Creation and annihilation of artificial magnetic skyrmions with the electric field

Recent theory and experiments show that artificial magnetic skyrmions can be stabilized at room temperature without the need for the external magnetic field,casting strong potentials for the device applications.In this work,we study the electric field manipulation of artificial magnetic skyrmions imprinted by Co disks on CoPt multilayers utilizing the micromagnetic simulations.We find that the reversible annihilation and creation of skyrmions can be realized with the electric field via the strain mediated magnetoelastic coupling.In addition,we also demonstrate controllable manipulation of individual skyrmion,which opens a new platform for constructing magnetic field-free and low-energy dissipation skyrmion based media.

Room-temperature creation and manipulation of skyrmions in MgO/FeNiB/Mo multilayers

Magnetic skyrmions in multilayer structures are considered as a new direction for the next generation of storage due to their small size,strong anti-interference ability,high current-driven mobility,and compatibility with existing spintronic technology.In this work,we present a tunable room temperature skyrmion platform based on multilayer stacks of MgO/FeNiB/Mo.We systematically studied the creation of magnetic skyrmions in MgO/FeNiB/Mo multilayer structures with perpendicular magnetic anisotropy(PMA).In these structures,the magnetic anisotropy changes from PMA to in-plane magnetic anisotropy(IMA)as the thickness of FeNiB layer increases.By adjusting the applied magnetic field and electric current,stable and high-density skyrmions can be obtained in the material system.The discovery of this material broadens the exploration of new materials for skyrmion and promotes the development of spintronic devices based on skyrmions.

磁性Skyrmions信息存储器的微磁学模拟

为了解决当前存储信息技术的发展问题,人们发现了一种新型的高密度信息载体——磁性Skyrmions.实现对磁性Skyrmions生成和输运的微观调控是完成其器件化过程中至关重要的一步.本文基于微磁学模拟方法,通过OOMMF软件首先在纳米盘模型中详细研究了自旋极化电流注入对磁性Skyrmions生成的影响.在局域电流注入过程中,调节自旋极化电流密度、电流注入时间和注入电流面积,得到了不同注入电流面积下阈值电流密度以及注入时间对Skyrmions拓扑数的影响;在全局电流注入中,实现了两种手性Skyrmions的生成,并讨论了模型尺寸对于Skyrmions拓扑数和尺寸的影响,对于低能耗、高密度新型Skymions信息存储器的研发提供了理论指导.

SKYRMIONS IN GROSS-PITAEVSKII FUNCTIONALS

In Bose-Einstein condensates （BECs）, skyrmions can be characterized by pairs of linking vortex rings coming from two-component wave functions. Here we construct skyrmions by studying critical points of Gross-Pitaevskii functionals with two-component wave functions. Using localized energy method, we rigorously prove the existence, and describe the configurations of skyrmions in such BECs.

1-25 Fractional Skyrmions and Their Molecules

We study a Skyrme-type model with a quadratic potential for a field with S2 vacua. The model contains molecules of half Skyrmions, each of them is a global (anti-)monopole with baryon number 1=2. We numerically construct solutions with baryon numbers one through six, and find stable solutions which look like beads on rings. We also construct a molecule with fractional Skyrmions having the baryon numbers 1=3+2=3, by adding a linear potential term.

1-26 Gravitating BPS Skyrmions

The BPS Skyrme model has many exact analytic solutions in flat space. We generalize the model to a curved space or spacetime and find that the solutions can only be BPS for a constant time-time component of the metric tensor. We find exact solutions on the curved spaces: a 3-sphere and a 3-hyperboloid; and we further find an analytic gravitating Skyrmion on the 3-sphere. For the case of a nontrivial time-time component of the metric, we suggest a potential for which we find analytic solutions on anti-de Sitter and de Sitter spacetimes in the limit of no gravitational backreaction. We take the gravitational coupling into account in numerical solutions and show that they are well approximated by the analytic solutions for weak gravitational coupling.

