Voltage manipulation of skyrmions is a promising path towards low-energy spintronic devices. Here, voltage effects on skyrmions in a GdOx/Gd/Co/Pt heterostructure are observed experimentally. The results show that the skyrmion density can be both enhanced and depleted by the application of an electric field, along with the ability, at certain magnetic fields to completely switch the skyrmion state on and off. Further, a zero magnetic field skyrmion state can be stablized under a negative bias voltage using a defined voltage and magnetic field sequence. The voltage effects measured here occur on a few-second timescale, suggesting an origin in voltage-controlled magnetic anisotropy rather than ionic effects. By investigating the skyrmion nucleation rate as a function of temperature, we extract the energy barrier to skyrmion nucleation in our sample. Further, micromagnetic simulations are used to explore the effect of changing the anisotropy and Dzyaloshinskii-Moriya interaction on skyrmion density. Our work demonstrates the control of skyrmions by voltages, showing functionalities desirable for commercial devices.
Magnetic skyrmions are topological magnetic spin structures exhibiting particle-like behaviour. They are of strong interest from a fundamental viewpoint and for application, where they have potential to act as information carriers in future low-power computing technologies. Importantly, skyrmions have high physical stability because of topological protection. However, they have potential to deform according to their local energy environment. Here we demonstrate that, in regions of high exchange energy density, skyrmions may exhibit such extreme deformation that spontaneous merging with nearest…
Skyrmions have become one of the most visited topics during the last decade in condensed matter physics. In this work, and by means of analytical calculations and micromagnetic simulations, we explore the effect of the magnetostatic field generated by a magnetic tip on the stability of skyrmions. Our results show that the interaction energy between the tip and the skyrmion plays a fundamental role in the stabilization of Néel skyrmions confined in nanodisks, allowing its nucleation and annihilation, and also providing precise control of its size and polarity. Based on our results, we propose a…
When magnetic skyrmions are moved via currents, they do not strictly travel along the path of the current, instead their motion also gains a transverse component. This so-called skyrmion Hall effect can be detrimental in potential skyrmion devices because it drives skyrmions towards the edge of their hosting material where they face potential annihilation. Here we experimentally modify a skyrmion model system - an atomic Pd/Fe bilayer on Ir(111) - by decorating the film edge with ferromagnetic Co/Fe patches. Employing spin-polarized scanning tunneling microscopy, we demonstrate that this ferro…
Magnetic skyrmions are nano-scale magnetic states that could be used in various spintronics devices. A central issue is the mechanism and rate of various possible annihilation processes and the lifetime of metastable skyrmions. While most studies have focused on classical over-the-barrier mechanism for annihilation, it is also possible that quantum mechanical tunneling through the energy barrier takes place. Calculations of the lifetime of magnetic skyrmions in a two-dimensional lattice are presented and the rate of tunneling compared with the classical annihilation rate. A remarkably strong v…
In this work, we utilize voltage controlled magnetic anisotropy (VCMA) to manipulate magnetic skyrmions that are fixed in space. Memory devices based on this strategy can potentially be of smaller footprint and better energy efficiency than current-controlled motion-based skyrmionic devices. To demonstrate VCMA induced manipulation of skyrmions, we fabricate antiferromagnet/ferromagnet/oxide heterostructure films where skyrmions can be stabilized without any external magnetic field due to the presence of exchange bias. These isolated skyrmions were annihilated by applying a voltage pulse that …
We demonstrate the controlled generation and annihilation of (anti)skyrmions with tunable chirality in magnetic heterostructures by means of micromagnetic simulations. By making use of magnetic (anti)vortices in patterned ferromagnetic layer, we stabilize full lattices of (anti)skyrmions in an underlying skyrmionic thin film in a reproducible manner. The stability of the (anti)skyrmion depends on the polarization of the (anti)vortex, whereas their chirality is given by those of the (anti)vortices. Furthermore, we demonstrate that the core coupling between the (anti)vortices and (anti)skyrmions…
