Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications

Strain-enhanced Dzyaloshinskii-Moriya interaction at Co/Pt interfaces

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is an essential ingredient for stabilizing chiral spin configurations in spintronic applications. Here, via first-principles calculations, we reveal the influence of lattice strain on DMI in Co/Pt interface. We observed a considerable enhancement for a certain lattice strain. Furthermore, a direct correlation is established between the DMI and interlayer distances dominated by the strain, which is attributed to a hybridization of electronic orbitals. This hybridization has also been presented as the microscopic origin of the interfacial DMI. We anticipate that our predictions provide new insights into the control of interfacial DMI for skyrmion-based spintronic devices.

Skyrmion-skyrmion interaction in a magnetic film

Interaction of two skyrmions stabilized by the ferromagnetic exchange, Dzyaloshinskii-Moriya interaction (DMI), and external magnetic field has been studied numerically on a 2D lattice of size large compared to the separation,d, between the skyrmions. We show that two skyrmions of the same chirality (determined by the symmetry of the crystal) repel. In accordance with earlier analytical results, their long-range pair interaction falls out with the separation as exp(-d/δH), whereδHis the magnetic screening length, independent of the DMI. The prefactor in this expression depends on the DMI that drives the repulsion. The latter results in the spiral motion of the two skyrmions around each other, with the separation between them growing logarithmically with time. When two skyrmions of the total topological chargeQ= 2 are pushed close to each other, the discreteness of the atomic lattice makes them collapse into one skyrmion of chargeQ= 1 below a critical separation. Experiment is proposed that would allow one to measure the interaction between two skyrmions by holding them in positions with two magnetic tips. Our findings should be of value for designing topologically protected magnetic memory based upon skyrmions.

Spontaneous creation and annihilation dynamics and strain-limited stability of magnetic skyrmions

Magnetic skyrmions are topological magnetic spin structures exhibiting particle-like behaviour. They are of strong interest from a fundamental viewpoint and for application, where they have potential to act as information carriers in future low-power computing technologies. Importantly, skyrmions have high physical stability because of topological protection. However, they have potential to deform according to their local energy environment. Here we demonstrate that, in regions of high exchange energy density, skyrmions may exhibit such extreme deformation that spontaneous merging with nearest neighbours or spawning new skyrmions is favoured to attain a lower energy state. Using transmission electron microscopy and a high-speed imaging detector, we observe dynamics involving distinct configurational states, in which transitions are accompanied by spontaneous creation or annihilation of skyrmions. These observations raise important questions regarding the limits of skyrmion stability and topological charge conservation, while also suggesting a means of control of skyrmion creation and annihilation.

Tuning the Properties of Zero-Field Room Temperature Ferromagnetic Skyrmions by Interlayer Exchange Coupling

Magnetic materials offer an opportunity to overcome the scalability and energy consumption limits affecting the semiconductor industry. New computational device architectures, such as low-power solid state magnetic logic and memory-in-logic devices, have been proposed which rely on the unique properties of magnetic materials. Magnetic skyrmions, topologically protected quasi-particles, are at the core of many of the newly proposed spintronic devices. Many different materials systems have been shown hosting ferromagnetic skyrmions at room temperature. However, a magnetic field is a key ingredient to stabilize skyrmions, and this is not desirable for applications, due to the poor scalability of active components generating magnetic fields. Here we report the observation of ferromagnetic skyrmions at room temperature and zero magnetic field, stabilized through interlayer exchange coupling (IEC) between a reference magnet and a free magnet. Most importantly, by tuning the strength of the IEC, we are able to tune the skyrmion size and areal density. Our findings are relevant to the development of skyrmion-based spintronic devices suitable for general-use applications which go beyond modern nanoelectronics.

