In chiral magnets, localized topological magnetic whirls, magnetic skyrmions, can be moved by spin polarized electric currents. Upon increasing the current strength, with prospects for high-speed skyrmion motion for spintronics applications in mind, isolated skyrmions deform away from their typical circular shape. We analyze the influence of spin-transfer torques on the shape of a single skyrmion, including its stability upon adiabatically increasing the strength of the applied electric current. For rather compact skyrmions at uniaxial anisotropies well above the critical anisotropy for domain wall formation, we find for high current densities that the skyrmion assumes a non-circular shape with a tail, reminiscent of a shooting star. For larger and hence softer skyrmions close to the critical anisotropy, in turn, we observe a critical current density above which skyrmions become unstable. We show that above a second critical current density the shooting star solution can be recovered also for these skyrmions.
Skyrmion-based spin torque nano-oscillators are potential next-generation microwave signal generators. However, ferromagnetic skyrmion-based spin torque nano-oscillators cannot reach high oscillation frequencies. In this work, we propose to use the circular motion of an antiferromagnetic skyrmion to create the oscillation signal in order to overcome this obstacle. Micromagnetic simulations demonstrate that the antiferromagnetic skyrmion-based spin torque nano-oscillators can produce high frequencies (tens of GHz). Furthermore, the speed of the circular motion for an antiferromagnetic skyrmion …
Chiral magnets like MnSi form lattices of skyrmions, i.e. magnetic whirls, which react sensitively to small electric currents j above a critical current density jc. The interplay of these currents with tiny gradients of either the magnetic field or the temperature can induce a rotation of the magnetic pattern for j>jc. Either a rotation by a finite angle of up to 15 degree or -- for larger gradients -- a continuous rotation with a finite angular velocity is induced. We use Landau-Lifshitz-Gilbert equations extended by extra damping terms in combination with a phenomenological treatment of pinn…
We investigate the torque field and skyrmion movement at an interface between a ferromagnet hosting a skyrmion and a material with strong spin-orbit interaction. We analyze both semiconductor materials and topological insulators using a Hamiltonian model that includes a linear term. The spin torque inducing current is considered to flow in the single band limit therefore a quantum model of current is used. Skyrmion movement due spin transfer torque proves to be more difficult in presence of spin orbit interaction in the case where only interface in-plane currents are present. However, edge eff…
Here we study the effect of an additional interfacial spin-transfer torque, as well as the well established spin-orbit torque and bulk spin-transfer torque, on skyrmion collections - group of skyrmions dense enough that they are not isolated from on another - in ultrathin heavy metal / ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show the experimen…
Reliable transport of magnetic skyrmions is required for any future skyrmion-based information processing devices. Here we present a micromagnetic study of the in-plane current-driven motion of a skyrmion in a ferromagnetic nanotrack with spatially sinusoidally varying Gilbert damping and/or non-adiabatic spin-transfer torque coefficients. It is found that the skyrmion moves in a sinusoidal pattern as a result of the spatially varying Gilbert damping and/or non-adiabatic spin-transfer torque in the nanotrack, which could prevent the destruction of the skyrmion caused by the skyrmion Hall effec…
Skyrmions can be driven by spin-orbit torques as a result of the spin Hall effect. Here we model an additional contribution in ultra-thin multilayers, arising from the spin accumulation at heavy metal / ferromagnetic interfaces and observe the effects on a large range of skyrmion diameters. The combination of the interfacial spin-transfer torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles for skyrmion diameters less than 100 nm. We show that this additional term has a significant effect on the skyrmion dynamics and l…
In epitaxial MnSi/Si(111) films, the in-plane magnetization saturation is never reached due to the formation of specific surface chiral modulations with the propagation direction perpendicular to the film surfaces [Wilson et al. Phys. Rev. B 88, 214420 (2013)]. In this paper we show that the occurrence of such chiral surface twists is a general effect attributed to all bulk and con- fined magnetic crystals lacking inversion symmetry. We present experimental investigations of this phenomenon in nanolayers of MnSi/Si(111) supported by detailed theoretical analysis within the standard phenomenolo…
We theoretically study the skyrmion-number dependence of spin-transfer torque acting on magnetic bubbles. The skymrion number of magnetic bubbles can take any integer value depending on the magnetic profile on its circumference and the size of the bubble. We find that the transverse motion of a bubble with respect to the charge current is greatly suppressed as the absolute value of skyrmion number departs from unity, whereas the longitudinal motion is less sensitive.