A method for finding minimum energy paths of transitions in magnetic systems is presented and used to determine the mechanism and estimate the activation energy of skyrmion and antivortex annihiliation in nano-systems. The path is optimized with respect to orientation of the magnetic vectors while their magnitudes are fixed or obtained from separate calculations. The curvature of the configuration space is taken into account by: (1) using geodesics to evaluate distances and displacements of the system during the optimization, and (2) projecting the path tangent and the magnetic force on the ta…
We study annihilation mechanisms of small first- and second-order skyrmions and antiskyrmions on the frustrated $J_1-J_2-J_3$ square lattice with broken inversion symmetry (DMI). We find that annihilation happens via the injection of the opposite topological charge in the form of meron or antimeron nucleation. Overall, the exchange frustration generates a complex energy landscape with not only many (meta)stable and unstable local energy solutions, but also many possible paths connecting them. Whenever possible, we compute the activation energy and attempt frequency for the annihilation of isol…
Breathing oscillations of skyrmions in chiral antiferromagnets can be excited by a temporal modification of the Dzyaloshinskii-Moriya interaction or magnetocrystalline anisotropy strength. We employ an adiabatic approximation and derive a formula for the potential that directly implies breathing oscillations. We study the nonlinear regime and the features of larger amplitude oscillations. We show that there is a maximum amplitude supported by the potential. As a consequence, we predict theoretically and observe numerically skyrmion annihilation events due to excitation of large amplitude breat…
Magnetic skyrmions hold promise for spintronic devices. To explore the dynamical properties of skyrmions in devices, a nanoscale method to image spin textures in response to a stimulus is essential. Here, we apply a technique for operando electrical current pulsing of chiral magnetic devices in a Lorentz transmission electron microscope. In ferromagnetic multilayers with interfacial Dzyaloshinskii-Moriya interaction (DMI), we study the creation and annihilation of skyrmions localized by point-like pinning sites due to defects. Using a combination of experimental and micromagnetic techniques, w…
Magnetic skyrmions are intriguing topological spin textures that promise future high-density spintronic devices. The creation of magnetic skyrmions has been understood based on the energetics of skyrmions, but the detailed dynamic process of the skyrmion creation remains unclear. Here topological evolution in conversion from uneven domains to Néel-skyrmions is investigated using micromagnetic simulations. We find that, rather than the overall topological charge, annihilation of novel topological defects, i.e., recently suggested domain wall skyrmions, dominantly govern the skyrmion creation pr…
Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle point textures and energy barriers of large skyrmions. The sign of the spin stiffne…
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…
Since the 1950s, topological solitons have been used to describe elementary particles[1-3] and particle-like field configurations[4-13] that appear in almost all branches of physics ranging from subatomic to cosmological scales[3,14-16]. In this context, formation and annihilation of particles corresponds to topological phase transitions, whose actual process and mechanism remain elusive. Here, we show that annihilation of an isolated skyrmion in helimagnets as the applied magnetic field increases initiates at its center point by a local magnetization reversal. At the critical field, a soft mo…
Magnetic skyrmions are believed to be the promising candidate of information carriers in spintronics. However, the skyrmion Hall effect due to the nontrivial topology of skyrmions can induce a skyrmion accumulation or even annihilation at the edge of the devices, which hinders the real-world applications of skyrmions. In this work, we theoretically investigate the current-driven skyrmion motion on magnetic nanotubes which can be regarded as "edgeless" in the tangential direction. By performing micromagnetic simulations, we find that the skyrmion motion exhibits a helical trajectory on the nano…
In a broad range of applied magnetic fields and material parameters isolated magnetic skyrmions condense into skyrmion lattices. While the geometry of isolated skyrmions and their lattice counterparts strongly depend on field and Dzyaloshinski-Moriya interaction, this issue has not been adequately addressed in previous studies. Meanwhile, this information is extremely important for applications, because the skyrmion size and the interskyrmion distance have to be tuned for skyrmion based memory and logic devices. In this investigation we elucidate the size and density-dependent phase diagram sh…