Tunable Magnetic Antiskyrmion Size and Helical Period from Nanometers to Micrometers in a D2d Heusler Compound

Skyrmions and antiskyrmions are magnetic nano-objects with distinct chiral, noncollinear spin textures that are found in various magnetic systems with crystal symmetries that give rise to specific Dzyaloshinskii-Moriya exchange vectors. These magnetic nano-objects are associated with closely related helical spin textures that can form in the same material. The skyrmion size and the period of the helix are generally considered as being determined, in large part, by the ratio of the magnitude of the Heisenberg to that of the Dzyaloshinskii-Moriya exchange interaction. In this work, it is shown by real-space magnetic imaging that the helix period λ and the size of the antiskyrmion d_aSk in the D_2d compound Mn_1.4 PtSn can be systematically tuned by more than an order of magnitude from ≈100 nm to more than 1.1 µm by varying the thickness of the lamella in which they are observed. The chiral spin texture is verified to be preserved even up to micrometer-thick layers. This extreme size tunability is shown to arise from long-range magnetodipolar interactions, which typically play a much less important role for B20 skyrmions. This tunability in size makes antiskyrmions very attractive for technological applications.

Atomistic Perspective of Long Lifetimes of Small Skyrmions at Room Temperature

The current development to employ magnetic skyrmions in novel spintronic device designs has led to a demand for room-temperature-stable skyrmions of ever smaller size. We present extensive studies on skyrmion stability in atomistic magnetic systems in two- and three-dimensional geometries. We show that for materials described by the same micromagnetic parameters, the variation of the atomistic exchange between different neighbors, the stacking order, and the number of layers of the atomic lattice can significantly influence the rate of the thermally activated decay of a skyrmion. These factors alone are important considerations, but we show that their combination can open up novel avenues of materials design in the search for sub-10 nm skyrmions, as their lifetime can be extended by several orders of magnitude.

Investigation of the Role of Rare-Earth Elements in Spin-Hall Topological Hall Effect in Pt/Ferrimagnetic-Garnet Bilayers

Topological magnetic textures such as skyrmions are being extensively studied for their potential application in spintronic devices. Recently, low-damping ferrimagnetic insulators (FMI) such as Tm₃Fe₅O₁₂ have attracted significant interest as potential candidates for hosting skyrmions. Here, we report the detection of the spin-Hall topological Hall effect (SH-THE) in Pt/Tm₃Fe₅O₁₂ and Pt/Y₃Fe₅O₁₂ bilayers grown on various orientations of Gd₃Ga₅O₁₂ substrates as well as on epitaxial buffer layers of Y₃Sc₂Al₃O₁₂, which separates the FMI from the substrate without sacrificing the crystal quality. The presence of SH-THE in all of the bilayers and trilayers provides evidence that rare-earth ions in either the FMI or substrate may not be critical for inducing an interfacial Dzyaloshinskii-Moriya interaction that is necessary to stabilize magnetic textures. Additionally, the use of substrates with various crystal orientations alters the magnetic anisotropy, which shifts the temperatures and strength of the SH-THE.

Intrinsic Mixed Bloch-Néel Character and Chirality of Skyrmions in Asymmetric Epitaxial Trilayers

Recent advances in the stabilization and manipulation of chiral magnetization configurations in systems consisting of alternating atomic layers of ferromagnetic and nonmagnetic materials hold promise for innovation in spintronics technology. The low dimensionality of the systems promotes spin orbit driven interfacial effects like antisymmetric Dzyaloshinskii-Moriya interactions (DMI) and surface magnetic anisotropy, whose relative strengths may be tuned to achieve stable nanometer sized magnetic objects with fixed chirality. While in most of the cases this is obtained by engineering complex multilayers stacks in which interlayer dipolar fields become important, we consider here a simple epitaxial trilayer in which a ferromagnet, with variable thickness, is embedded between a heavy metal and graphene. The latter enhances the perpendicular magnetic anisotropy of the system, promotes a Rashba-type DMI, and can sustain very long spin diffusion lengths. We use a layer-resolved micromagnetic model to describe the magnetization textures and their chirality. Our results demonstrate that for Co thicknesses larger than 3.6 nm, a skyrmion having an intrinsic mixed Bloch-Néel character is stabilized in the entire (single) Co layer.

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.