Rotation Stabilises 2D Skyrmions

We present a study of 2D Skyrmions under rotation. The purpose of this study is to establish the result of the rotation on the stability of 2D Skyrmions. Usually the 2D skyrmions are metastable unless the underlying geometry introduces a characteristic length or e.g. magnetic fifield is present in the problem. We have used a previous study of the rotating plane which proves the appearance of curvature as a result of the rotation. The curvature of the rotating disk introduces length and plays here the role of strength of the angular momentum of the field. We have shown that this additional length scale introduced by the curvature stabilises the 2D Skyrnions under

Lorentz transmission electron microscopy for magnetic skyrmions imaging

Magnetic skyrmions have interesting properties,including their small size,topological stability,and extremely low threshold current for current-driven motion.Therefore,they are regarded as promising candidates for next-generation magnetic memory devices.Lorentz transmission electron microscopy(TEM)has an ultrahigh magnetic domain resolution(~2 nm),it is thus an ideal method for direct real-space imaging of fine magnetic configurations of ultra-small skyrmions.In this paper,we describe the basic principles of Lorentz-TEM and off-axis electron holography and review recent experimental developments in magnetic skyrmion imaging using these two methods.

Zero-field skyrmions in FeGe thin films stabilized through attaching a perpendicularly magnetized single-domain Ni layer

A numerical study reports that the zero-field skyrmions in Fe Ge thin films are stabilized when a Fe Ge layer is exchange coupled to a single-domain Ni layer,which has been magnetized perpendicularly.Due to the small thickness,an easy-plane anisotropy in the Fe Ge layer is taken into account,and the skyrmion-crystal state is favored to appear for low anisotropies and intermediate Fe Ge/Ni interlayer exchange couplings,and finally transformed from a labyrinth-like and into an out-ofplane uniform state for the large couplings or into an in-plane state for the high anisotropies.Furthermore,the maximum skyrmion charge number is bigger for the periodic and fixed boundary conditions with an out-of-plane magnetization;on the contrary,the Bloch-type skyrmions can be frozen and stabilized for the larger couplings on the fixed boundary with an in-plane magnetization,similar to the experimental results of the magnetic-field-induced skyrmions.Finally,the skyrmion charge number and diameter both decrease if the nonmagnetic defects exist,and the skyrmion centers are prone to being captured by defect sites.This work evidences that the ensembles of homochiral skyrmions stabilized in the multilayers fabricated by well-established technologies present a roadmap to design new classes of the materials that can host skyrmions.

Dynamics of magnetic skyrmions

We review the recent progress on the magnetic skyrmions in chiral magnetic materials. The magnetic skyrmion is a topological spin configuration with localized spatial extent, which could be thought of as an emergent rigid particle, owing to its particular topological and chiral properties. Static skyrmionic configurations have been found in various materials with different transport and thermodynamic properties. The magnetic skyrmions respond to externally applied fields in a very unique way, and their coupling to other quasiparticles in solid-state systems gives rise to the emergent electrodynamics.Being not only theoretically important, the magnetic skyrmion is also very promising to be the information carrier in next generation spintronic devices.

Magnetic skyrmions:Basic properties and potential applications

Magnetic skyrmions are particle-like topological magnetic textures that are potential information carriers in future spintronics.An enormous body of research confirms their existence in a broad range of magnetic materials since their first discovery in 2009.To date,magnetic skyrmions can not only be found in asymmetric systems but also in centrosymmetric ones.Notably,engineered magnetic multilayers are promising structures for skyrmion-based spintronics because they can stabilize small-sized skyrmions at room temperature and facilitate their electric manipulation.In this overview,we introduce the topological nature,their special properties,and nucleation methods of skyrmions,and show their potential for applications.Perspectives on skyrmionic devices and developments toward other,more three-dimensional particle-like magnetic nanostructures,are discussed at the end.

