Magnetic skyrmions are topological spin configurations in materials with chiral Dzyaloshinskii-Moriya interaction (DMI), that are potentially useful for storing or processing information. To date, DMI has been found in few bulk materials, but can also be induced in atomically thin magnetic films in contact with surfaces with large spin-orbit interactions. Recent experiments have reported that isolated magnetic skyrmions can be stabilized even near room temperature in few-atom thick magnetic layers sandwiched between materials that provide asymmetric spin-orbit coupling. Here we present the minimum-energy path analysis of three distinct mechanisms for the skyrmion collapse, based on ab initio input and the performed atomic-spin simulations. We focus on the stability of a skyrmion in three atomic layers of Co, either epitaxial on the Pt(111) surface, or within a hybrid multilayer where DMI nontrivially varies per monolayer due to competition between different symmetry-breaking from two sides of the Co film. In laterally finite systems, their constrained geometry causes poor thermal stability of the skyrmion toward collapse at the boundary, which we show to be resolved by designing the high-DMI structure within an extended film with lower or no DMI.
Skyrmions are localized solitonic spin textures with protected topology, which are promising as information carriers in ultra-dense and energy-efficient logic and memory devices. Recently, magnetic skyrmions have been observed in magnetic thin films, and are stabilized by the extrinsic interfacial Dzyaloshinskii-Moriya interaction (DMI) and/or external magnetic fields. The specific effects in magnetic monolayer materials have not been thoroughly studied. Here, we investigate the intrinsic magnetic skyrmions in a family of monolayer Janus van der Waals magnets, MnSTe, MnSeTe, VSeTe, and MnSSe, …
The purpose of the research is the construction of the analytical model for description of spin-polarized current-driven ferromagnetic domain wall motion with a skyrmion building block. The dependence of velocity of ferromagnetic domain wall motion with a skyrmion building block is found as a function of driving torques and an external magnetic field strength.
The fabrication of a skyrmion circuit which stabilizes skyrmions is important to realize micro- to nano-sized skyrmion devices. One example of promising skyrmion-based device is Brownian computers, which have been theoretically proposed, but not realized. It would require a skyrmion circuit in which the skyrmion is stabilized and easily movable. However, the usual skyrmion circuits fabricated by etching of the ferromagnetic film decrease the demagnetization field stabilizing the skyrmions, and thus prevent their formation. In this study, a skyrmion Brownian circuit implemented in a continuous …
Magnetic skyrmions are topological magnetization textures that are characterized by the homotopy group of two dimensional spheres. Despite years of intensive research on skyrmions, the fundamental problem of the inertia of a skyrmion in driven motion remains unresolved. By properly taking into account a direct coupling between skyrmion motion and the correspondingly excited magnons, we identify a dynamical mass for the skyrmion in motion. The direct coupling between skyrmion motion and magnons can be employed to engineer skyrmion dynamics with magnons through ingenious material and geometry de…
The dynamics of magnetic skyrmion driven by spin-polarized current is theoretically studied in the chiral ferromagnetic film with spatially modulated Dzyaloshinskii-Moriya interaction. Three cases including linear, sinusoidal, and periodic rectangular modulations have been considered, where the increase, decrease, and the periodic modification of the size and velocity of the skyrmion have been observed in the microscopic simulations. These phenomena are well explained by the Thiele equation, where an effective force on the skyrmion is induced by the inhomogeneous Dzyaloshinskii-Moriya interact…
Time dependence of the size and chirality of a ferromagnetic skyrmion in a Heisenberg model with the magnetic field on a square lattice has been studied analytically and numerically. The lattice and the magnetic field generate strong time dependence of the skyrmion chirality. Due to nonlinearity, the lattice alone also generates strong intrinsic damping that leads to the skyrmion collapse via the emission of spin waves. In the absence of the magnetic field the collapse is slow for a large skyrmion but it becomes exponentially fast in the presence of the Landau-Lifshitz damping when the field i…
The effect of the Dzyaloshinsky-Moriya interaction on the magnetic structure of an ordered FePt monolayer deposited on Pt (111) surface has been investigated. In the ground state, the pronounced anisotropic geometry of the FePt layer with alternating Fe and Pt chains gives rise to a helimagnetic structure with a strong difference in the helicity period along the chains and perpendicular to them. In the presence of an external magnetic field, the region of stable Skyrmion magnetic structures in the $B-T$ phase diagram has been demonstrated via Monte Carlo simulations using the parameters obtain…
Skyrmion Excitations in the $ν=-1$ Quantum Hall state in Monolayer Graphene
Shandong Normal University（山东师范大学）；Institute of Mathematical Sciences, CIT Campus（马德拉斯理工学院数学研究所）；Homi Bhabha National Institute（霍米·巴巴国家研究所）；University of Kentucky（肯塔基大学）
