We study the geometrical conditions for stabilizing magnetic skyrmions in cylindrical nanostrips and nanotubes of ferromagnetic materials with chiral interactions. We obtain the low-temperature equilibrium state of the system implementing a simulation annealing technique for a classical spin Hamiltonian with competing isotropic exchange and chiral interactions, radial anisotropy and an external field. We address the impact of surface curvature on the formation, the shape and the size of magnetic skyrmions. We demonstrate that the evolution of the skyrmion phase with the curvature is controlled by the competition between two characteristic lengths, namely the curvature radius, $R$ (geometrical length) and the skyrmion radius, $R_{sk}$ (physical length). In narrow nanotubes ($R<R_{sk}$) the skyrmion phase evolves to a stripe phase, while in wide nanotubes ($R>R_{sk}$) a mixed skyrmion-stripe phase emerges. Most interestingly, the mixed phase is characterized by spatially separated skyrmions from stripes owing to the direction of the applied field relative to the surface normal. In the stability regime ($R \gtrsim R_{sk}$) skyrmions remain circular and preserve their size as a consequence of their topological protection. Zero-field skyrmions are shown to be stable on curved nanoelements with free boundaries within the same stability region ($R\gtrsim R_{sk}$). The experimental and technological perspectives from the stability of skyrmions on cylindrical surfaces are discussed.
Geometric symmetry and size-dependent skyrmion phase transitions in magnetic nanostructures
School of Materials and Physics, China University of Mining and Technology（中国矿业大学材料科学与工程学院）；College of Physics and Information Engineering, Shanxi Normal University（山西师范大学物理与信息工程学院）
Magnetic skyrmions have the potential to provide solutions for low-power, high-density data storage and processing. One of the major challenges in developing skyrmion-based devices is the skyrmions' magnetic stability in confined helimagnetic nanostructures. Through a systematic study of equilibrium states, using a full three-dimensional micromagnetic model including demagnetisation effects, we demonstrate that skyrmionic textures are the lowest energy states in helimagnetic thin film nanostructures at zero external magnetic field and in absence of magnetocrystalline anisotropy. We also report…
Increasing amounts of information force the continuous improvement of information storage and processing technologies, further device miniaturization, and their efficiency increase. Magnetic skyrmions, topological quasiparticles, and the smallest stable magnetic textures possess intriguing properties and potential for data storage applications. Hybrid nanostructures with elements of different magnetization orientations can offer additional advantages for developing skyrmion-based spintronic and magnonic devices. We show that an Néel-type skyrmion confined within a nanodot placed on top of a fe…
A magnetic skyrmionium is a nontopological soliton, which has a doughnut-like out-of-plane spin texture in thin films, and can be phenomenologically viewed as a coalition of two topological magnetic skyrmions with opposite topological numbers. Due to its zero topological number ($Q=0$) and doughnut-like structure, the skyrmionium has its distinctive characteristics as compared to the skyrmion with $Q=\pm 1$. Here we systematically study the generation, manipulation and motion of a skyrmionium in ultrathin magnetic nanostructures by applying a magnetic field or a spin-polarized current. It is f…
Magnetic skyrmions are chiral spin structures that have recently been observed at room temperature (RT) in multilayer thin films. Their topological stability should enable high scalability in confined geometries - a sought-after attribute for device applications. While umpteen theoretical predictions have been made regarding the phenomenology of sub-100 nm skyrmions confined in dots, in practice their formation in the absence of an external magnetic field and evolution with confinement remain to be established. Here we demonstrate the confinement-induced stabilization of sub-100 nm RT skyrmion…
Synthetic antiferromagnet (SAF) nanostructures with interfacial Dzyaloshinskii-Moriya interaction can host topologically distinct spin textures such as skyrmions and thus are regarded as promising candidates for both spintronics and magnonics applications. Here, we present comprehensive micromagnetic simulations of such material systems and discuss the rich phase diagrams that contain various types of magnetic configurations. Aside from the static properties, we further discuss the resonant excitations of the calculated magnetic states which include individual skyrmions and skyrmioniums. Final…