Magnetic skyrmions:materials,manipulation,detection,and applications in spintronic devices

Magnetic skyrmions are vortex-like spin configurations that possess nanometric dimensions,topological stability,and high controllability through various external stimuli.Since their first experimental observation in helimagnet MnSi in 2009,magnetic skyrmions have emerged as a highly promising candidate for carrying information in future high-performance,low-energy-consumption,non-volatile information storage,and logical calculation.In this article,we provide a comprehensive review of the progress made in the field of magnetic skyrmions,specifically in materials,manipulation,detection,and application in spintronic devices.Firstly,we introduce several representative skyrmion material systems,including chiral magnets,magnetic thin films,centrosymmetric materials,and Van der Waals materials.We then discuss various methods for manipulating magnetic skyrmions,such as electric current and electric field,as well as detecting them,mainly through electrical means such as the magnetoresistance effect.Furthermore,we explore device applications based on magnetic skyrmions,such as track memory,logic computing,and neuromorphic devices.Finally,we summarize the challenges faced in skyrmion research and provide future perspectives.

Progress on elliptical magnetic skyrmions

Magnetic skyrmions,the topological spin textures firstly observed in chiral magnets,have aroused huge interest due to their emergent electromagnetism and potential applications in spintronics.Over the last decade,significant efforts have been devoted to skyrmion generation,stabilization,and dynamics.In most cases,the theoretical and experimental investigations have been performed in the materials where the skyrmions have a circular shape.As we know,magnetic anisotropy(K_(u))and Dzyaloshinskii-Moriya interaction(DMI)play key roles in the stabilization of the skyrmions in chiral magnets.Therefore,modifying the Kand DMI provide new degrees of freedom for studying the related physics and applications of skyrmions in addition to engineering their energetics and sizes.In this review,the latest progress on the study of the anisotropic deformation of magnetic skyrmions(i.e.,elliptical magnetic skyrmions)is summarized.The physical origins and important advantages of elliptical magnetic skyrmions are mainly focused on.This review gives an insight into the understanding of the physical mechanisms of elliptical magnetic skyrmion-hosting systems.

Elongation of skyrmions by Dzyaloshinskii-Moriya interaction in helimagnetic films

Distortion of skyrmions arouses much attention recently due to the exotic topologic al and dynamic properties.Investigating the formation mechanism and dynamical behavior of the deformed skyrmions promotes practical spintronic applications.Elongation,as a typical form of deformation,has been discovered both in experiments and in theories.However,the intrinsic mechanism is absent.Here,the coexistence of zero-field circular and elongated skyrmions in helimagnetic films is observed.The elongated skyrmions,which are determined by the intrinsic Dzyaloshinskii-Moriya interaction(DMI),carry the same topological charge as the circular ones and show the skyrmion Hall effect.Currentdriven dynamics reveal again the significant role of the intrinsic DMI playing in the skyrmion elongation.

Generation and manipulation of skyrmions and other topological spin structures with rare metals

Skyrmions are nano-scale quasi-particles with topological protection,which have potential applications in next-generation spintronics-based information storage.Numerous papers have been published to review various aspects of skyrmions,including physics,materials and applications.However,no review paper has focused on rare metals which play important roles in nucleating and manipulating skyrmions and other topological states.In this paper,various roles of rare metals have been classified and summarized,which can tune Curie temperature(TC),Dzyaloshinskii-Moriya interaction(DMI),magnetocrystalline anisotropy,Ruderman-Kittel-Kasuya-Yosida(RKKY)interaction and four-spin interaction so as to trigger the generation of skyrmions and other topological spin structures.The materials covered include typical B20 crystals,various layered systems with interfacial DMI,frustrated materials,antiferromagnets,ferrimagnets,twodimensional(2D)materials,etc.In addition,the rare-earth(RE)permanent magnets can provide an energy barrier and enrich the dynamic behaviors of skyrmions,which has also been reviewed.

Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile,while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Magnetic skyrmions in curved geometries

In curved geometries,a lot of novel curvaturedriven effects are discovered due to the curvature-induced effective anisotropy and Dzyaloshinskii-Moriya interaction.Curvature effect also provides means to modify conventional results and launch new functionalities in study of magnetic skyrmions.Magnetic skyrmions are particle-like spin textures with topological protections.It has been found in several magnetic materials and has been one of the research hotspots in magnetism and spintronics as the carriers of information.BothDzyaloshinskii-Moriya interaction and anisotropy have significant effects on the formation and stability of magnetic skyrmions.The magnetic skyrmions in curved geometries show some novel characteristics,and the study in this field may promote the development of magnetic skyrmions.This article provides a review of the present state of the research on skyrmions in curved geometries including curved nanotracks,thin films with curved defect,nanotubes,spherical and hemispherical shells.The reviewmainly covers three aspects,the formation and stability of skyrmions,the shape and size of skyrmions,and the dynamical behaviors of skyrmions in curved geometries.

Single-bit full adder and logic gate based on synthetic antiferromagnetic bilayer skyrmions

Skyrmion-based devices are promising candi-dates for non-volatile memory and low-delay time com-putation.Many skyrmion-based devices execute operation by controlling skyrmion trajectory,which can be impeded by the skyrmion Hall effect.Here,the design of skyrmion-based arithmetic devices built on synthetic antiferromag-netic(SyAF)structures is presented,where the structure can greatly suppress skyrmion Hall effect.In this study,the operations of skyrmion-based half adder,full adder,and XOR logic gate are executed by introducing geometric notches and tilted edges,which can annihilate or diverge skyrmion.Performance of these skyrmion-based devices is evaluated,where the delay time and energy-delay product of the single-bit full adder are 1.95 ns and 2.50×10^(-22)Js,which are only 12%and 79%those of the previously proposed skyrmion-based single-bit full adder.This improvement is significant in the construction of ripple-carry adder and ripple-carry adder-subtractor.Therefore,our skyrmion-based SyAF arithmetic device is a promising candidate to develop high-speed spintronic devices.

The relation between the radii and the densities of magnetic skyrmions

Compared with the traditional magnetic bubble,a skyrmion has a smaller size,and better stability and therefore is considered as a very promising candidate for future memory devices.When skyrmions are manipulated,erased and created,the density of skyrmions can be varied,however the relationship between the radii and the densities of skyrmions needs more exploration.In this paper,we study this problem both theoretically and by using the lattice simulation.The average radius of skyrmions as a function of material parameters,the strength of the external magnetic field and the density of skyrmions is obtained and verified.With this explicit function,the skyrmion radius can be easily predicted,which is helpful for the future study of skyrmion memory devices.

Electric field manipulation of magnetic skyrmions

Magnetic skyrmions are vortex-like swirling spin textures that are promising candidates for carrying information bits in future magnetic memories or logic circuits.To build skyrmionic devices,researchers must electrically manipulate magnetic skyrmions to enable easy integration into modern semiconductor technology.This operation generally uses a spin-polarized current,which unavoidably causes high energy dissipation and Joule heating.Thus,the electric-field strategy is a hopeful alternative for electrically manipulating the skyrmions due to the strategy’s negligible Joule heating and low energy cost.In this review,we systematically summarize the theoretical and experimental development of the electricalfield manipulation of magnetic skyrmions over the past decade.We review the following magnetic systems and physical mechanisms:(ⅰ)ultra-thin multilayer films with accumulation and release of interfacial charge,(ⅱ)singlephase multiferroic material with magneto-electric coupling,(ⅲ)ferromagnetic/ferroelectric(FM/FE)multiferroic heterostructure with magneto-elastic coupling.Finally,we consider future developmental trends in the electric-field manipulation of magnetic skyrmions and other topological magnetic domain structures.