Magnetic Skyrmions Research Articles

Skyrmions in synthetic antiferromagnets and their nucleation via electrical current and ultra-fast laser illumination

Magnetic skyrmions are topological spin textures that hold great promise as nanoscale information carriers in non-volatile memory and logic devices. While room-temperature magnetic skyrmions and their current-induced motion were recently demonstrated, the stray field resulting from their finite magnetisation and their topological charge limit their minimum size and reliable motion. Antiferromagnetic skyrmions allow to lift these limitations owing to their vanishing magnetisation and net zero topological charge, promising ultra-small and ultra-fast skyrmions. Here, we report on the observation of isolated skyrmions in compensated synthetic antiferromagnets at zero field and room temperature using X-ray magnetic microscopy. Micromagnetic simulations and an analytical model confirm the chiral antiferromagnetic nature of these skyrmions and allow the identification of the physical mechanisms controlling their size and stability. Finally, we demonstrate the nucleation of synthetic antiferromagnetic skyrmions via local current injection and ultra-fast laser excitation.

Skyrmion transport driven by pure voltage generated strain gradient

The magnetic skyrmion transport driven by pure voltage-induced strain gradient is proposed and studied via micromagnetic simulation. Through combining the skyrmion with multiferroic heterojunction, a voltage-induced uniaxial strain gradient is adjusted to move skyrmions. In the system, a pair of short-circuited trapezoidal top electrodes can generate the symmetric strain. Due to the symmetry of strain, the magnetic skyrmion can be driven with a linear motion in the middle of the nanostrip without deviation. We calculate the strain distribution generated by the trapezoidal top electrodes pair, and further investigate the influence of the strain intensity as well as the strain gradient on the skyrmion velocity. Our findings provide a stable and low-energy regulation method for skyrmion transport.

Formation of magnetic biskyrmions mediated by an intrinsic emergent monopole-antimonopole pair

Various properties and potential technological applications of magnetic skyrmions have stimulated a flourishing interest in topological spin textures. Among them, biskyrmions with a rare topological charge of two are observed but their existence is still under debate. In this work, we present the formation of biskyrmion bubbles mediated by emergent monopoles via micromagnetic simulations. We find that biskyrmion bubbles and trivial bubbles share a unified three-dimensional structure, in which the relative position of an intrinsic emergent monopole-antimonopole pair dominates the two-dimensional topological property at the middle plane of magnetic uniaxial films. Biskyrmion bubbles can be transformed from trivial bubbles by the motion of emergent monopoles in confined geometry, paving the way for developing devices. These results highlight the three-dimensional aspect of skyrmion-related nanostructures and the versatile roles of emergent monopoles in topological spin textures.

Inhibition of Skyrmion Hall Effect by a Stripe Domain Wall

Magnetic skyrmions are topologically protected particlelike spin textures initially discovered in chiral magnetic materials. When driven by an electric current, magnetic skyrmions move at a certain angle (i.e., skyrmion Hall angle) with respect to the driving current due to the Magnus force, giving rise to the so-called skyrmion Hall effect (SHE). The SHE often leads to skyrmion annihilation at the sample edge, which is detrimental for practical applications. In this work, we study, experimentally and through micromagnetic simulations, the current-driven dynamics of skyrmion bubbles (SBs) in $\mathrm{Pt}/\mathrm{Co}/\mathrm{Ru}$ multilayer stacks. It is observed that, under certain circumstances, a long stripe domain will form and align along the sample edge, which separates the skyrmion bubbles from the edge and avoids their annihilation at the edge. Furthermore, the velocity of the skyrmion bubbles can be increased by the stripe domain wall (DW) through the DW-SB interaction, as predicted in our early theory. Our results deepen our understanding of skyrmion dynamics and pave the way to the realization of highly efficient information processing and computing devices based on ultrafast skyrmion motion.

Weakly pinned skyrmion liquid in a magnetic heterostructure

Magnetic skyrmions are topological quasiparticles that can be formed in systems with particular magnetic interactions. Here, the authors study dense arrays of skyrmions in a thin film heterostructure, showing that the skyrmions form a liquid, the properties of which depend strongly on the size and density of the skyrmions. The presence of pinning sites alters the behavior of the skyrmion liquid compared to typical liquids, but these pinning sites are shown to have a narrow energy distribution compatible with proposed applications.