We introduce a new class of isolated magnetic skyrmions emerging within tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The asymmetric magnetic structure of these skyrmions is associated with an intricate pattern of the energy density, which exhibits positive and negative asymptotics with respect to the surrounding state with a ferromagnetic moment tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion interaction has an anisotropic character and can be either attractive or repulsive depending on the relative orientation of the skyrmion pair. We invest…
Implementation of skyrmion based energy efficient and high-density data storage devices requires aggressive scaling of skyrmion size. Ferrimagnetic materials are considered to be a suitable platform for this purpose due to their low saturation magnetization (i.e. smaller stray field). However, we show by performing rigorous micromagnetic simulation that such scaling of skyrmion size by lowering saturation magnetization while applicable in infinite films or where the skyrmion size is very small compared to the film's lateral dimension, does not hold in confined geometries. We also found in conf…
We report the current-driven dynamics of frustrated skyrmions in an antiferromagnetically exchange coupled bilayer system, where the bilayer skyrmion consists of two monolayer skyrmions with opposite skyrmion numbers $Q$. We show that the in-plane current-driven bilayer skyrmion moves in a straight path, while the out-of-plane current-driven bilayer skyrmion moves in a circular path. It is found that the in-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one at a large ratio of $β/α$, where $α$ and $β$ denote the damping parameter and non-adiabatic spin tr…
Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Neel walls and quantify the DMI induced by the Pd capp…
Magnetic skyrmions are quasiparticle configurations in a magnetic film that can act as information carrying bits for ultrasmall, all-electronic nonvolatile memory. The skyrmions can be nucleated and driven by spin-orbit torque from a current driven in a heavy metal underlayer. Along its gyrotropic path, a Magnus force can cause a skyrmion to be annihilated at the boundaries. By combining interfacial and bulk Dzyaloshinskii-Moriya interactions (DMIs), for instance by using a B20 material on top of a heavy metal layer with high spin-orbit coupling, it is possible to engineer a hybrid skyrmion th…
We theoretically reveal that pure eigenmodes of an isolated magnetic skyrmion embedded in a ferromagnetic environment can be selectively activated using microwave electric fields without exciting gigantic ferromagnetic resonances, in contrast to conventional methods using microwave magnetic fields. We also demonstrate that this selective activation of a skyrmion can efficiently drive its translational motion in a ferromagnetic nanotrack under application of an external magnetic field inclined from the normal direction. We find that a mode with combined breathing and rotational oscillations ind…
We theoretically study the current-induced dynamics of a domain wall in a ferromagnetic nanotube by developing a theory for the orbital angular momentum of a domain wall and the current-induced torque on it. Specifically, a domain wall with nontrivial magnetization winding along the circumference is shown to possess finite orbital angular momentum, which is proportional to the product of its Skyrmion charge and position, and the current is shown to exert a torque changing the orbital angular momentum of the domain wall and thereby drives it. The current-induced torque is interpreted as the tra…
We show how a Dzyaloshinskii-Moriya interaction can be generated in an ultrathin metal film from the induced internal electric field created by an ultrashort electromagnetic pulse. This interaction does not require structural inversion-symmetry breaking, and its amplitude can be tuned depending on the amplitude of the field. We perform first-principles calculations to estimate the strength of the field-induced magnetoelectric coupling for ferromagnetic Fe, Co, and Ni, and antiferromagnetic Mn, as well as FePt alloys. Last, using atomistic simulations, we demonstrate how an isolated antiferroma…
A magnetic skyrmion is a topological magnetization structure with a nanometric size and a well-defined swirling spin distribution, which is anticipated to be an essential building block for novel skyrmion-based device applications. We study the motion of magnetic skyrmions in multilayer synthetic antiferromagnetic (SAF) racetracks as well as in conventional monolayer ferromagnetic (FM) racetracks at finite temperature. There is an odd-even effect of the constituent FM layer number on the skyrmion Hall effect (SkHE). Namely, due to the suppression of the SkHE, the magnetic skyrmion has no trans…
An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.
A quantal model description of a discrete localized skyrmion singularity embedded in a ferromagnetic environment is proposed. It allows discussing the importance of various parameters in the appearance of a quantal skyrmion singularity. Analysis of the skyrmion reveals a few specific quantal properties: presence of a whole series of skyrmion states, non-classical nature of the local spins, presence of superposition states and presence of extra-skyrmion states due to the quantization of the central spin of the singularity. The interaction of an electron, tunneling or substrate, with the skyrmio…
We point out that a peculiar annihilation of a vortex-antovortex pair observed numerically by Hertel and Schneider [Phys. Rev. Lett. 97, 177202 (2006)] represents the formation and subsequent decay of a skyrmion.