We compute annihilation rates of metastable magnetic skyrmions using a form of Langer's theory in the intermediate-to-high damping (IHD) regime. For a Néel skyrmion, a Bloch skyrmion, and an antiskyrmion, we look at two possible paths to annihilation: collapse and escape through a boundary. We also study the effects of a curved vs. a flat boundary, a second skyrmion and a non-magnetic defect. We find that the skyrmion's internal modes play a dominant role in the thermally activated transitions compared to the spin-wave excitations and that the relative contribution of internal modes depends on…
When magnetic skyrmions move under spin orbit torque in magnetic nanowires, they experience a skyrmion Hall effect, which pushes them towards the nanowire edge where they risk being annihilated; this puts an upper limit on how fast they can be driven. However, the same magnetic multilayer harboring skyrmions can sustain a Néel-type strip domain wall along the nanowire length, potentially keeping the skyrmions separated from the edge. Here we study the interplay between current driven skyrmions and domain walls and find that they increase the annihilation current and allow the skyrmions to move…
Controllable writing and deleting of nanoscale magnetic skyrmions are key requirements for their use as information carriers for next-generation memory and computing technologies. While several schemes have been proposed, they require complex fabrication techniques or precisely tailored electrical inputs, which limits their long-term scalability. Here we demonstrate an alternative approach for writing and deleting skyrmions using conventional electrical pulses within a simple, two-terminal wire geometry. X-ray microscopy experiments and micromagnetic simulations establish the observed skyrmion…
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.
Magnetic skyrmions are chiral nanoscale spin textures which are usually induced by Dzyaloshinskii-Moriya interaction (DMI). Recently, magnetic skyrmions have been observed in two-dimensional (2D) van der Waals (vdW) ferromagnetic materials, such as Fe$_{3}$GeTe$_{2}$. The electric control of skyrmions is important for their potential application in low-power memory technologies. Here, we predict that DMI and magnetic skyrmions in a Fe$_{3}$GeTe$_{2}$ monolayer can be controlled by ferroelectric polarization of an adjacent 2D vdW ferroelectric In$_{2}$Se$_{3}$. Based on density functional theor…
Magnetic skyrmions are key candidates for novel memory, logic, and neuromorphic computing. An essential property is their topological protection caused by the whirling spin texture as described by a robust integer winding number. However, the realization on an atomic lattice leaves a loophole for switching the winding number via concerted rotation of individual spins. Hence, understanding the unwinding microscopically is key to enhance skyrmion stability. Here, we use spin polarized scanning tunneling microscopy to probe skyrmion annihilation by individual hot electrons and obtain maps of the …
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 $-$ localized chiral spin structures $-$ show great promise for spintronic applications. The recent discovery of two-dimensional (2D) magnetic materials opened new opportunities for exploring such topological spin structures in atomically thin van der Waals (vdW) materials. Despite recent progress in stabilizing metastable skyrmions in 2D magnets, their diameters are still beyond 100~nm and their lifetime, which is essential for applications, has not been explored yet. Here, using first-principles calculations and atomistic spin simulations, we predict that compressive mecha…
In the cubic chiral magnet Fe$_{1-x}$Co$_{x}$Si a metastable state comprising of topologically nontrivial spin whirls, so-called skyrmions, may be preserved down to low temperatures by means of field cooling the sample. This metastable skyrmion state is energetically separated from the topologically trivial ground state by a considerable potential barrier, a phenomenon also referred to as topological protection. Using magnetic force microscopy on the surface of a bulk crystal, we show that certain positions are preferentially and reproducibly decorated with metastable skyrmions, indicating tha…
Inevitable for the basic principles of skyrmion racetrack-like applications is not only their confined motion along one-dimensional channels but also their controlled creation and annihilation. Helical magnets have been suggested to naturally confine the motion of skyrmions along the tracks formed by the helices, which also allow for high-speed skyrmion motion. We propose a protocol to create topological magnetic structures in a helical background. We furthermore analyse the stability and current-driven motion of the skyrmions in a helical background with in-plane uniaxial anisotropy fixing th…