Current-driven dynamics of skyrmions in the presence of pinning at finite temperatures

Magnetic skyrmions are topological solitons in magnetic materials with broken spatial inversion symmetry. They offer potential as an information carrier for future low-power memory and computing systems owing to the small size and relatively low driving current compared to traditional devices. To develop applications such as racetrack memory at ambient temperature, the interaction of current-driven motion, pinning and thermal fluctuations must be investigated. The skyrmion dynamics at finite temperatures are shown using the expanded Thiele equation, and the relationship between critical depinning current and temperature is established with regard to different damping constants. Furthermore, we found that the Thiele equation still is insufficient to describe the dynamics of skyrmion precisely at low temperatures with the presence of pinning. Moreover, we have shown that the skyrmion Hall angle is dependent on the driving current in the presence of the pinning effect at various finite temperatures.

Tuning skyrmions in B20 compounds by 4d and 5d doping

Skyrmion stabilization in novel magnetic systems with the B20 crystal structure is reported here, primarily based on theoretical results. The focus is on the effect of alloying on the $3d$ sublattice of the B20 structure by substitution of heavier $4d$ and $5d$ elements, with the ambition to tune the spin-orbit coupling and its influence on magnetic interactions. State-of-the-art methods based on density functional theory are used to calculate both isotropic and anisotropic exchange interactions. Significant enhancement of the Dzyaloshinskii-Moriya interaction is reported for $5d$-doped FeSi and CoSi, accompanied by a large modification of the spin stiffness and spiralization. Micromagnetic simulations coupled to atomistic spin-dynamics and ab initio magnetic interactions reveal the spin-spiral nature of the magnetic ground state and field-induced skyrmions for all these systems. Especially small skyrmions $\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ are predicted for ${\mathrm{Co}}_{0.75}{\mathrm{Os}}_{0.25}\mathrm{Si}$, compared to $\ensuremath{\sim}148\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ for ${\mathrm{Fe}}_{0.75}{\mathrm{Co}}_{0.25}\mathrm{Si}$. Convex-hull analysis suggests that all B20 compounds considered here are structurally stable at elevated temperatures and should be possible to synthesize. This prediction is confirmed experimentally by synthesis and structural analysis of the Ru-doped CoSi systems discussed here, both in powder and in single-crystal forms.

High-temperature non-centrosymmetric magnets for skyrmionics

Such topological spin textures as magnetic skyrmions and antiskyrmions have attracted significant interest in recent years owing to their rich variety of underlying physics and potential applications in next-generation magnetic devices. In the domain of applications, it is essential to stabilize the topological spin textures over a wide range of temperatures, including room temperature, and manipulate them with various external stimuli. Significant developments have been made in room-temperature skyrmions and antiskyrmions arising from the Dzyaloshinskii–Moriya interaction (DMI) in several magnetic materials with broken inversion symmetry. In this Perspective, we review recent progress in non-centrosymmetric magnets with bulk DMI, which host skyrmions and antiskyrmions above room temperature. We first provide an overview of room-temperature Bloch-type skyrmions and the robustness of their metastability, the variety of their forms, and their dynamics in Co–Zn–Mn alloys with a β-Mn-type chiral structure. We then focus on room-temperature antiskyrmions as well as their topological transformations in Heusler alloys with D2d symmetry and Pd-doped (Fe,Ni)3P with S4 symmetry. The robust skyrmions and antiskyrmions, with versatile tunability in these non-centrosymmetric materials at room temperature, represent a step toward the long-sought milestone of “skyrmionics.”

Skyrmion Creation and Annihilation by Electric Current Vorticity

Motivated by the recent experiment done by Yu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> [X. Z. Yu, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et. al.</i> , Sci. Adv., 6, 25, eaaz9744 (2020)] on magnetic skyrmion creation and annihilation by electric currents in FeGe devices with a notch structure, we examine the interaction between the electric current vorticity near the notch and localized spins, and obtain three effects of the current vorticity on the localized spins. The first one is an effective Zeeman field induced by the current vorticity. This effective Zeeman field is responsible for skyrmion creation. The second effect is a vorticity-induced Dzyaloshinskii–Moriya (DM) interaction with the direction of the DM vector being parallel to the vorticity direction and is different from the vector of the intrinsic DM interaction. This vorticity-induced DM interaction makes the skyrmions distorted. The third effect is a spin current due to the gradient of the vorticity and the spin current drives the magnetic skyrmions far from the notch. Our theory opens a new path to design the magnetic textures by using structural settings.

