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 leads to rapidly decreasing skyrmion Hall angles for small skyrmion diameters, as well as a skyrmion Hall angle versus skyrmion velocity dependence nearly independent of the surface roughness characteristics. Also, the effect of various disordered energy landscapes, in the form of surface roughness, on the skyrmion Hall angle and velocity is shown to be largely drive-dependent. Our results show good agreement with those found in experiments thus concluding that the interfacial spin-transfer torque should be included in micromagnetics simulations for the reproduction of experimental results.
Neél skyrmions originate from interfacial Dzyaloshinskii Moriya interaction (DMI). Recent studies have explored using ferromagnet to host Neél skyrmions for device applications. However, challenges remain to reduce the size of skyrmion to near 10 nm. Amorphous rare-earth-transitional-metal ferrimagnets are attractive alternative materials to obtain ultrasmall skyrmions at room temperature. Their intrinsic perpendicular magnetic anisotropy and tunable magnetization provides a favorable environment for skyrmion stability. In this work, we employ atomistic stochastic Landau-Liftshitz-Gilbert (LLG…
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 …
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…
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…
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 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…
The presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) may lead to the appearance of Néel skyrmions in ferromagnetic films. These topologically protected structures, whose diameter is as small as a few nanometers, can be nowadays stabilized at room temperature and have been proposed for the realization of artificial magnonic crystals and new spintronic devices, such as racetrack memories. In this perspective, it is of utmost importance to analyze their dynamical properties in the GHz range, i.e. in the operation range of current communication devices. Here we exploited the softwar…
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…
In the Kerr rotation geometry, magneto optic memory devices typically suffer from low figure-of-merit (FOM) and long write times. We show that skyrmions formed at the interface of a thin-film multiferroic and a topological insulator can give rise to high FOM magneto optic Kerr effects (MOKEs). Huge differential MOKE can arise in parts of the phase diagram. Resonance like features in the MOKE spectra arising from the induced low energy TI bandgap, the multiferroic-film thickness, and the high energy Drude like behavior are resolved and explained. The Fermi level dependence of the MOKE signature…
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…
Spin-orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin-orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin-orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin-orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimen…
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…
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…
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…
Interfacial orbital transmission, conversion, and mechanical torque in metals
Aix-Marseille Université（艾克斯-马赛大学）；Korea University（高丽大学）；Forschungszentrum Jülich（于利希研究中心）；Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学）；Norwegian University of Science and Technology（挪威科技大学）
Effective interfacial Dzyaloshinskii-Moriya interaction and skyrmion stabilization in ferromagnet/paramagnet and ferromagnet/superconductor hybrid systems
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 present measurements of spin orbit torques generated by Ir as a function of film thickness in sputtered Ir/CoFeB and Ir/Co samples. We find that Ir provides a damping-like component of spin orbit torque with a maximum spin torque conductivity 1.4e5 in SI unit and a maximum spin-torque efficiency of 0.04, which is sufficient to drive switching in an 0.8 nm film of CoFeB with perpendicular magnetic anisotropy. We also observe a surprisingly large field like spin orbit torque. Measurements as a function of Ir thickness indicate a substantial contribution to the FLT from an interface mechanism …
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…
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…
An enhancement of the spin-orbit effects arising on an interface between a ferromagnet (FM) and a heavy metal (HM) is possible through the strong breaking of the structural inversion symmetry in the layered films. Here we show that the introduction of an ultrathin W interlayer between Co and Ru in Ru/Co/Ru films enables to preserve perpendicular magnetic anisotropy (PMA) and simultaneously induce a large interfacial Dzyaloshinskii-Moriya interaction (iDMI). We find that the Ru/Co/W/Ru films have PMA up to 0.35 nm of the nominal thickness of W (tW). The study of the spin-wave propagation in the…
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…
The topological Hall effect is used extensively to study chiral spin textures in various materials. However, the factors controlling its magnitude in technologically-relevant thin films remain uncertain. Using variable temperature magnetotransport and real-space magnetic imaging in a series of Ir/Fe/Co/Pt heterostructures, here we report that the chiral spin fluctuations at the phase boundary between isolated skyrmions and a disordered skyrmion lattice result in a power-law enhancement of the topological Hall resistivity by up to three orders of magnitude. Our work reveals the dominant role of…
In bilayer systems consisting of an ultrathin ferromagnetic layer adjacent to a metal with strong spin-orbit coupling, an applied in-plane current induces torques on the magnetization. The torques that arise from spin-orbit coupling are of particular interest. Here, we calculate the current-induced torque in a Pt-Co bilayer to help determine the underlying mechanism using first principles methods. We focus exclusively on the analogue to the Rashba torque, and do not consider the spin Hall effect. The details of the torque depend strongly on the layer thicknesses and the interface structure, pr…
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…
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…
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…
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…
Janus skyrmion: Interfacial quasiparticle with two-faced helicity
Waseda University（早稻田大学）；The Hong Kong University of Science and Technology（香港科技大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Finding efficient ways of manipulating magnetic bits is one of the core goals in spintronic research. Electrically-generated spin-orbit torques (SOTs) are good candidates for this and the search for materials capable of generating highly-efficient SOTs has gained a lot of traction in the recent years. While antiferromagnet/ferromagnet bilayer structures have been employed extensively for passive applications, e.g. by using exchange bias fields, their active properties are not yet widely employed. Here we show the presence of large interfacial SOTs in bilayer of a ferromagnet and the two-dimens…
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…
We investigate an interfacial spin-transfer torque and $β$-term torque with alternating current (AC) parallel to a magnetic interface. We find that both torques are resonantly enhanced as the AC frequency approaches to the exchange splitting energy. We show that this resonance allows us to estimate directly the interfacial exchange interaction strength from the domain wall motion. We also find that the $β$-term includes an unconventional contribution which is proportional to the time derivative of the current and exists even in absence of any spin relaxation processes.
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…
Using the first-principles non-equilibrium Green's function technique with supercell disorder averaging, we study the influence of interfacial intermixing on the spin-orbit torque in Co$\mid$Pt bilayers. Intermixing is modeled by inserting one or more monolayers of a disordered CoPt alloy between Co and Pt. Dampinglike torque is moderately enhanced by interfacial intermixing, while the fieldlike torque, which is small for abrupt interfaces, is strongly enhanced and becomes comparable to the dampinglike torque. The enhancement of the fieldlike torque is attributed to the interface between Co an…
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 …