We study the modification of micromagnetic configurations in nanostructures, due to the Dzyaloshinskii-Moriya interaction (DMI) that appear at the interface of an ultrathin film. We show that this interaction leads to new micromagnetic boundary conditions that bend the magnetization at the edges. We explore several cases of ultrathin film nanostructures that allow analytical calculations (1D systems, domain walls, cycloids and skyrmions), compare with fully numerical calculations, and show that a good physical understanding of this new type of micromagnetics can be reached. We particularly foc…
Recent studies have demonstrated that skyrmionic states can be the ground state in thin-film FeGe disk nanostructures in the absence of a stabilising applied magnetic field. In this work, we advance this understanding by investigating to what extent this stabilisation of skyrmionic structures through confinement exists in geometries that do not match the cylindrical symmetry of the skyrmion -- such as as squares and triangles. Using simulation, we show that skyrmionic states can form the ground state for a range of system sizes in both triangular and square-shaped FeGe nanostructures of $10\,\…
We report the direct evidence of field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of external magnetic field the character of such long-range skyrmion interactions change from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skrymion-edge distances as function of applied magnetic field shows quantitative agreement with the results of micro…
In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exi…
In this letter we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the external magnetic field applied. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these dia…
Bias-field control of the Neel skyrmion nonlinearity in a confined nanostructure
Kotel’nikov Institute of Radio-Engineering and Electronics of RAS（俄罗斯科学院科捷利尼科夫无线电电子研究所）；Moscow Institute of Physics and Technology (National Research University)（莫斯科物理技术学院（国立大学））；Bauman Moscow State Technical University（鲍曼莫斯科国立技术大学）；National Research University Moscow Power Engineering Institute（莫斯科动力学院国立研究大学）
We study the magnetic field dependence of the dielectric response of large cylindrical molecules such as nanotubes. When a field-induced level crossing takes place, an applied electric field causes a linear instead of the usual quadratic Stark effect. This results in a large dielectric response. Explicit calculations are performed for doped nanotubes and a rich structure in the real part of the low-frequency dielectric function $ε'(H)$ is found when a magnetic field is applied along the cylinder axis. It is suggested that studies of $ε'(H, T)$ can serve as a spectroscopic tool for the investig…
Topological magnetic charge Q is a fundamental parameter that describes the magnetic domains and determines their intriguing electromagnetic properties. The ability to switch Q in a controlled way by electrical methods allows for flexible manipulation of electromagnetic behavior in future spintronic devices. Here we report the room-temperature current-controlled topological magnetic transformations between Q = -1 skyrmions and Q = 0 stripes or type-II bubbles in a kagome crystal Fe$_3$Sn$_2$. We show that the reproducible and reversible skyrmion-bubble and skyrmion-stripe transformations can b…
Magnetic skyrmions are localized particle-like nontrivial swirls that are promising in building high-performance topological spintronic devices. The read-out functions in skyrmionic devices require the translation of magnetic skyrmions to electrical signals. Here, we report combined real-space magnetic imaging and anisotropic magnetoresistance studies on dipolar skyrmions. A single skyrmion chain and single skyrmion are observed using Lorentz transmission electron microscopy imaging. Meanwhile, the field, helicity, and skyrmion count dependence of anisotropic magnetoresistance of the Fe3Sn2 na…
We study the recently introduced 'critically coupled' model of magnetic Skyrmions, generalising it to thin films with curved geometry. The model feels keenly the extrinsic geometry of the film in three-dimensional space. We find exact Skyrmion solutions on spherical, conical and cylindrical thin films. Axially symmetric solutions on cylindrical films are described by kinks tunnelling between 'vacua'. For the model defined on general compact thin films, we prove the existence of energy minimising multi-Skyrmion solutions and construct the (resolved) moduli space of these solutions.