Tuning interfacial Dzyaloshinskii-Moriya interactions in thin amorphous ferrimagnetic alloys

Skyrmions can be stabilized in magnetic systems with broken inversion symmetry and chiral interactions, such as Dzyaloshinskii-Moriya interactions (DMI). Further, compensation of magnetic moments in ferrimagnetic materials can significantly reduce magnetic dipolar interactions, which tend to favor large skyrmions. Tuning DMI is essential to control skyrmion properties, with symmetry breaking at interfaces offering the greatest flexibility. However, in contrast to the ferromagnet case, few studies have investigated interfacial DMI in ferrimagnets. Here we present a systematic study of DMI in ferrimagnetic CoGd films by Brillouin light scattering. We demonstrate the ability to control DMI by the CoGd cap layer composition, the stack symmetry and the ferrimagnetic layer thickness. The DMI thickness dependence confirms its interfacial nature. In addition, magnetic force microscopy reveals the ability to tune DMI in a range that stabilizes sub-100 nm skyrmions at room temperature in zero field. Our work opens new paths for controlling interfacial DMI in ferrimagnets to nucleate and manipulate skyrmions.

Magnetostatic interaction between two bubble skyrmions

A detailed analytic and numerical analysis of the interaction between two bubble skyrmions has been carried out. The results from the micromagnetic calculations show that when the skyrmions are in the same plane, the magnetic parameters vary weakly as a function of the separation between them. On the other hand, when the skyrmions are located in the same vertical axis, the magnetic parameters show a strong variation as a function of the separation of the skyrmions. In particular, when a magnetic disk is over another, there is a transition from a Bloch-like skyrmion configuration to a Néel-like skyrmion configuration as the distance between the disks decreases, as a consequence of the magnetostatic interaction. Therefore, it is possible to stabilize a bubble skyrmion with a Néel configuration without the Dzyaloshinskii-Moriya interaction. Thus, these results can be used for the control of the skyrmion parameters in magnetic spintronic devices that need to use these configurations.

Direct Demonstration of Topological Stability of Magnetic Skyrmions via Topology Manipulation

Topological protection precludes a continuous deformation between topologically inequivalent configurations in a continuum. Motivated by this concept, magnetic skyrmions, topologically nontrivial spin textures, are expected to exhibit topological stability, thereby offering a prospect as a nanometer-scale nonvolatile information carrier. In real materials, however, atomic spins are configured as not continuous but discrete distributions, which raises a fundamental question if the topological stability is indeed preserved for real magnetic skyrmions. Answering this question necessitates a direct comparison between topologically nontrivial and trivial spin textures, but the direct comparison in one sample under the same magnetic fields has been challenging. Here we report how to selectively achieve either a skyrmion state or a topologically trivial bubble state in a single specimen and thereby experimentally show how robust the skyrmion structure is in comparison with the bubbles. We demonstrate that topologically nontrivial magnetic skyrmions show longer lifetimes than trivial bubble structures, evidencing the topological stability in a real discrete system. Our work corroborates the physical importance of the topology in the magnetic materials, which has hitherto been suggested by mathematical arguments, providing an important step toward ever-dense and more-stable magnetic devices.

Voltage-controlled skyrmion-based nanodevices for neuromorphic computing using a synthetic antiferromagnet

Spintronics exhibits significant potential for a neuromorphic computing system with high speed, high integration density, and low dissipation. In this article, we propose an ultralow-dissipation skyrmion-based nanodevice composed of a synthetic antiferromagnet (SAF) and a piezoelectric substrate for neuromorphic computing. Skyrmions/skyrmion bubbles can be generated in the upper layer of an SAF with a weak anisotropy energy (E _a). Applying a weak electric field on the heterostructure, interlayer antiferromagnetic coupling can be manipulated, giving rise to a continuous transition between a large skyrmion bubble and a small skyrmion. This thus induces a variation of the resistance of a magnetic tunneling junction that can mimic the potentiation/depression of a synapse and the leaky-integral-and-fire function of a neuron at a cost of a very low energy consumption of 0.3 fJ. These results pave a way to ultralow power neuromorphic computing applications.

