Sayantika Bhowal, S. Satpathy, Pratik Sahu
Skyrmions were originally introduced in Particle Physics as a possible mechanism to explain the stability of particles. Lately the concept has been applied in Condensed Matter Physics to describe the newly discovered topologically protected magnetic configurations called the magnetic Skyrmions. This elementary review introduces the concept at a level suitable for beginning students of Physics.
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Axisymmetric solitonic states (chiral skyrmions) have been predicted theoretically more than two decades ago. However, until recently they have been observed in a form of skyrmionic condensates (hexagonal lattices and other mesophases). In this paper we report experimental and theoretical investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers two years ago (Science 341 , 636 (2013)). The results of spin-polarized scanning tunneling microscopy analyzed within the continuum and discrete models provide a consistent description of isolated skyrmions in thin layers. The exi…
A magnetic skyrmion is a topological object that can exist as a solitary embedded in the vast ferromagnetic phase, or coexists with a group of its "siblings" in various stripy phases as well as skyrmion crystals (SkXs). Isolated skyrmions and skyrmions in an SkX are circular while a skyrmion in other phases is a stripe of various forms. Unexpectedly, the sizes of the three different types of skyrmions depend on material parameters differently. For chiral magnetic films with exchange stiffness constant $A$, the Dzyaloshinskii-Moriya interaction (DMI) strength $D$, and perpendicular magnetic ani…
Symmetry breaking together with strong spin-orbit interaction give rise to many exciting phenomena within condensed matter physics. A recent example is the existence of chiral spin textures, which are observed in magnetic systems lacking inversion symmetry. These chiral spin textures, including domain walls and magnetic skyrmions, are both fundamentally interesting and technologically promising. For example, they can be driven very efficiently by electrical currents, and exhibit many new physical properties determined by their real-space topological characteristics. Depending on the details of…
Magnetic phase transitions are a test bed for exploring the physics of non-equilibrium phenomena in condensed matter, which become even more complex when topological constraints are involved. In particular, the investigation of skyrmions and skyrmion lattices offers insight into fundamental processes of topological-charge creation and annihilation upon changing the magnetic state. Nonetheless, the exact physical mechanisms behind these phase transitions remain unresolved. Here, we have systematically compared ultra-thin films with isotropic and anisotropic Dzyaloshinskii-Moriya interactions (D…
This article aims at giving a general presentation of spintronics, an important field of research developing today along many new directions in physics of condensed matter. We tried to present simply the physical phenomena involved in spintronics -- no equations but many schematics. We also described the applications of spintronics, those of today and those expected to have an important impact on the next developments of the information and communication technologies.
Magnetic skyrmions (or vortices) are spatially inhomogeneous spin textures localized in nanoscale cylindrical regions. Topological protection and small size make skyrmions especially attractive for the study of spin topology and technologies wherein information is carried by the electron spin further to, or instead of the electron charge. Despite achievements in the synthesis of materials where axisymmetric magnetic skyrmions can be stabilized and characterized, there is disproportionate progress in elucidating the basic properties. The Perspective aims to bridge this gap and deliver an intell…
The dynamics of antiferromagnets is a current hot topic in condensed matter physics and spintronics. However, the dynamics of insulating antiferromagnets cannot be excited by an electric current, which is a method usually used to manipulate ferromagnetic metals. Here, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to manipulate insulating antiferromagnetic textures. We analytically and numerically study the dynamics of an antiferromagnetic skyrmion driven by a magnetic anisotropy gradient. Our analytical calculations demonstrate that such a magnet…
Higher-dimensional magnetic Skyrmions
本文将二维手性磁体中的磁Skyrmion理论推广至三维及$S^3$目标空间的高维理论，需4维磁化矢量，可通过合成维度实现；研究发现引入Skyrme项后能谱扩展为亚稳态、不稳定及稳定孤子态。
The effects of Landau level mixing and finite thickness of the two-dimensional electron gas on the relative stability of skyrmion and single spin-flip excitations at Landau level filling factor $ν=1$ have been investigated. Landau level mixing is studied by fixed-phase diffusion Monte Carlo and finite thickness is included by modifying the effective Coulomb interaction. Both Landau level mixing and finite thickness lower skyrmion excitation energies and favor skyrmions with fewer spin flips. However, the two effects do not work `coherently'. When finite thickness is included the effect of Land…
Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for experimental investigation of topological solitons and understanding of their nonsingular field configurations. Here we introduce a paradigm of facile skyrmionic networks with mutually-orthogonal orientations of constituent isolated skyrmions. Such networks are envisioned as a novel concept of spintronic devices and are presumably responsible for precursor …
RKKY-like interactions between two magnetic skyrmions
本研究揭示了Skyrmion之间的RKKY类相互作用，具有各向异性与周期性振荡特性，为Skyrmion超结构设计提供了新原理。
Starting with a Chern-Simons theory, we derive an effective action for interacting quantum Hall skyrmions that takes into account both large-distance physics and short-distance details as well. We numerically calculate the classical static skyrmion profile from this action and find excellent agreement with other, microscopic calculations over a wide range of skyrmion sizes including the experimentally relevant one. This implies that the essential physics of this regime might be captured by a continuum classical model rather than resorting to more microscopic approaches. We also show that the s…
Controlling electric and magnetic properties of matter by laser beams is actively explored in the broad region of condensed matter physics, including spintronics and magneto-optics. Here we theoretically propose an application of optical and electron vortex beams carrying intrinsic orbital angular momentum to chiral ferro- and antiferro- magnets. We analyze the time evolution of spins in chiral magnets under irradiation of vortex beams, by using the stochastic Landau-Lifshitz-Gilbert equation. We show that beam-driven nonuniform temperature lead to a class of ring-shaped magnetic defects, what…
We present a Hartree-Fock study of the competition between disorder and interactions in quantum Hall ferromagnets near $ν=1$. We find that the ground state at $ν=1$ evolves with increasing interaction strength from a quasi-metallic paramagnet, to a partially spin-polarized ferromagnetic Anderson insulator, and to a fully spin-polarized ferromagnet with a charge gap. Away from $ν=1$, the ground state evolves from a conventional Anderson insulator, to a conventional quasiparticle glass, and finally to a ferromagnetic Skyrmion quasiparticle glass. These different regimes can be measured in low-te…
Particle-continuum-medium duality of skyrmions
本文揭示了斯格明子兼具粒子与连续介质特性的对偶性，打破了其不可分割的传统认知，阐明了其作为构建模块或粘合剂形成级联斯格明子袋等复合结构的规则与物理机制。
Time-reversal invariant topological skyrmion phases
本文引入了在时间反演不变系统中实现的拓扑斯格明子相，揭示了由$\mathbb{Z}_2$自旋斯格明子不变量定义的隐藏体-边界对应关系，为二维系统提供了更精细的拓扑描述，并指出可通过ARPES和输运测量验证。
This is a narrative of the basic theoretical ideas of axisymmetric two-dimensional solitons and of their connection to basic experiments on magnetic compounds. A shortened and edited version appeared in Physics Today.
Topological solitons have been studied for decades in classical field theories, and have started recently to impact condensed matter physics. Among those solitons, magnetic skyrmions are two-dimensional particle-like objects with a continuous winding of the magnetization, and magnetic Hopfions are three-dimensional topological solitons that can be formed from a closed loop of a twisted skyrmion string. Whereas intense research is underway with magnetic skyrmions towards a fundamental understanding and potential applications in advanced storage and logic devices, the experimental creation and c…
Magnetic skyrmions have recently attracted great attentions. However they are harbored in very limited numbers of magnets up to now. The search of new helimagnetic materials is thus an urgent topic in the field of skyrmion physics. In this letter, we provide a guideline on this issue, and discuss the possibility of realizing skyrmions in a new family of molybdenum nitrides $A_2$Mo$_3$N ($A$=Fe, Co, and Rh). By means of the first-principles calculations, the electronic and magnetic structures are calculated and the existence of strong Dzyaloshinskii-Moriya interaction is demonstrated.
Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir Computing paradigm does not require any knowledge of the reservoir topology or node weights for training purposes and can therefore utilize naturally existing networks formed by a wide variety of physical processes. Most efforts prior to this have focused on utilizing memristor techniques to implement recursive neural networks. This paper examines the potential of s…
After a decade of intense theoretical and experimental efforts, demonstrating braiding of Majorana modes remains an unsolved problem in condensed matter physics due to platform specific challenges. In this work, we propose topological superconductor -- magnetic multilayer heterostructures with on-chip microwave cavity readout as a novel platform for initializing, braiding and reading out Majorana modes. Stray fields from a skyrmion in the magnetic layers can nucleate a vortex in the topological superconducting layer. Such a vortex is known to host Majorana bound states at its core. Through ana…
Magnetic skyrmions are nanoscale whirls of magnetism that can be propagated with electrical currents. The repulsion between skyrmions inspires their use for reversible computing based on the elastic billiard ball collisions proposed for conservative logic in 1982. Here we evaluate the logical and physical reversibility of this skyrmion logic paradigm, as well as the limitations that must be addressed before dissipation-free computation can be realized.