Structure and Field Evolution of Magnetic Skyrmions in Co/Pt-Based Multilayers by In-Situ Electron Holography

Structure and Field Evolution of Magnetic Skyrmions in Co/Pt-Based Multilayers by In-Situ Electron Holography

Majorana bound states with chiral magnetic textures

The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. This Tutorial is aimed at students at the graduate level.

Creating arbitrary sequences of mobile magnetic skyrmions and antiskyrmions

Magnetic skyrmions and their antiparticles, the antiskyrmions, are stable magnetic solitons existing down to the nanometer scale. Their stability and size as well as the possibility to propel them by, e.g., electric currents make them promising candidates for use in memory devices, such as racetrack memories. Skyrmions and antiskyrmions share those same advantages individually, but may annihilate each other when they coexist in the same device. Yet, combining them to represent logical bits of 0 (skyrmion) and 1 (antiskyrmion) in one device opens new possibilities to create new types of densely packed racetrack memory devices. For this, a controlled creation and annihilation procedure, i.e., a writing or deletion operation, is necessary. Here, we propose a method to create arbitrary sequences of coexisting skyrmions and antiskyrmions by rotations of the magnetic moments at the edge of a rectangular slab. The skyrmions and antiskyrmions remain stable and do not annihilate each other.

Artificial skyrmion in magnetic multilayers

A magnetic skyrmion is a promising candidate for information carrier in future logic functional devices, ultra-density storage devices, and neuromorphic computing. The presence of interfacial Dzyaloshinskii–Moriya interaction in magnetron sputtered multilayers results in the spontaneous nucleation of magnetic skyrmion. However, the precise control of position and arrangement of magnetic skyrmion spontaneously nucleated in multilayers is still a significant challenge. Artificial skyrmion, generated by various external stimuli, shows high promise for manipulating the spatially ordered arrangement on demand. In this review, we summarize the progress of artificial skyrmion with various formation mechanisms. After introducing the concept of artificial skyrmion, we will focus on several methods of producing artificial skyrmion in magnetic multilayers using spin texture imprinting, integrated bias magnet, local magnetic field gradient, optical irradiation, and nanolithography. In the end, we give a perspective of the potential applications of artificial skyrmions for cavity magnonics and quantum spintronics.

Realization of the skyrmionic logic gates and diodes in the same racetrack with enhanced and modified edges

Magnetic skyrmions are topological quasiparticles with nanoscale size and high mobility, which have potential applications in information storage and spintronic devices. Here, we computationally investigate the dynamics of isolated skyrmions in a ferromagnetic racetrack, where magnetic properties of the edges are enhanced and modified, forming a channel with lower magnetic anisotropy for skyrmion motion. It is found that the rectangular notch at the edge can have a pinning effect on the skyrmion and enrich the dynamics of the skyrmion. Based on the racetrack with modified edges and the notch, we design a racetrack that realizes the skyrmionic logic AND, OR, and NOT gates as well as the diode in the same magnetic racetrack. It is found that the driving current density could be much smaller than those used in previous designs of skyrmion-based logic gates. By slightly altering the shape of the racetrack, we also design the NAND and NOR gates. Finally, we study the feasibility of our design at finite temperatures. Our results may contribute to the design of nonvolatile spintronic devices with integrated multiple functions and ultra-low energy consumption.

Anisotropy of exchange and Dzyaloshinskii-Moriya interactions effects on the stabilization of Néel-type skyrmions

In this work, the effect of uniaxial stress on the stability of magnetic skyrmion is studied by use of Monte Carlo simulations. The classical Heisenberg model with anisotropic exchanges and Dzyaloshinskii-Moriya interactions is applied to correlate the stress behavior. We calculate magnetization M and skyrmion number Q to estimate the phase transition points, use the spin configurations and their Fourier transform to determine the region of skyrmion state. The h − T phase diagram show the area of skyrmion state is larger with stress than without stress. These results are interpreted qualitatively by the energy competitions between Zeeman, exchanges and Dzyaloshinskii-Moriya interactions. The simulated results suggest that anisotropy induced by uniaxial stress can stabilize the skyrmion phase.