Magnetic skyrmions are promising candidates as information carriers in a new generation of memories. How to generate and stabilize skyrmions is essential for their successful application to technology. Here we theoretically demonstrate that arrays of skyrmions can be imprinted in ultrathin ferromagnetic films in large numbers by bringing a magnetic nanostructured template close to the film. Two kind of templates, allowed by present-day nanotechnologies, are studied: arrays of ferromagnetic nanorods and superconducting vortices. Skyrmions are generated when exposing magnetic films to the templa…
Devising magnetic nanostructures with spatially heterogeneous Dzyaloshinskii-Moriya interaction (DMI) is a promising pathway towards advanced confinement and control of magnetic skyrmions in potential devices. Here we discuss theoretically how a skyrmion interacts with a heterochiral interface using micromagnetic simulations and analytic arguments. We show that a heterochiral interface deflects the trajectory of ferromagnetic (FM) skyrmions, and that the extent of such deflection is tuned by the applied spin-polarized current and the difference in DMI across the interface. Further, we show tha…
We consider clean cylindrical nanostructures with an applied longitudinal static magnetic field. Without Coulomb interaction, the field induces, for particular values, points of degeneracy where a change of ground state takes place due to Aharonov-Bohm effect. The Coulomb potential introduces interaction between the electronic configurations. As a consequence, when there is degeneracy, the ground state of the system becomes a many body state - unable to be described by a mean-field theory - and a gap is opened. To study this problem, we propose a variational multireference wave function which …
So far magnetic domain walls in one-dimensional structures have been described theoretically only in the cases of flat strips, or cylindrical structures with a compact cross-section, either square or disk. Here we describe an extended phase diagram unifying the two pictures, extensively covering the (width,thickness) space. It is derived on the basis of symmetry and phase-transition arguments, and micromagnetic simulations. A simple classification of all domain walls in two varieties is proposed on the basis of their topology: either with a combined transverse/vortex character, or of the Bloch…
We report that in cylindrical nanorods skyrmion chains, i.e., three-dimensional spin textures, emerge dynamically, as revealed by micromagnetic simulations. The skyrmion-chain state occurs when the diameter of the rod is larger than the helical pitch length of the material, and the number of skyrmions on the chain is proportional to the length of the nanorod. This finding provides a deeper understanding of the interplay between geometry and skyrmionic symmetry, and shows how spatial confinement can stabilize spontaneous topological spin textures.
Magnetic Skyrmions and multiferroics are the most interesting objects in nanostructure science that have great potential in future spin-electronic technology. The study of multiferroic Skyrmions has attracted much interest in recent years. This article reports magnetic Bloch Skyrmions induced by an electric driving field in a composite bilayer (chiral-magnetic/ferroelectric bilayer) lattice. By using the spin dynamics method, we use a classical magnetic spin model and an electric pseudospin model, which are coupled by a strong magnetoelectric coupling in the dynamical simulations. Interestingl…
Magnetic skyrmions are nanoscale spin whirlpools that promise breakthroughs in future spintronic applications. Controlled generation of magnetic skyrmions by electric current is crucial for this purpose. While previous studies have demonstrated this operation, the topological charge of the generated skyrmions is determined by the direction of the external magnetic fields, thus is fixed. Here, we report the current-induced skyrmions creation in a chiral magnet FeGe nanostructure by using the \emph{in-situ} Lorentz transmission electron microscopy. We show that magnetic skyrmions or antiskyrmion…
We report the creation and real-space observation of magnetic structures with well-defined topological properties and a lateral size as low as about 150 nm. They are generated in a thin ferrimagnetic film by ultrashort single optical laser pulses. Thanks to their topological properties, such structures can be classified as Skyrmions of a particular type that does not require an externally applied magnetic field for stabilization. Besides Skyrmions, we are able to generate magnetic features with topological characteristics that can be tuned by changing the laser fluence. The stability of such f…
We study the stability and energetics associated to skyrmions appear- ing as excitations on curved surfaces. Using a continuum model we show that the presence of cylindrically radial and azimuthal fields destabilizes the skyrmions that appear in the absence of an external field. Weak fields generate fractional skyrmions while strong magnetic fields yield stable 2{$π$}- skyrmions, which have their widths diminished by the magnetic field strength. Under azimuthal fields vortex appear as stable states on the curved surface.