The theoretical study considers chiral spin texture induced in a 2D electron gas (2DEG) by magnetic skyrmions. We calculate the electron gas spin density as a linear response to the exchange interaction between the 2DEG and the magnetization field of a magnetic skyrmion. Two physically distinct regimes occur. When the size of the skyrmion is larger than the inverse Fermi wavevector $k_F^{-1}$, the spin density response follows the magnetization profile of the skyrmion. In the opposite case of a small skyrmion the emerging spin structure of 2DEG has a characteristic size of $k_F^{-1}$ and the r…
Effective Theory of Ultrafast Skyrmion Nucleation
针对激光诱导超快斯格明子成核缺乏直观物理机制理解的问题，提出粗粒化有效理论，通过热激活描述成核与湮灭过程，与模拟及实验吻合且降低计算复杂度，还为优化及预测新湮灭路径提供指导。
The Reservoir Computing (RC) paradigm posits that sufficiently complex physical systems can be used to massively simplify pattern recognition tasks and nonlinear signal prediction. This work demonstrates how random topological magnetic textures present sufficiently complex resistance responses for the implementation of RC as applied to A/C current pulses. In doing so, we stress how the applicability of this paradigm hinges on very general dynamical properties which are satisfied by a large class of physical systems where complexity can be put to computational use. By harnessing the complex res…
Skyrmions and skyrmion crystal (SkX) discovered in chiral magnets show unique physical properties due to their nontrivial topology such as the stability against the annihilation and the motion driven by the ultralow current density, which can be advantageous for the device applications such as magnetic memories. Especially, the chiral dynamics, i.e., the velocity perpendicular to the force acting on a skyrmion, is a key to avoid the impurity potential and enhances its mobility. However, the collective pinning of SkX occurs by the disorder, which is crucial for its low energy properties. Here, …
Understanding the physical properties of magnetic skyrmions is important for fundamental research with the aim to develop new spintronic device paradigms where both logic and memory can be integrated at the same level. Here, we show a universal model based on the micromagnetic formalism that can be used to study skyrmion stability as a function of magnetic field and temperature. We consider ultrathin, circular ferromagnetic magnetic dots. Our results show that magnetic skyrmions with a small radius compared to the dot radius are always metastable, while large radius skyrmions form a stable gro…
Audio Classification with Skyrmion Reservoirs
本文提出一种基于斯格明子混合储层的物理储层计算方法，在纳秒级时间尺度上实现语音数字分类，准确率达97.4%、词错误率低于1%，为物质内储层计算树立了新基准。
The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBS), 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 sys…
The static and dynamic states of Néel skyrmions in ultrathin ferromagnetic films with interfacial Dzyaloshinskii-Moriya interaction (DMI) have been micromagnetically simulated as functions of the interfacial DMI strength and applied static magnetic field. Findings reveal that while the breathing, counterclockwise (CCW) and clockwise (CW) rotational eigenmodes exist in the skyrmion lattice (SkL) phase, only the first two modes are present in the isolated skyrmion (ISk) phase. Additionally, the eigenfrequency of the CCW mode is insensitive to the magnetic-field driven SkL-ISk phase transition, a…
Skyrmions, novel topologically stable spin vortices, hold promise for next-generation magnetic storage due to their nanoscale domains to enable high information storage density and their low threshold for current-driven motion to enable ultralow energy consumption. One-dimensional (1D) nanowires are ideal hosts for skyrmions since they not only serve as a natural platform for magnetic racetrack memory devices but also can potentially stabilize skyrmions. Here we use the topological Hall effect (THE) to study the phase stability and current-driven dynamics of the skyrmions in MnSi nanowires. Th…
Magnetic Skyrmion: From Fundamental Physics to Pioneering Applications
本文综述了磁性斯格明子从基础物理到存储与计算应用的进展，涵盖拓扑概念、读写机制及类脑计算与拓扑量子计算潜力。
The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modelled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statist…
Ultrafast manipulations of nanoscale skyrmioniums
本文通过高通量微磁模拟提出纳米尺度 skyrmioniums 的超快产生、切换、极性反转与稳定驱动方法，并揭示相关拓扑磁结构机制。
Magnetic skyrmion, vortex-like swirling topologically stable spin configurations, is appealing as information carrier for future nanoelectronics, owing to the stability, small size and extremely low driving current density. One of the most promising applications of skyrmion is to build racetrack memory (RM). Compared to domain wall-based RM (DW-RM), skyrmion-based RM (Sky-RM) possesses quite a few benefits in terms of energy, density and speed etc. Until now, the fundamental behaviors, including nucleation/annihilation, motion and detection of skyrmion have been intensively investigated. Howev…