We derive thermomagnonic torque and its "$β$-type" dissipative correction from the stochastic Landau-Lifshitz-Gilbert equation. The "$β$-type" dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Se…
We propose that topological spin currents flowing in topologically non-trivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic non-adiabatic torque of the form ${\bf T}_t\sim [(\partial_x{\bf m}\times\partial_y{\bf m})\cdot{\bf m}]\partial_y{\bf m}$. We show that this torque, which is absent in one-dimensional domain walls and/or non-topological textures, is responsible for the enhanced non-adiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be cr…
A skyrmion can be stabilized in a nanodisc geometry in a ferromagnetic material with Dzyaloshinskii-Moriya (DM) interaction. We apply spin torque uniform in space and time and observe numerically that the skyrmion is set in steady rotational motion around a point off the nanodisc center. We give a theoretical description of the emerging auto-oscillation dynamics based on the coupling of the rotational motion to the breathing mode of the skyrmion and to the associated oscillations of the in-plane magnetization. The analysis shows that the achievement of auto-oscillations in this simple set-up i…
The length scale of the magnetization gradients in chiral magnets is determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even conventional spin-transfer torques are controlled by the relativistic spin-orbit coupling in these systems, and additional relativistic corrections to the current-induced torques and magnetization damping become important for a complete understanding of the current-driven magnetization dynamics. We theoretically study the effects of reactive and dissipative homogeneous spin-orbit torques and anisotropic damping on the current-driven skyrmion dynamics…
Spin torque nano-oscillator has been extensively studied both theoretically and experimentally in recent decades due to its potential applications in future microwave communication technology and neuromorphic computing. In this work, we present a skyrmion-based spin torque nano-oscillator driven by a spatially uniform direct current, where the skyrmion is confined by two pinning sites. Different from other skyrmion-based oscillators that arise from the circular motion or the breathing mode of a skyrmion, the steady-state oscillatory motions are produced by the periodic deformation of an elonga…
We study both analytically and numerically the edge of two-dimensional ferromagnets with Dzyaloshinskii-Moriya (DM) interactions, considering both chiral magnets and magnets with interface-induced DM interactions. We show that in the field-polarized ferromagnetic phase magnon states exist which are bound to the edge, and we calculate their spectra within a continuum field theory. Upon lowering an external magnetic field, these bound magnons condense at a finite momentum and the edge becomes locally unstable. Micromagnetic simulations demonstrate that this edge instability triggers the creation…
We study the dynamics of skyrmions under spin-transfer torque in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. In particular, we study the motion of a topological skyrmion with skyrmion number $Q=1$ and a non-topological skyrmionium with $Q=0$ using their linear momentum, virial relations, and numerical simulations. The non-topological $Q=0$ skyrmionium is accelerated in the direction of the current flow and it either reaches a steady state with constant velocity, or it is elongated to infinity. The steady-state velocity is given by a balance between current and dissipation and ha…
The effect of the spatially varying spin current on a skyrmion is numerically investigated. It is shown that an inhomogeneous current density induces an elongation of the skyrmion. This elongation can be controlled using current pulses of different strength and duration. Long current pulses lead to a splitting that forms two replicas of the initial skyrmion while for short pulses the elongated skyrmion relaxes back to its initial circular state through rotation in the MHz-GHz frequency range. The frequency is dependent on the strength of the damping coefficient.