Mechanical Acceleration and Control of the Thermal Motion of a Magnetic Skyrmion

Engineering the kinetic motion of magnetic skyrmions shows great potential in spintronics. Particularly, as a natural property, temperature plays a significant role in the dynamics of skyrmions. For instance, the nonlinear and the rectilinear motions of skyrmions driven by spin-transfer torque and local energy imbalance in temperature gradients, respectively, have been explored. Although existing studies have already implied the multiphysics field-controlled property of skyrmion thermal motion, the investigation of mechanically controlled skyrmion motions in temperature gradients is absent, and the kinematic equation is unclear. Here, we employ a phase-field model to simulate the effect of mechanical strain on skyrmion motion in a temperature gradient, and demonstrate that the strain-induced anisotropic deformation of skyrmions increases the driving force and accelerates their motion. To model the mechanical effect, we propose a kinematic equation for describing the relationship between skyrmion velocity and multiphysics field variables. Lastly, the potential application of the mechanically controlled skyrmion thermal motion is demonstrated via tip indentation simulations. This work provides the thermodynamic mechanism and kinematic equation for mechanically accelerated skyrmion thermal motions, which is expected to be a guidance for future research on skyrmion dynamics and application of functional devices.

Robust and Programmable Logic-In-Memory Devices Exploiting Skyrmion Confinement and Channeling Using Local Energy Barriers

Magnetic skyrmions are promising candidates for logic-in-memory applications, intrinsically merging high density non-volatile data storage with computing capabilities, owing to their nanoscale size, fast motion, and mutual repulsions. However, concepts proposed so far suffer from reliability issues as well as inefficient conversion of magnetic information to electrical signals. In this paper, we propose a logic-in-memory device which exploits skyrmion confinement and channeling using anisotropy energy barriers to achieve reliable data storage and synchronous shift in racetracks combined with cascadable and reprogrammable logics relying purely on magnetic interactions. The device combines a racetrack shift register based on skyrmions confined in nanodots with Full Adder (FA) gates. The designed FA is reprogrammable and cascadable and can also be used to perform simple logic operations such as AND, OR, NOT, NAND, XOR and NXOR. The monolithic design of the logic gate and the absence of any complex electrical contacts makes the device ideal for integration with conventional CMOS circuitry.

Bio-inspired computing with magnetic skyrmions using deep learning

Spintronic systems demonstrate significant value due to variety of features that can be used in bio-inspired computing applications. Skyrmion is a magnetic nanostructure which can be used as an information carrier. In this paper, we simulate vortex-free Gaussian wave packet by incorporating spin–orbit coupling (SoC) into three-component Bose–Einstein condensates (BECs). We next observe that skyrmions can be naturally generated from vortex-free Gaussian wave packet, further these structurally asymmetric devices are constructed and initial device classifications are carried out. A spin device consisting of vertically-stacked multiple skyrmions is proposed termed as skyrmion spintronic synapse (SkSS) and skyrmion spintronic Neuron (SkSN). This paper depicts training the neural network with surrogate gradients with deep learning strategies using topologically nontrivial spin textures. The current popular Graphics Processing Unit (GPU)-based neural network computations are compared with the proposed method. This research paves a way for a neuromorphic computing systems on exotic topological solitons.

Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator.

Magnetic skyrmions are compact chiral spin textures that exhibit a rich variety of topological phenomena and hold potential for the development of high-density memory devices and novel computing schemes driven by spin currents. Here, we demonstrate the room-temperature interfacial stabilization and current-driven control of skyrmion bubbles in the ferrimagnetic insulator Tm3Fe5O12 coupled to Pt, showing the current-induced motion of individual skyrmion bubbles. The ferrimagnetic order of the crystal together with the interplay of spin-orbit torques and pinning determine the skyrmion dynamics in Tm3Fe5O12 and result in a strong skyrmion Hall effect characterized by a negative deflection angle and hopping motion. Further, we show that the velocity and depinning threshold of the skyrmion bubbles can be modified by exchange coupling Tm3Fe5O12 to an in-plane magnetized Y3Fe5O12 layer, which distorts the spin texture of the skyrmions and leads to directional-dependent rectification of their dynamics. This effect, which is equivalent to a magnetic ratchet, is exploited to control the skyrmion flow in a racetrack-like device.

Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

We investigate an instability toward a square-lattice formation of magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal (SkX) based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii–Moriya (DM) interaction built in the lattice structure becomes the origin of the square SkX in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square SkX is constituted of the SkXs with different helicities in each layer due to the staggered DM interaction. Furthermore, we show that the interplay between the staggered DM interaction and the interlayer exchange interaction gives rise to a double-Q state with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square SkX in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.