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…
We calculate low-frequency gyrotropic spin excitation modes of the skyrmion ground state ultrathin cylindrical magnetic dots. The skyrmion is assumed to be stabilized at room temperature and zero external magnetic field due to an interplay of the isotropic and Dzyaloshinskii-Moriya exchange interactions, perpendicular magnetic anisotropy and magnetostatic interaction. We consider Bloch- and Neel-type magnetic skyrmions and assume that the dot magnetization does not depend on the thickness coordinate. The skyrmion gyrotropic frequencies are calculated in GHz range as a function of the skyrmion …
We have constructed a lattice Wigner-Weyl code that generalizes the Buot-Jensen algorithm to the calculation of electron transport in two-dimensional circular-cylindrically symmetric structures, where the Wigner function equation is solved self-consistently with the Poisson equation. Almost all of the numerical simulations to date have dealt with the restriction of the problem to one dimensional transport. In real devices, electrons are not confined to a single dimension and the coulombic potential is fully present and felt in three dimensions. We show the derivation of the 2D equation in cyli…
The effect of homogeneous electric field on the energy spectrum, wave functions of electron and oscillator strengths of intra-band quantum transitions in a double cylindrical quantum ring (GaAs/Al$_{x}$Ga$_{1-x}$As) is studied within the approximations of effective mass and rectangular potentials. The calculations are performed using the method of expansion of quasiparticle wave function over a complete set of cylindrical wave functions obtained as exact solutions of Schrödinger equation for an electron in a nanostructure without electric field. It is shown that the electric field essentially …
Magnetic skyrmions are particle-like topological excitations recently discovered in chiral magnets. Their small size, topological protection and the ease with which they can be manipulated by electric currents generated much interest in using skyrmions for information storage and processing. Recently, it was suggested that skyrmions with additional degrees of freedom can exist in magnetically frustrated materials. Here, we show that dynamics of skyrmions and antiskyrmions in nanostripes of frustrated magnets is strongly affected by complex spin states formed at the stripe edges. These states c…
Magnetic skyrmions and multiferroics are the most interesting objects in nanostructure science that have great potential in future spin-electronic technology. The study of the multiferroic skyrmions has attracted much interest in recent years. This paper reports on the magnetic skyrmions induced by an electric driving field on a composite multiferroic lattice. By using the spin dynamics method, we use a classical magnetic spin model and an electric pseudospin model, which are coupled by a strong magnetoelectric coupling in the dynamical simulations. Interestingly, we observe some skyrmion-like…
Using the Finsler geometry modeling (FG) technique without spontaneous magnetic anisotropy, we numerically study the stability and morphology of geometrically confined skyrmions experimentally observed in nanodots. We find a confinement effect that stabilizes skyrmions for a low external magnetic field without mechanical stresses by decreasing the diameter of the cylindrical lattice and strain effects that cause the sky and vortex to emerge under the zero magnetic field. Moreover, the obtained MC data on the morphological changes are also consistent with the reported experimental data.