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

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

Room-temperature stabilization of antiferromagnetic skyrmions in synthetic antiferromagnets

Room-temperature skyrmions in ferromagnetic films and multilayers show promise for encoding information bits in new computing technologies. Despite recent progress, ferromagnetic order generates dipolar fields that prevent ultrasmall skyrmion sizes, and allows a transverse deflection of moving skyrmions that hinders their efficient manipulation. Antiferromagnetic skyrmions shall lift these limitations. Here we demonstrate that room-temperature antiferromagnetic skyrmions can be stabilized in synthetic antiferromagnets (SAFs), in which perpendicular magnetic anisotropy, antiferromagnetic coupling and chiral order can be adjusted concurrently. Utilizing interlayer electronic coupling to an adjacent bias layer, we demonstrate that spin-spiral states obtained in a SAF with vanishing perpendicular magnetic anisotropy can be turned into isolated antiferromagnetic skyrmions. We also provide model-based estimates of skyrmion size and stability, showing that room-temperature antiferromagnetic skyrmions below 10 nm in radius can be anticipated in further optimized SAFs. Antiferromagnetic skyrmions in SAFs may thus solve major issues associated with ferromagnetic skyrmions for low-power spintronic devices.

Complex magnetism of B20-MnGe: from spin-spirals, hedgehogs to monopoles

B20 compounds are the playground for various non-trivial magnetic textures such as skyrmions, which are topologically protected states. Recent measurements on B20-MnGe indicate no clear consensus on its magnetic behavior, which is characterized by the presence of either spin-spirals or three-dimensional objects interpreted to be a cubic lattice of hedgehogs and anti-hedgehogs. Utilizing a massively parallel linear scaling all-electron density functional algorithm, we find from full first-principles simulations on cells containing thousands of atoms that upon increase of the compound volume, the state with lowest energy switches across different magnetic phases: ferromagnetic, spin-spiral, hedgehog and monopole.

Magnetic skyrmions in FePt nanoparticles having Reuleaux 3D geometry: a micromagnetic simulation study

The magnetization reversal in magnetic FePt nanoelements having Reuleaux 3D geometry is studied using micromagnetic simulations employing Finite Element discretizations. Magnetic skyrmions are revealed in different systems generated by the variation of the magnitude of the magnetocrystalline anisotropy which was kept normal to the nanoelement's base and parallel to the applied external field. The topological quantity of skyrmion number is computed in order to characterize micromagnetic configurations exhibiting skyrmionic formations. Micromagnetic configurations with a wide range of skyrmion numbers between -3 and 3 are indicative for the existence of one or multiple skyrmions that have been detected and stabilized in a range of external fields. Internal magnetic structures are shown consisting of Bloch type skyrmionic entities in the bulk altered to Néel skyrmions on the nanoelement's bottom and top base surfaces. The actual sizes of the formed skyrmions and the internal magnetization structures were computed. In particular, the sizes of the generated and persistent skyrmions were calculated as functions of the magnetocrystalline anisotropy value and of the applied external magnetic field. It is shown that the size of skyrmions is linearly dependent on the external field value. The slope of the linear curve can be controlled by the magnetocrystalline anisotropy value. The magnetic skyrmions can be created for FePt magnetic systems lacking of chiral interactions by designing the geometry-shape of the nanoparticle and by controlling the value of magnetocrystalline anisotropy.

Formation and current-induced motion of synthetic antiferromagnetic skyrmion bubbles

Skyrmion, a topologically-protected soliton, is known to emerge via electron spin in various magnetic materials. The magnetic skyrmion can be driven by low current density and has a potential to be stabilized in nanoscale, offering new directions of spintronics. However, there remain some fundamental issues in widely-studied ferromagnetic systems, which include a difficulty to realize stable ultrasmall skyrmions at room temperature, presence of the skyrmion Hall effect, and limitation of velocity owing to the topological charge. Here we show skyrmion bubbles in a synthetic antiferromagnetic coupled multilayer that are free from the above issues. Additive Dzyaloshinskii-Moriya interaction and spin-orbit torque (SOT) of the tailored stack allow stable skyrmion bubbles at room temperature, significantly smaller threshold current density or higher speed for motion, and negligible skyrmion Hall effect, with a potential to be scaled down to nanometer dimensions. The results offer a promising pathway toward nanoscale and energy-efficient skyrmion-based devices.