In this work we compute the torque field present in a ferromagnet in contact with a metallic nanowire when a skyrmion is present. If the nanowire is narrow enough the current is carried by a single conduction band. In this regime the classical torque model breaks down and we show that a skyrmion driven by spin transfer torque moves in a different direction than predicted by the classical model. However, the amount of charge current required to move a skyrmion with a certain velocity in the single band regime is similar to a classical model of torque where it is implicitly assumed current trans…
Using micromagnetic simulation, we investigate the self-sustained oscillation of magnetic skyrmion in a ferromagnetic circular nanodot, driven by spin-torque which is generated from a reference layer of a circular nanopillar device. We demonstrate, by lowering the value of uniaxial anisotropy constant ($K_u$), the velocity of the skyrmion can be increased and using this property, gyration frequency of the skyrmion oscillator can be enhanced. Annihilation of the skyrmion at higher current densities, limit the gyration frequency of the oscillator, whereas by modifying the $K_u$ value at the edge…
A model for a spin-torque nano-oscillator based on the self-sustained oscillation of a magnetic skyrmion is presented. The system involves a circular nanopillar geometry comprising an ultrathin film free magnetic layer with a strong Dzyaloshinkii-Moriya interaction and a polariser layer with a vortex-like spin configuration. It is shown that spin-transfer torques due to current flow perpendicular to the film plane leads to skyrmion gyration that arises from a competition between geometric confinement due to boundary edges and the vortex-like polarisation of the spin torques. A phenomenology fo…
Magnetic skyrmionium is a skyrmion-like spin texture with nanoscale size and high mobility. It is a topologically trivial but dynamically stable structure, which can be used as a non-volatile information carrier for next-generation spintronic storage and computing devices. Here, we study the dynamics of a skyrmionium driven by the spin torque in a ferrimagnetic nanotrack. It is found that the direction of motion is jointly determined by the internal configuration of a skyrmionium and the spin polarization vector. Besides, the deformation of a skyrmionium induced by the intrinsic skyrmion Hall …
It is well known that skyrmions can be driven using spin-orbit torques due to the spin-Hall effect. Here we show an additional contribution in multilayered stacks arises from vertical spin currents due to inter-layer diffusion of a spin accumulation generated at a skyrmion. This additional interfacial spin torque is similar in form to the in-plane spin transfer torque, but is significantly enhanced in ultra-thin films and acts in the opposite direction to the electron flow. The combination of this diffusive spin torque and the spin-orbit torque results in skyrmion motion which helps to explain…
It is widely believed that the skyrmion Hall effect, often disruptive for device applications, vanishes for overall topologically trivial structures such as (synthetic) antiferromagnetic skyrmions and skyrmioniums due to a compensation of Magnus forces. In this manuscript, however, we report that in contrast to the case of spin-transfer torque driven skyrmion motion, this notion is generally false for spin-orbit torque driven objects. We show that the skyrmion Hall angle is directly related to their helicity and imposes an unexpected roadblock for developing faster and lower input racetrack me…
Recent progress in all-electrical nucleation, detection and manipulation of magnetic skyrmions has unlocked the tremendous potential of skyrmion-based spintronic devices. Here, we show via micromagnetic simulations that the stable magnetic oscillations of STNO radiate spin waves (SWs) that can be scattered in the presence of skyrmions in the near vicinity. Interference between SWs emitted by the STNO and SWs scattered by the skyrmion gives rise to interesting dynamics that leads to amplification or attenuation of STNO's magnetic oscillations. In the presence of strong Dzyaloshinskii-Moriya int…
In the present work, using micromagnetic simulation, we show that the magnetic coupling effect plays a very important role in the process of creation of skyrmions in a coupled system of spin-torque nano-oscillators (STNO). First, we have determined the magnetic ground state in an isolated STNO for different values of perpendicular uniaxial anisotropy (PUA) and Dzyaloshinskii-Moriya interaction (DMI). Next, we have applied a perpendicular pulse polarized current density (J) and found that it is possible to create a metastable Néel skyrmion from a disk whose ground state is a single magnetic dom…
Skyrmions and antiskyrmions in magnetic ultrathin films are characterised by a topological charge describing how the spins wind around their core. This topology governs their response to forces in the rigid core limit. However, when internal core excitations are relevant, the dynamics become far richer. We show that current-induced spin-orbit torques can lead to phenomena such as trochoidal motion and skyrmion-antiskyrmion pair generation that only occurs for either the skyrmion or antiskyrmion, depending on the symmetry of the underlying Dzyaloshinskii-Moriya interaction. Such dynamics are in…
Magnetic skyrmions are topologically-protected spin textures with attractive properties suitable for high-density and low-power spintronic device applications. Much effort has been dedicated to understanding the dynamical behaviours of the magnetic skyrmions. However, experimental observation of the ultrafast dynamics of this chiral magnetic texture in real space, which is the hallmark of its quasiparticle nature, has so far remained elusive. Here, we report nanosecond-dynamics of a 100 nm-size magnetic skyrmion during a current pulse application, using a time-resolved pump-probe soft X-ray im…