Magnetic phase transitions are a test bed for exploring the physics of non-equilibrium phenomena in condensed matter, which become even more complex when topological constraints are involved. In particular, the investigation of skyrmions and skyrmion lattices offers insight into fundamental processes of topological-charge creation and annihilation upon changing the magnetic state. Nonetheless, the exact physical mechanisms behind these phase transitions remain unresolved. Here, we have systematically compared ultra-thin films with isotropic and anisotropic Dzyaloshinskii-Moriya interactions (D…
We experimentally study the thermoelectrical signature of individual skyrmions in chiral Pt/Co/Ru multilayers. Using a combination of controlled nucleation, single skyrmion annihilation, and magnetic field dependent measurements the thermoelectric signature of individual skyrmions is characterized. The observed signature is explained by the anomalous Nernst effect of the skyrmions spin structure. Possible topological contributions to the observed thermoelectrical signature are discussed. Such thermoelectrical characterization allows for non-invasive detection and counting of skyrmions and enab…
The stability of two-dimensional chiral skyrmions in a tilted magnetic field is studied. It is shown that by changing the direction of the field and its magnitude, one can continuously transform chiral skyrmion into a skyrmion with opposite polarity and vorticity. This turned inside out skyrmion can be considered as an antiparticle for ordinary axisymmetric skyrmion. For any tilt angle of the magnetic field, there is a range of its absolute values where two types of skyrmions may coexist. In a tilted field, the potentials for inter-skyrmion interactions are characterized by the presence of loc…
A self-consistent field theory is introduced and used to investigate the thermodynamics and spin dynamics of an $S = 1$ quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. It is shown that the Skyrmion carries a phase transition to the ferromagnetic phase of first order with increasing temperature, while the magnetization of the surrounding ferromagnet undergoes a phase transition of second order when changing to the paramagnetic phase. Furthermore, the electric field driven annihilation process of the Sk…
Magnetic skyrmions are the self-organized topological spin textures behaving like particles. Because of their fast creation and typically long lifetime, experimental verification of skyrmion's creation/annihilation processes has been challenging. Here we successfully track skyrmions dynamics in defect-introduced Co9Zn9Mn2, by using pump-probe Lorentz transmission electron microscope. Following the nanosecond-photothermal excitation, we resolve 160-nm-skyrmion's proliferation at <1 ns, contraction at 5 ns, drift from 10 ns to 4 microsecond and coalescence at 5 microsecond. These motions relay t…
Solitonic magnetic excitations such as domain walls and, specifically, skyrmionics enable the possibility of compact, high density, ultrafast,all-electronic, low-energy devices, which is the basis for the emerging area of skyrmionics. The topological winding of skyrmion spins affects their overall lifetime, energetics and dynamical behavior. In this review, we discuss skyrmionics in the context of the present day solid state memory landscape, and show how their size, stability and mobility can be controlled by material engineering, as well as how they can be nucleated and detected. Ferrimagnet…
We investigate the skyrmion formation process in nano-structured FeGe Hall-bar devices by measurements of topological Hall effect, which extracts the winding number of a spin texture as an emergent magnetic field. Step-wise profiles of topological Hall resistivity are observed in the course of varying the applied magnetic field, which arise from instantaneous changes in the magnetic nano-structure such as creation, annihilation, and jittering motion of skyrmions. The discrete changes in topological Hall resistivity demonstrate the quantized nature of emergent magnetic flux inherent in each sky…
Magnetic skyrmions and their anti-particles, the antiskyrmions, are stable magnetic solitons existing down to the nanometer scale. Their stability and size as well as the possibility to propel them by, e.g., electric currents make them promising candidates for the use in memory devices, such as racetrack memories. Skyrmions and antiskyrmions share those same advantages individually, but may annihilate each other when they coexist in the same device. Yet, combining them to represent logical bits of 0 (skyrmion) and 1 (antiskyrmion) in one device opens new possibilities to create new types of de…