We provide a derivation of a spin Skyrmion number classification for two-dimensional topological superconductors constructed from ferromagnetic and Rashba spin-orbit coupled semiconductor-superconductor heterostructures. We show that in the non-trivial topological phase, characterized by a non-zero Chern number, there is always a topological spin texture in the occupied bands represented by a Skyrmion number. The Skyrmion number has the advantage of being both physically intuitive and directly measurable using spin-sensitive band structure imaging techniques. In addition, we show that the Skyr…
Magnetic skyrmion is a promising building block for developing information storage and computing devices. It can be stabilized in a ferromagnetic thin film with the Dzyaloshinskii-Moriya interaction (DMI). The moving ferromagnetic skyrmion may show the skyrmion Hall effect, that is, the skyrmion shows a transverse shift when it is driven by a spin current. Here, we numerically and theoretically study the current-driven dynamics of a ferromagnetic nanoscale skyrmion in the presence of the anisotropic DMI, where the skyrmion has an elliptical shape. The skyrmion Hall effect of the elliptical sky…
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…
Magnetic skyrmions have potential applications in next-generation spintronics devices with ultralow energy consumption. In this work, the current-driven skyrmion motion in a narrow ferromagnetic nanotrack with voltage-controlled magnetic anisotropy (VCMA) is studied numerically. By utilizing the VCMA effect, the transport of skyrmion can be unidirectional in the nanotrack, leading to a one-way information channel. The trajectory of the skyrmion can also be modulated by periodically located VCMA gates, which protects the skyrmion from destruction by touching the track edge. In addition, the loc…
Exotic spin textures viz. chiral domain wall, vortices, skyrmion, skyrmionium, etc. have recently emerged as active field of research because of their potential applications in high density data storage technology and logic gate computing. Magnetic skyrmionium is a skyrmion like soliton, which carries zero topological quantum number. Skyrmioniums are superior to conventional skyrmions in ferromagnets due to their negligible skyrmion hall effect and higher velocity. The physical properties of both skyrmion and skyrmionium have been investigated rigorously in ferromagnetic systems. Recent observ…
Materials hosting magnetic skyrmions at room temperature could enable new computing architectures as well as compact and energetically efficient magnetic storage such as racetrack memories. In a racetrack device, information is coded by the presence/absence of magnetic skyrmions forming a chain that is moved through the device. The skyrmion Hall effect that would eventually lead to an annihilation of the skyrmions at the edges of the racetrack can be suppressed for example by anti-ferromagnetically-coupled skyrmions. However, avoiding modifications of the inter-skyrmion distances in the racetr…
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…
Magnetic skyrmion crystals are topological magnetic textures arising in the chiral ferromagnetic materials with Dzyaloshinskii-Moriya interaction. The magnetostatic fields generated by magnetic skyrmion crystals are first studied by micromagnetic simulations. For Néel-type skyrmion crystals, the fields will vanish on one side of the crystal plane, which depend on the helicity; while for Bloch-type skyrmion crystals, the fields will distribute over both sides, and are identical for the two helicities. These features and the symmetry relations of the magetostatic fields are understood from the m…
Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $ν=0,\pm 1$. Notably the ground state at $ν=0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $ν=\pm 1,0$ by using exact di…
Theoretical calculations of thermally activated decay of skyrmions in systems comprising several magnetic monolayers are presented, with a special focus on bilayer systems. Mechanisms of skyrmion collapse are identified and corresponding energy barriers and thermal collapse rates are evaluated as functions of the interlayer exchange coupling and mutual stacking of the monolayers using transition state theory and an atomistic spin Hamiltonian. In order to contrast the results to monolayer systems, the magnetic interactions within each layer are chosen so as to mimic the well-established Pd/Fe/I…
Using micromagnetic simulations we demonstrate core reversal of a fixed magnetic skyrmion by modulating the perpendicular magnetic anisotropy of a nanomagnet with an electric field. We can switch reversibly between two skyrmion states and two ferromagnetic states, i.e. skyrmion states with the magnetization of the core pointing down/up and periphery pointing up/down, and ferromagnetic states with magnetization pointing up/down, by sequential increase and decrease of the perpendicular magnetic anisotropy. The switching between these states is explained by the fact that the spin texture correspo…
We use the continuum micromagnetic framework to derive the formulas for compact skyrmion lifetime due to thermal noise in ultrathin ferromagnetic films with relatively weak interfacial Dzyaloshinskii-Moriya interaction. In the absence of a saddle point connecting the skyrmion solution to the ferromagnetic state, we interpret the skyrmion collapse event as ``capture by an absorber'' at microscale. This yields an explicit Arrhenius collapse rate with both the barrier height and the prefactor as functions of all the material parameters, as well as the dynamical paths to collapse.