Bidirectional motion of antiferromagnetic skyrmions driven by competing spin torques
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Beihang University（北京航空航天大学）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新研究院）；The Hong Kong University of Science and Technology（香港科技大学）；University of Science and Technology of China（中国科学技术大学）；ShanghaiTech University（上海科技大学）
Magnetic skyrmions can be driven by an applied spin-polarized electron current which exerts a spin-transfer torque on the localized spins constituting the skyrmion. However, the longitudinal dynamics is plagued by the skyrmion Hall effect which causes the skyrmions to acquire a transverse velocity component. We show how to use spin-orbit interaction to control the skyrmion Hall angle and how the interplay of spin-transfer and spin-orbit torques can lead to a complete suppression of the transverse motion. Since the spin-orbit torques can be controlled all-electronically by a gate voltage, the s…
Magnetic skyrmions are particle-like topological spin configurations, which can carry binary information and thus are promising building blocks for future spintronic devices. In this work, we investigate the relationship between the skyrmion dynamics and the characteristics of injected current in a skyrmion-based spin torque nano-oscillator, where the excitation source is introduced from a point nano-contact at the center of the nanodisk. It is found that the skyrmion will move away from the center of the nanodisk if it is driven by a spin-polarized current; however, it will return to the init…
Spin pumping is a widely recognized method to generate the spin current in the spintronics, which is acknowledged as a fundamentally dynamic process equivalent to the spin-transfer torque. In this work, we theoretically verify that the oscillating spin current can be pumped from the microwave-motivated breathing skyrmion. The skyrmion spin pumping can be excited by a relatively low frequency compared with the ferromagnetic resonance (FMR) and the current density is larger than the ordinary FMR spin pumping. Based on the skyrmion spin pumping, we build a high reading-speed racetrack memory mode…
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…
We formulate a general microscopic approach to spin-orbit torques in thin ferromagnet/heavy-metal bilayers in linear response to electric current or electric field. The microscopic theory we develop avoids the notion of spin currents and spin-Hall effect. Instead, the torques are directly related to a local spin polarization of conduction electrons, which is computed from generalized Kubo-Středa formulas. A symmetry analysis provides a one-to-one correspondence between polarization susceptibility tensor components and different torque terms in the Landau-Lifshitz-Gilbert equation for magnetiza…
Skyrmions dynamics in the approximation of point-particle skyrmions is considered in the multiferroic insulators, where the spiral magnetic structure is accompanied by finite electric dipole moment. The skyrmion motion is studied in the gradients of perpendicular magnetic and electric fields. The nonuniform magnetic field with a fixed gradient magnitude leads to the spiral motion, where skyrmion circulates in the plane perpendicular to the direction of magnetic field. The frequency of circulation is fixed by the derivative of the external magnetic field and the magnitude of the dipole moment. …
Magnetic skyrmions are particle-like topological excitations that recently generated much interest as candidates for future spintronic devices based on skyrmion small size, enhanced topological stability, and/or mutual interaction. Here we examine the properties of isolated skyrmions in a frustrated chiral magnet with competing Dzyaloshinskii-Moriya and frustrated exchange interactions. We show that the skyrmion size drastically decreases even for small values of competing stabilization mechanisms. Skyrmion mutual interaction remains attracting as is inherent for frustrated skyrmions, but the …
We demonstrate that the nontrivial magnetic texture of antiferromagnetic skyrmions (AFM-Sks) promotes a non-vanishing topological spin Hall effect (TSHE) on the flowing electrons. This results in a substantial enhancement of the non-adiabatic torque and hence improves the skyrmion mobility. This non-adiabatic torque increases when decreasing the skyrmion size, and therefore scaling down results in a much higher torque efficiency. In clean AFM-Sks, we find a significant boost of the TSHE close to van Hove singularity. Interestingly, this effect is enhanced away from the band gap in the presence…
We formulate and study the general boundary conditions dictating the magnetization profile in the vicinity of an interface between magnets with dissimilar properties. Boundary twists in the vicinity of an edge due to Dzyaloshinskii-Moriya interactions have been first discussed in [Wilson et al., Phys. Rev. B 88, 214420 (2013)] and in [Rohart and Thiaville, Phys. Rev. B 88, 184422 (2013)]. We show that in general case the boundary conditions lead to the magnetization profile corresponding to the Néel, Bloch, or intermediate twist. We explore how such twists can be utilized for creation of skyrm…
In this work, we investigated the spin dynamics in a slab of chiral magnets induced by an alternating (ac) spin current. Periodic trajectories of the skyrmion in real space are discovered under the ac current as a result of the Magnus and viscous forces, which originate from the Gilbert damping, the spin transfer torque, and the $ β$-nonadiabatic torque effects. The results are obtained by numerically solving the Landau-Lifshitz-Gilbert equation and can be explained by the Thiele equation characterizing the skyrmion core motion.