The skyrmion-substrate interaction is an important issue to consider when studying particle-like skyrmions in nanostructures, which may strongly affect the skyrmion dynamics and lead to complex dynamic phenomena. Here, we report the current-driven dynamic behaviors of particle-like skyrmions interacting with the funnel obstacle in a ferromagnetic layer. We computationally demonstrate that a funnel obstacle with enhanced perpendicular magnetic anisotropy can be used to modify the dynamics of skyrmions due to the repulsive skyrmion-funnel interaction, which could generate several nontrivial effe…
Magnetic cylindrical nanowires are very fascinating objects where the curved geometry allows many novel magnetic effects and a variety of non-trivial magnetic structures. Micromagnetic modelling plays an important role in revealing the magnetization distribution in magnetic nanowires, often not accessible by imaging methods with sufficient details. Here we review the magnetic properties of the shape anisotropy-dominated nanowires and the nanowires with competing shape and magnetocrystalline anisotropies, as revealed by micromagnetic modelling. We discuss the variety of magnetic walls and magne…
The potential for application of magnetic skyrmions in high density storage devices provides a strong drive to investigate and exploit their stability and manipulability. Through a three-dimensional micromagnetic hysteresis study, we investigate the question of existence of skyrmions in cylindrical nanostructures of variable thickness. We quantify the applied field and thickness dependence of skyrmion states, and show that these states can be accessed through relevant practical hysteresis loop measurement protocols. As skyrmionic states have yet to be observed experimentally in confined helima…
Magnetic skyrmions are nontrivial spin textures which resist external perturbations, being promising candidates for the next generation recording devices. Nevertheless, a major challenge in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures under ambient conditions and zero applied field. Here, we demonstrate for the first time the formation and stabilization of magnetic skyrmions on arrays of self-assembled hexagonal nanodomes taking advantage of the intrinsic properties of its curved geometry. Magnetic force microscopy images from the arrays of 100…
The evolution of skyrmion crystal encapsulates skyrmion critical behaviors, such as nucleation, deformation and annihilation. Here, we achieve a tunable evolution of artificial skyrmion crystal in nanostructured synthetic antiferromagnet multilayers, which are comprised of perpendicular magnetic multilayers and nanopatterned arrays of magnetic nanodots. The out-of-plane magnetization hysteresis loops and first-order reversal curves show that the nucleation and annihilation of the artificial skyrmion can be controlled by tuning the diameter of and spacing between the nanodots. Moreover, when th…
The curvature effect on the electronic states of a deformed cylindrical conducting surface of variable diameter is theoretically investigated. The quantum confinement of electrons normal to the curved surface results in an effective potential energy that affects the electronic structures of the system at low energies. This suggests the possibility that ballistic transport of electrons in low-dimensional nanostructures can be controlled by inducing a local geometric deformation.
One method of creating and annihilating skyrmions in confined geometries is to use Voltage-Controlled Magnetic Anisotropy (VCMA) [1, 2, 3]. Previous study shows that robust voltage controlled ferromagnetic reversal from up to down state in the soft layer of a perpendicular Magnetic Tunnel Junction (p-MTJ) can be achieved by creating and subsequently annihilating an intermediate skyrmion state [4] in the presence of room temperature thermal noise and anisotropy variation across grains [4]. However, when scaling to 20 nm, thermal noise can annihilate the skyrmions, for example, by randomly movin…
We report on the effect of the lateral confinement and a perpendicular magnetic field on isolated room-temperature magnetic skyrmions in sputtered Pt/Co/MgO nanotracks and nanodots. We show that the skyrmions size can be easily tuned by playing on the lateral dimensions of the nanostructures and by using external magnetic field amplitudes of a few mT, which allow to reach sub-100 nm diameters. Our XMCD-PEEM observations also highlight the important role of the pinning on the skyrmions size and stability under an out-of-plane magnetic field. Micromagnetic simulations reveal that the effect of l…
Antiferromagnets as active elements of spintronics can be faster than their ferromagnetic counterparts and more robust to magnetic noise. Owing to the strongly exchange-coupled magnetic sublattice structure, antiferromagnetic order parameter dynamics are qualitatively different and thus capable of engendering novel device functionalities. In this review, we discuss antiferromagnetic textures -- nanoparticles, domain walls, and skyrmions, -- under the action of different spin torques. We contrast the antiferromagnetic and ferromagnetic dynamics, with a focus on the features that can be relevant…
Magnetic skyrmions are knot-like quasiparticles. They are candidates for non-volatile data storage in which information is moved between fixed read and write terminals. Read-out operation of skyrmion-based spintronic devices will rely upon electrical detection of a single magnetic skyrmion within a nanostructure. Here, we present Pt/Co/Ir nanodiscs which support skyrmions at room temperature. We measured the Hall resistivity whilst simultaneously imaging the spin texture using magnetic scanning transmission x-ray microscopy (STXM). The Hall resistivity is correlated to both the presence and si…
This paper presents a six-band k.p theory for wurtzite semiconductor nanostructures with cylindrical symmetry. Our work extends the formulation of Vahala and Sercel [Physical Review Letters 65, 239 (1990)] to the Rashba-Sheka-Pikus Hamiltonian for wurtzite semiconductors, without the need for the axial approximation. Results comparing our formulation for studying the electronic structure of wurzite quantum dots with the conventional formulation are given.