Skyrmions are topologically protected, two-dimensional, localized hedgehogs and whorls of spin. Originally invented as a concept in field theory for nuclear interactions, skyrmions are central to a wide range of phenomena in condensed matter. Their realization at room temperature (RT) in magnetic multilayers has generated considerable interest, fueled by technological prospects and the access granted to fundamental questions. The interaction of skyrmions with charge carriers gives rise to exotic electrodynamics, such as the topological Hall effect (THE), the Hall response to an emergent magnet…
Machine learning techniques to construct detailed phase diagrams for skyrmion systems
该研究使用卷积神经网络结合蒙特卡罗模拟，对包含铁磁交换和DM相互作用的自旋模型进行相分类，成功构建了详细的磁场-温度相图，并准确识别了复杂的中间拓扑相。
Magnetic skyrmions are small swirling topological defects in the magnetization texture stabilized by the protection due to their topology. In most cases they are induced by chiral interactions between atomic spins existing in non-centrosymmetric magnetic compounds or in thin films in which inversion symmetry is broken by the presence of an interface. The skyrmions can be extremely small with diameters in the nanometer range and, importantly, they behave as particles that can be moved, created or annihilated, making them suitable for abacus-type applications in information storage, logic or neu…
The ideal limit of rhombohedral graphene: Dynamical skyrmion lattices and their excitations
本文提出菱面体石墨烯的理想极限，解析证明短程排斥可稳定层赝自旋斯格明子晶格并产生陈能带，从而揭示莫尔体系中相互作用驱动拓扑的实空间机制及其集体激发。
Laminar and transiently disordered dynamics of a magnetic skyrmion pipe flow
本研究揭示了磁性斯格明子在管道通道中流动的层流与瞬态无序动力学，发现驱动电流可调控其晶格结构与流宽，并促发管流向明渠流转变，揭示了斯格明子的流体特性。
We discover that the multiple degrees of freedom associated with magnetic skyrmions: size, position, and chirality, can all be used to control the Josephson effect and 0-pi transitions occurring in superconductor/magnetic skyrmion/superconductor junctions. In the presence of two skyrmions, the Josephson effect depends strongly on their relative chirality and leads to the possibility of a chirality-transistor effect for the supercurrent where the critical current is changed by several orders of magnitude simply by reversing the chirality of a magnetic skyrmion. Moreover, we demonstrate that the…
Diffusion asymmetry of repulsive skyrmions in structured environment
研究揭示了磁通在结构环境中因相互作用产生的不对称扩散行为，通过不对称门控实现动态调控，为磁学、活物质和统计物理提供新见解。
Theoretical investigation demonstrates that the composite bilayer (i.e., chiral-magnetic/ferroelectric bilayer) offers the possibility of electric-induced magnetic Skyrmions [Phys. Rev. B \textbf{94}, 014311 (2016)]. In this Article, we propose a micromagnetic model to physically manipulate magnetic Bloch Skyrmions propagating in a chiral-magnetic thin film with a polarized ferroelectric essential to drive the system through the converse magnetoelectric effect. Effects caused by different velocities of the propagation, sizes of the thin film, and strength of the magnetoelectric couplings stron…
We deal with magnetic structures that attain integer and half-integer skyrmion numbers. We model and solve the problem analytically, and show how the solutions appear in materials that engender distinct, very specific physical properties, and use them to describe their topological features. In particular, we found a way to model skyrmion with a large transition region correlated with the presence of a two-peak skyrmion number density. Moreover, we run into the issue concerning the topological strength of a vortex-like structure and suggest an experimental realization, important to decide how t…
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…
We discuss the contribution of magnetic Skyrmions to the Hall viscosity and propose a simple way to identify it in experiments. The topological Skyrmion charge density has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In an electrically neutral system, the Skyrmion charge density is directly related to the thermal Hall conductivity. These results are direct consequences of the field theory Ward identities, which relate various physical quantities based on symmetries and have been previously applied to quantum Hall systems.
Magnetic skyrmions have been the subject of extensive experimental studies in ferromagnetic thin films and multilayers, revealing a diversity in their size, stability and internal structure. While the orthodox skyrmion theory focuses on the Dzyaloshinskii-Moryia interaction (DMI) and neglects higher-order energy terms, it is becoming clear that the full stray field energy needs to be taken into account to understand these recent observations. Here we present a micromagnetic study based on rigorous mathematical analysis which allows to account for the full stray field energy in the thin film an…
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