Statistical Thermodynamics of Chiral Skyrmions in a Ferromagnetic Material

Solitons are a challenging topic in condensed matter physics and materials science because of the interplay between their topological and physical properties and for the crucial role they play in topological phase transitions. Among them, chiral skyrmions hosted in ferromagnetic systems are axisymmetric solitonic states attracting a lot of attention for their dazzling physical properties and technological applications. In this paper, the equilibrium statistical thermodynamics of chiral magnetic skyrmions developing in a ferromagnetic material having the shape of an ultrathin cylindrical dot is investigated. This is accomplished by determining via analytical calculations for both Néel and Bloch skyrmions: (1) the internal energy of a single chiral skyrmion; (2) the partition function; (3) the free energy; (4) the pressure; and (5) the equation of state of a skyrmion diameters population. To calculate the thermodynamic functions for points (2)–(5), the derivation of the average internal energy and of the configurational entropy is crucial. Numerical calculations of the thermodynamic functions for points (1)–(5) are applied to Néel skyrmions. These results could advance the field of materials science with special regard to low-dimensional magnetic systems.

Isolated zero field sub-10 nm skyrmions in ultrathin Co films

Due to their exceptional topological and dynamical properties magnetic skyrmions—localized stable spin structures—show great promise for spintronic applications. To become technologically competitive, isolated skyrmions with diameters below 10 nm stable at zero magnetic field and at room temperature are desired. Despite finding skyrmions in a wide spectrum of materials, the quest for a material with these envisioned properties is ongoing. Here we report zero field isolated skyrmions at T = 4 K with diameters below 5 nm observed in the virgin ferromagnetic state coexisting with 1 nm thin domain walls in Rh/Co atomic bilayers on Ir(111). These spin structures are investigated by spin-polarized scanning tunneling microscopy and can also be detected using non-spin-polarized tips via the noncollinear magnetoresistance. We demonstrate that sub-10 nm skyrmions are stabilized in these ferromagnetic Co films at zero field due to strong frustration of exchange interaction, together with Dzyaloshinskii–Moriya interaction and large magnetocrystalline anisotropy.

Isolated skyrmions with diameters below 10 nm stabilized at zero magnetic field are of great technological relevance to the future spintronic applications. Here the authors report stabilization of zero field isolated skyrmions with diameters smaller than 5 nm in Rh/Co atomic bilayers on the Ir(111) surface.

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

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

Robust Formation of Ultrasmall Room-Temperature Neél Skyrmions in Amorphous Ferrimagnets from Atomistic Simulations

Neél skyrmions originate from interfacial Dzyaloshinskii Moriya interaction (DMI). Recent studies have explored using thin-film ferromagnets and ferrimagnets to host Neél skyrmions for spintronic applications. However, it is unclear if ultrasmall (10 nm or less) skyrmions can ever be stabilized at room temperature for practical use in high density parallel racetrack memories. While thicker films can improve stability, DMI decays rapidly away from the interface. As such, spins far away from the interface would experience near-zero DMI, raising question on whether or not unrealistically large DMI is needed to stabilize skyrmions, and whether skyrmions will also collapse away from the interface. To address these questions, we have employed atomistic stochastic Landau-Lifshitz-Gilbert simulations to investigate skyrmions in amorphous ferrimagnetic GdCo. It is revealed that a significant reduction in DMI below that of Pt is sufficient to stabilize ultrasmall skyrmions even in films as thick as 15 nm. Moreover, skyrmions are found to retain a uniform columnar shape across the film thickness due to the long ferrimagnetic exchange length despite the decaying DMI. Our results show that increasing thickness and reducing DMI in GdCo can further reduce the size of skyrmions at room temperature, which is crucial to improve the density and energy efficiency in skyrmion based devices.

Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk

When two magnetic skyrmions - whirl-like, topologically protected quasiparticles - form a bound pair, a biskyrmion state with a topological charge of NSk = ±2 is constituted. Recently, especially the case of two partially overlapping skyrmions has brought about great research interest. Since for its formation the individual skyrmions need to posses opposite in-plane magnetizations, such a biskyrmion cannot be stabilized by the Dzyaloshinskii-Moriya-interaction (DMI), which is the interaction that typically stabilizes skyrmions in non-centrosymmetric materials and at interfaces. Here, we show that these biskyrmions can be stabilized by the dipole-dipole interaction in centrosymmetric materials in which the DMI is forbidden. Analytical considerations indicate that the bound state of a biskyrmion is energetically preferable over two individual skyrmions. As a result, when starting from two skyrmions in a micromagnetic simulation, a biskyrmion is formed upon relaxation. We propose a scheme that allows to control this biskyrmion formation in nanodisks and analyze the individual steps.

Direct current-tunable MHz to multi-GHz skyrmion generation and control

Skyrmions offer high density, low power, and nonvolatile memory functionalities due to their nanoscale and topologically-protected chiral spin structures. For integrated high-bandwidth devices, one needs to control skyrmion generation and propagation rates using current. Here, we introduce a skyrmion initialization and control method to generate periodic skyrmions from 114 MHz to 21 GHz using spin-polarized direct current. We first initialize a stable magnetic domain profile that is pinned between a notch and a rectangular constriction using a DC pulse. Next, we pass spin-polarized DC charge current to eject periodic skyrmions at a desired frequency. By changing the DC current density, we demonstrate in micromagnetic simulations that skyrmion generation frequencies can be controlled reversibly over more than seven octaves of frequencies. By using domain pinning and current-driven skyrmion motion, we demonstrate a highly tunable and DC-controlled skyrmion signal source, which pave the way towards ultra wideband, compact and integrated skyrmionic circuits.

Dynamics of skyrmion in disordered chiral magnet of thin film form

Magnetic skyrmion is a topological spin texture characterized by the mapping from the two dimensional real space to the unit sphere. It is realized in chiral magnets under an external magnetic field in the plane perpendicular to it. In thin film samples, which are most relevant to the applications, the thickness of the system parallel to the magnetic field is finite, and a skyrmion turns into a skyrmion string, which is often assumed to be a straight rod. There are phenomena related to the internal degrees of freedom along the string, e.g., the monopole and anti-monopole creation/annihilation, corresponding to the change in the skyrmion number. However, the role of this finite thickness in the topological stability and dynamics has not been explored yet. Here we study theoretically the current-driven dynamics of a skyrmion string under disorder potential by systematically changing the thickness of the sample to reveal the dynamical phase diagram in the plane of current density and thickness. We found the three regions, i.e., (i) pinned skyrmion string, (ii) moving depinned skyrmion string, and (iii) annihilation of skyrmion string, for thin and thick limits while (iii) is missing in the intermediate case. This indicates that there is the optimal range of thickness for the topological stability of skyrmion string enhanced compared with a two-dimensional skyrmion. This result provides a way to design and control skyrmions in thin films and interfaces of finite thickness.

Current-driven coherent skyrmion generation

The next-generation logic and memory devices using magnetic skyrmions as spintronic information carriers are frequently studied, thanks to their remarkable magnetic stability, extremely compact size and very-low-cost driving forces within nanotracks. In order to realize skyrmion-based spintronic devices, understanding the skyrmion generation and their dynamics are essential. In this study, we have carried out a systematic micromagnetic simulation study on coherent magnetic skyrmion generation in which we theoretically engineered nanotracks by embedding an anti-notch to a channel of certain width. We found that the drift velocity and the skyrmion generation frequency can be tailored by the applied spin-polarized DC current density. Moreover, skyrmion generation is crucially affected by both damping and nonadiabaticity parameters, as well as the geometry of the anti-notch. We anticipate that our predictions provide rational basis for skyrmion-based devices in which skyrmions are used as information carriers, and influence future discussions.