We present a comprehensive micromagnetic model of isolated axisymmetric skyrmions in magnetic multilayers with perpendicular anisotropy. Most notably, the essential role of the internal dipolar field is extensively considered with a minimum amount of assumptions on the magnetization profiles. The tri-dimensional structure of the multilayered skyrmions is modeled by their radial profiles in each layer. We first compare the results of the model against a full micromagnetic description in Cartesian coordinates. Our model combines information on both layer-dependent size and chirality of the skyrm…
During the last years, topologically protected collective modes of the magnetization have called much attention. Among these, skyrmions and merons have been the object of intense study. In particular, topological skyrmions are objects with an integer skyrmion number $Q$ while merons have a half-integer skyrmion charge $q$. In this work, we consider a $Q=1$ skyrmion, composed by a meron and an antimeron (bimeron), displacing in a ferromagnetic racetrack, disputing a long-distance competition with its more famous counterpart, the typical $Q=1$ cylindrically symmetrical skyrmion. Both types of to…
The recently invented cylindrical geometric space defect is applied to the electron behaviour in the system which can be regarded as a simplified model of a double-wall nanotube. By solving the Schrodinger equation in the region of space with cylindrical geometric defect we explore the influence of such geometric defect on the energy gap and charge distribution. The effect is qualitatively similar to the one obtained earlier by means of traditional simulation methods. In general, the geometric approach can not compete with the known methods of theoretical study of the nanostructures, such as m…
Cylindrical magnetic nanowires are promising systems for the development of three-dimensional spintronic devices. Here, we simulate the evolution of magnetic states during fabrication of strongly-coupled cylindrical nanowires with varying degrees of overlap. By varying the separation between wires, the relative strength of exchange and magnetostatic coupling can be tuned. Hence leading to the formation of six fundamental states as a function of both inter-wire separation and wire height. In particular, two complex three-dimensional magnetic states, a 3D Landau Pattern and a Helical Domain wall…
The magnetic field associated with a picosecond intense electron pulse is shown to switch locally the magnetization of extended films and nanostructures and to ignite locally spin waves excitations. Also, topologically protected magnetic textures such as skyrmions can be imprinted swiftly in a sample with a residual Dzyaloshinskii-Moriya spin-orbital coupling. Characteristics of the created excitations such as the topological charge or the width of the magnon spectrum can be steered via the duration and the strength of the electron pulses. The study points to a possible way for a spatiotempora…
We review recent results on the behaviour of the dielectric function of cylindrical nano-organic materials at very low frequencies in a magnetic field. For cylindrical structures - such as carbon nanotubes - the polarisability is shown to be a discontinuous function of a longitudinal magnetic field where plateau-like regions are separated by sudden jumps or peaks. A relation is pointed out between each discontinuity in the polarisability and the cross-over between ground and first excited states induced by the magnetic field. This one to one correspondence suggests to use measurements of the d…
Frequency of free magnetic vortex precession in circular soft ferromagnetic nano-cylinders (magnetic dots) of various sizes is an important parameter, used in design of spintronic devices (such as spin-torque microwave nano-oscillators) and characterization of magnetic nanostructures. Here, using a recently developed collective-variable approach to non-linear dynamics of magnetic textures in planar nano-magnets, this frequency and its amplitude-dependent shift are computed analytically and plotted for the full range of cylinder geometries. The frequency shift is positive in large planar dots, …
