperature is normally uniquely determined in terms of the lowest-energy state, i.e., the ground state. Here, recent results are summarized showing that under rapid cooling, this principle does not necessarily hold, and thus, the cooling rate is a control parameter of the lowest-temperature state beyond the framework of the thermoequilibrium phase diagram. Although the cooling rate utilized in low-temperature experiments is typically 2 × 10^-3 to 4 × 10^-1 K s^-1 , the use of optical/electronic pulses facilitates rapid cooling, such as 10² -10³ K s^-1 . Such an unconventionally high cooling rate allows some systems to kinetically avoid a first-order phase transition, resulting in a quenched charge/spin state that differs from the ground state. It is also demonstrated that quenched states can be exploited as a non-volatile state variable when designing phase-change memory functions. The present findings suggest that rapid cooling is useful for exploring and controlling the metastable electronic/magnetic state, which is potentially hidden behind the ground state.

Heuristic Description of Magnetoelectricity of Cu2OSeO3

CuO2SeO3 is an insulating material that hosts topologically nontrivial spin whirls, so-called skyrmions, and exhibits magnetoelectric coupling allowing to manipulate these skyrmions by means of electric fields. We report magnetic force microscopy imaging of the real-space spin structure on the surface of a bulk single crystal of CuO2SeO3. Based on measurements of the electric polarization using Kelvin-probe force microscopy, we develop a heuristic description of the magnetoelectric properties in CuO2SeO3. The model successfully describes the dependency of the electric polarization on the magnetization in all magnetically modulated phases.

Multidomain Skyrmion Lattice State in Cu2OSeO3

Magnetic skyrmions in chiral magnets are nanoscale, topologically protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu2OSeO3 single crystal, observed by soft resonant elastic X-ray scattering. This technique is an ideal tool to probe the magnetic order at the L3 edge of 3d metal compounds giving an average depth sensitivity of ∼50 nm. The single-domain 6-fold-symmetric skyrmion lattice can be broken up into domains, overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface or on the level of individual skyrmions, which will enable applications in the future.

Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks

Magnetic skyrmion is a nanosized magnetic whirl with nontrivial topology, which is highly relevant for applications on future memory devices. To enable the applications, theoretical efforts have been made to understand the dynamics of individual skyrmions in magnetic nanostructures. However, directly imaging the evolution of highly geometrically confined individual skyrmions is challenging. Here, we report the magnetic field-driven dynamics of individual skyrmions in FeGe nanodisks with diameters on the order of several skyrmion sizes by using Lorentz transmission electron microscopy. In contrast to the conventional skyrmion lattice in bulk, a series of skyrmion cluster states with different geometrical configurations and the field-driven cascading phase transitions are identified at temperatures far below the magnetic transition temperature. Furthermore, a dynamics, namely the intermittent jumps between the neighboring skyrmion cluster states, is found at elevated temperatures, at which the thermal energy competes with the energy barrier between the skyrmion cluster states.

Photodrive of magnetic bubbles via magnetoelastic waves

Precise control of magnetic domain walls continues to be a central topic in the field of spintronics to boost infotech, logic, and memory applications. One way is to drive the domain wall by current in metals. In insulators, the incoherent flow of phonons and magnons induced by the temperature gradient can carry the spins, i.e., spin Seebeck effect, but the spatial and time dependence is difficult to control. Here, we report that coherent phonons hybridized with spin waves, magnetoelastic waves, can drive magnetic bubble domains, or curved domain walls, in an iron garnet, which are excited by ultrafast laser pulses at a nonabsorbing photon energy. These magnetoelastic waves were imaged by time-resolved Faraday microscopy, and the resultant spin transfer force was evaluated to be larger for domain walls with steeper curvature. This will pave a path for the rapid spatiotemporal control of magnetic textures in insulating magnets.