First-Principles Prediction of Skyrmionic Phase Behavior in GdFe2 Films Capped by 4d and 5d Transition Metals

In atomic GdFe 2 films capped by 4d and 5d transition metals, we show that skyrmions with diameters smaller than 12 nm can emerge. The Dzyaloshinskii–Moriya interaction (DMI), exchange energy, and the magnetocrystalline anisotropy (MCA) energy were investigated based on density functional theory. Since DMI and MCA are caused by spin–orbit coupling (SOC), they are increased with 5d capping layers which exhibit strong SOC strength. We discover a skyrmion phase by using atomistic spin dynamic simulations at small magnetic fields of ∼1 T. In addition, a ground state that a spin spiral phase is remained even at zero magnetic field for both films with 4d and 5d capping layers.

Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet

Spintronics is a research field that aims to understand and control spins on the nanoscale and should enable next-generation data storage and manipulation. One technological and scientific key challenge is to stabilize small spin textures and to move them efficiently with high velocities. For a long time, research focused on ferromagnetic materials, but ferromagnets show fundamental limits for speed and size. Here, we circumvent these limits using compensated ferrimagnets. Using ferrimagnetic Pt/Gd₄₄Co₅₆/TaO_x films with a sizeable Dzyaloshinskii-Moriya interaction, we realize a current-driven domain wall motion with a speed of 1.3 km s^-1 near the angular momentum compensation temperature (T_A) and room-temperature-stable skyrmions with minimum diameters close to 10 nm near the magnetic compensation temperature (T_M). Both the size and dynamics of the ferrimagnet are in excellent agreement with a simplified effective ferromagnet theory. Our work shows that high-speed, high-density spintronics devices based on current-driven spin textures can be realized using materials in which T_A and T_M are close together.

Creation of Magnetic Skyrmion Bubble Lattices by Ultrafast Laser in Ultrathin Films

Magnetic skyrmions are topologically nontrivial spin textures which hold great promise as stable information carriers in spintronic devices at the nanoscale. One of the major challenges for developing novel skyrmion-based memory and logic devices is fast and controlled creation of magnetic skyrmions at ambient conditions. Here we demonstrate controlled generation of skyrmion bubbles and skyrmion bubble lattices from a ferromagnetic state in sputtered ultrathin magnetic films at room temperature by a single ultrafast (35 fs) laser pulse. The skyrmion bubble density increases with the laser fluence, and it finally becomes saturated, forming disordered hexagonal lattices. Moreover, we present that the skyrmion bubble lattice configuration leads to enhanced topological stability as compared to isolated skyrmions, suggesting its promising use in data storage. Our findings shed light on the optical approach to the skyrmion bubble lattice in commonly accessible materials, paving the road toward the emerging skyrmion-based memory and synaptic devices.

Single Chiral Skyrmions in Ultrathin Magnetic Films

The stability and sizes of chiral skyrmions in ultrathin magnetic films are calculated accounting for the isotropic exchange, Dzyaloshinskii⁻Moriya exchange interaction (DMI), and out-of-plane magnetic anisotropy within micromagnetic approach. Bloch skyrmions in ultrathin magnetic films with B20 cubic crystal structure (MnSi, FeGe) and Neel skyrmions in ultrathin films and multilayers Co/X (X = Ir, Pd, Pt) are considered. The generalized DeBonte ansatz is used to describe the inhomogeneous skyrmion magnetization. The single skyrmion metastability/instability area, skyrmion radius, and skyrmion width are found analytically as a function of DMI strength d . It is shown that the single chiral skyrmions are metastable in infinite magnetic films below a critical value of DMI d c , and do not exist at d > d c . The calculated skyrmion radius increases as d increases and diverges at d → d c - 0 , whereas the skyrmion width increases monotonically as d increases up to d c without any singularities. The calculated skyrmion width is essentially smaller than the one calculated within the generalized domain wall model.