We formulate a theory of skyrmion and antiskyrmion generation using magnetic field and charge current pulses. We show that the topological defect can be created at an edge of a system with Dzyaloshinskii-Moriya interaction (DMI) as well as at a boundary between regions with different DMI. We consider both perpendicular and in-plane (also known as magnetic bimerons) versions of skyrmions and antiskyrmions. We show that the magnetization twist in the vicinity of an edge or a boundary is described by a kink solution, the presence of which can instigate the generation of topological defects. We st…
Current-induced dynamics of twisted domain walls and skyrmions in ferromagnetic perpendicularly magnetized multilayers is studied through three-dimensional micromagnetic simulations and analytical modeling. It is shown that such systems generally exhibit a Walker breakdown-like phenomenon in the presence of current-induced damping-like spin-orbit torque. Above a critical current threshold, corresponding to typical velocities of the order tens of m/s, domain walls in some layers start to precess with frequencies in the gigahertz regime, which leads to oscillatory motion and a significant drop i…
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…
A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin Hall effect has recently been demonstrated. Here, we study the fundamental properties of this type of motion by combining micromagnetic simulations and a generalized Thiele equation. We find that the anisotropy gradient drives the skyrmion mainly along the direction perpendicular to the gradient, due to the conservative part of the torque. There is some slower motion along the direction parallel to the anisotropy gradient due to damping torque. When an appropriate spin Hall torque is added, the skyrmion vel…
Magnetic skyrmions are topologically protected states that are very promising for the design of the next generation of ultralow-power electronic devices. In this letter, we propose a magnetic tunnel junction based spin-transfer torque diode with a magnetic skyrmion as ground state and a perpendicular polarizer patterned as nanocontact for a local injection of the current. The key result is the possibility to achieve sensitivities (i.e. detection voltage over input microwave power) larger than 2000V/W for optimized contact diameters. Our results can be very useful for the identification of a ne…
Integrating topologically stabilized magnetic textures such as skyrmions as nanoscale information carriers into future technologies requires the reliable control by electric currents. Here, we uncover that the relevant skyrmion Hall effect, which describes the deflection of moving skyrmions from the current flow direction, acquires important corrections owing to anisotropic spin-orbit torques that alter the dynamics of topological spin structures. Thereby, we propose a viable means for manipulating the current-induced motion of skyrmions and antiskyrmions. Based on these insights, we demonstra…
Skyrmion nucleation induced by spin-transfer torques at an interface of a topological insulator and a ferromagnetic insulator is investigated. Due to strong spin-orbit coupling on a surface of topological insulators, which enhances the effect of spin torques, efficient manipulation of skyrmions is expected, and therefore, topological insulators could provide the ideal platform to achieve high-performance skyrmionic devices. Using micromagnetic simulations and energetics, we evaluate properties of the skyrmion nucleation on a surface of topological insulators, such as nucleation time, critical …
Spin transfer torque (STT) affords magnetic nanodevices the potential to act as memory, computing, and microwave elements operating at ultra-low currents and at a low energy cost. Spin transfer torque is not only effective in manipulating well-known magnetic structures, such as domain walls and vortices, but can also nucleate previously unattainable nano-magnetic objects, such as magnetic droplets and skyrmions. While the droplet and the skyrmion are both solitons, the former is inherently dynamic and non-topological, whereas the latter is static but topologically protected. Here we show that …
A moving magnetic skyrmion exhibits transverse deflection. This so-called skyrmion Hall effect has been explained by the Thiele equation. Here, we provide an alternative interpretation of the skyrmion Hall effect based on the dynamics of domain walls enclosing the skyrmion. We relate the spin-torque-induced local rotation of the domain wall segments to the shift of the skyrmion core, explaining the skyrmion Hall effect at the micromagnetic level. Bases on our intuitive interpretation, we also show that the skyrmion Hall effect can be suppressed by combining the spin-transfer and spin-orbit tor…
We review recent progresses towards an understanding of the Skyrmion Hall transport in insulating as well as conducting materials. First, we consider a theoretical breakthrough based on the quantum field theory Ward identity, a first principle analysis, relying on symmetries and conservation laws. Broken parity (inversion) symmetry plays a crucial role in Skyrmion Hall transport. In addition to the well known thermal and electric Hall conductivities, our analysis has led us to the discovery of a new and unforeseen physical quantity, Hall viscosity - an anti-symmetric part of the viscosity tens…
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 uniform motion of chiral magnetic skyrmions induced by a spin-transfer torque displays an intricate dependence on the skyrmions' topological charge and shape. We reveal surprising patterns in this dependence through simulations of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them through a geometric analysis of Thiele's equation. In particular, we show that the velocity distribution of topologically non-trivial skyrmions depends on their symmetry: it is a single circle for skyrmions of high symmetry and a family of circles for low-symmetry configurations. We also s…