Partially filled Landau levels host competing orders, with electron solids prevailing close to integer fillings before giving way to fractional quantum Hall liquids as the Landau level fills. Here, we report the observation of an electron solid with noncolinear spin texture in monolayer graphene, consistent with solidification of skyrmions---topological spin textures characterized by quantized electrical charge. In electrical transport, electron solids reveal themselves through a rapid metal-insulator transition in the bulk electrical conductivity as the temperature is lowered, accompanied by …
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…
Eigenmodes of synthetic antiferromagnetic skyrmions
Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马普研究所）；Center for Free-Electron Laser Science（自由电子激光科学中心）；University of Hamburg（汉堡大学）；University of Vienna（维也纳大学）；University of Southampton（南安普顿大学）
We explore the skyrmion formation and control possibilities in 2D magnets from the ubiquitous moiré pattern in vdW heterostructures. Using the example of a ferromagnetic monolayer on an antiferromagnetic substrate, we demonstrate a new origin of skyrmions in the 2D magnets, from the lateral modulation of interlayer magnetic coupling by the locally different atomic registries in moiré. The moiré skyrmions are doubly degenerate with opposite topological charge, and trapped at an ordered array of sites with the moiré periodicity that can be dramatically tuned by strain and interlayer translation.…
A magnetic skyrmion induced on a ferromagnetic topological insulator (TI) is a real-space manifestation of the chiral spin texture in the momentum space, and can be a carrier for information processing by manipulating it in tailored structures. Here, we fabricate a sandwich structure containing two layers of a self-assembled ferromagnetic septuple-layer TI, Mn(Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{4}$ (MnBST), separated by quintuple layers of TI, (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$ (BST), and observe skyrmions through the topological Hall effect in an intrinsic magnetic topological insulator for the fi…
Magnetic skyrmions are promising candidates for the next generation of spintronic devices due to their small size and topologically protected structure. One challenge for using these magnetic states in applications lies on controlling the nucleation process and stabilization that usually requires an external force. Here, we report on the evidence of skyrmions in unpatterned symmetric Pd/Co/Pd multilayers at room temperature without prior application of neither electric current nor magnetic field. By decreasing the ferromagnetic interlayer thickness, the tuning of the physical properties across…
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…
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…
Ultrathin ferromagnets with frustrated exchange and the Dzyaloshinskii-Moriya interaction can support topological solitons such as skyrmions and antiskyrmions, which are metastable and can be considered particle-antiparticle counterparts. When spin-orbit torques are applied, the motion of an isolated antiskyrmion driven beyond its Walker limit can generate skyrmion-antiskyrmion pairs. Here, we use atomistic spin dynamics simulations to shed light on the scattering processes involved in this pair generation. Under certain conditions a proliferation of these particles and antiparticles can appea…
We study the anomalous Hall effect in monolayers of transition-metal dichalcogenides 2H-$MX_2$ ($M$=Mo, W, and $X$=S, Se, Te) under a proximity effect of ferromagnetic substrate. If a proximity-induced exchange field is introduced, the spin-polarized energy bands in $K$ and $K'$ valleys are shifted in the opposite directions, and it causes the Hall effect by breaking time-reversal symmetry. The induced Hall effect is the most prominent in the valence band which has a large intrinsic spin splitting. Moreover, we find that tilting the magnetization from the perpendicular direction gives rise to …
We calculate in an analyical fashion the energies and net spins of skyrmions in fractional quantum Hall systems, based on the suggestion that skyrmion states are spontaneously $L_Z$ and $S_Z$ symmetry-breaking states. The quasihole-skyrmion state with a charge $-e/3$ around $ν$ = 1/3, where the ground state is known as a spin-polarized ferromagnetic state, is found to exist even in high magnetic fields up to about 7 T for GaAs samples.
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…
We study the collective dynamics of the Skyrmion crystal (SkX) in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. We show that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in non-collinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the SkX, and discuss effects of impurity pinning of Skyrmions.
We study the topological Hall effect in a diffusive ferromagnetic metal thin film by solving a Boltzmann transport equation in the presence of spin-flip scattering. A generalized spin diffusion equation is derived, which contains an additional source term associated with the gradient of the emergent magnetic field that arises, and its solution shows that spin accumulation may build up in the vicinity of the magnetic skyrmions. We show that the spin accumulation gives rise to a spin polarized diffusion current that in general suppresses that bulk topological Hall current. Only when the spin dif…
We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion and Néel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves…
A path method is implemented in order to precisely and generally describe the collapse of isolated skyrmions in a Co/Pt(111) monolayer, on the basis of atomic scale simulations. Two collapse mechanisms with different energy barriers are found. The most obvious path, featuring a homogeneous shrinking gives the largest energy, whereas the lowest energy barrier is shown to comply with the outcome of Langevin dynamics under a destabilizing field of 0.25 T, with a lifetime of 20~ns at around 80~K. For this lowest energy barrier path, skyrmion destabilization occurs much before any topology change, …