Magnetic skyrmion technology is promising for the next-generation spintronics-based memory and neuromorphic computing due to their small size, non-volatility and low depinning current density. However, the Magnus force originating from the skyrmion Hall effect causes the skyrmion to move along a curved trajectory, which may lead to the annihilation of the skyrmion in a nanotrack during current-induced skyrmion motion. Consequently, circuits utilizing skyrmionic motion need to be designed to limit the impact of the skyrmion Hall effect. In this work, we propose a design of an artificial neuron,…
The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls -- skyrmions -- driven along magnetic strips. Stability of the skyrmions is a critical issue for the realization of this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory ca…
Magnetic skyrmions are topological solitons that exhibit an increased stability against annihilation, and can be displaced with low current densities, making them a promising candidate as an information carrier. In order to demonstrate a viable skyrmion-based memory device, it is necessary to reliably and reproducibly nucleate, displace, detect, and delete the magnetic skyrmions. While the skyrmion displacement and detection have both been investigated in detail, much less attention has been dedicated to the study of the sub-ns dynamics of the skyrmion nucleation process. Only limited studies …
Skyrmions and skyrmion crystal (SkX) discovered in chiral magnets show unique physical properties due to their nontrivial topology such as the stability against the annihilation and the motion driven by the ultralow current density, which can be advantageous for the device applications such as magnetic memories. Especially, the chiral dynamics, i.e., the velocity perpendicular to the force acting on a skyrmion, is a key to avoid the impurity potential and enhances its mobility. However, the collective pinning of SkX occurs by the disorder, which is crucial for its low energy properties. Here, …
Magnetic multilayers are promising tuneable systems for hosting magnetic skyrmions at/above room temperature. Revealing their intriguing switching mechanisms and associated inherent electrical responses are prerequisites for developing skyrmionic devices. In this work, we theoretically demonstrate the annihilation of single skyrmions occurring through a multilayer structure, which is mediated by hopping dynamics of topological hedgehog singularities known as Bloch points. The emerging intralayer dynamics of Bloch points are dominated by the Dzyaloshinskii-Moriya interaction, and their propagat…
Topologically stable magnetic skyrmion has a much lower depinning current density that may be useful for memory as well as neuromorphic computing. However, skyrmion-based devices suffer from the Magnus force originating from the skyrmion Hall effect, which may result in unwanted skyrmion annihilation if the magnitude of the driving current gets too large. A design of an artificial neuron and a synapse using a synthetic antiferromagnetically coupled bilayer device, which nullifies the Magnus force, is demonstrated in this work. The leak term in the artificial leaky integrate-and-fire neuron is …
Magnetic skyrmion, vortex-like swirling topologically stable spin configurations, is appealing as information carrier for future nanoelectronics, owing to the stability, small size and extremely low driving current density. One of the most promising applications of skyrmion is to build racetrack memory (RM). Compared to domain wall-based RM (DW-RM), skyrmion-based RM (Sky-RM) possesses quite a few benefits in terms of energy, density and speed etc. Until now, the fundamental behaviors, including nucleation/annihilation, motion and detection of skyrmion have been intensively investigated. Howev…
Optimized control protocols for stable skyrmion creation using deep reinforcement learning
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Pohang University of Science and Technology（浦项科技大学）
Skyrmionic textures are being extensively investigated due to the occurrence of novel topological magnetic phenomena and their promising applications in a new generation of spintronic devices that take advantage of the robust topological stability of their spin structures. The development of practical devices relies on a detailed understanding of how skyrmionic structures can be formed, transferred, detected and annihilated. In this work, our considerations go beyond static skyrmions and theoretically show that the formation/annihilation of both skyrmions and antiskyrmions is enabled by the tr…
