Magnetic skyrmions are chiral spin textures which have attracted intense research for their fundamentally novel physics and potential applications as spintronic information carriers. The stability which makes them so potentially useful is a result of their underlying non-trivial topology. While skyrmions were originally predicted and observed in crystalline materials lacking inversion symmetry, some of the most promising host systems for skyrmions are multilayer thin films, where skyrmions have been stabilized at ambient conditions, which is critical for their use in real world devices. The skyrmions found in multilayer thin films have additional three-dimensional structure, with their domain wall helicities twisting through the thickness of the film to create a hybrid skyrmion composed of a Bloch-type core with Néel-type caps of opposite chiralities at the surfaces. In this work, we show that this three-dimensional variation creates additional knotted topological structure, providing an explanation for their exceptional stability in ambient conditions. We show that hybrid skyrmions can be described as half-integer Hopfions, and that their field lines have the knotted structure of the Hopf fibration. Furthermore, we show that the topological charge of partially twisted hybrid skyrmions can be related to the domain wall helicity at the surfaces, providing a straightforward way to connect experimental measurements to underlying topology.
We present micromagnetic simulations on resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 32 mT coinciding with a transition from Hopfions to magnetic torons. The modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space, and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. The marked differences in spin wave spectra between Hopfions, torons and target skyrmions can serve as fin…
A magnetic Hopfion is a three-dimensional topological soliton that consists of a closed loop of a twisted magnetic Skyrmion string. The results of numerical simulations are presented that demonstrate the existence of a stable Hopfion in a nanocylinder of a chiral magnet and an explicit analytic expression is shown to provide a reasonable approximation to the numerically computed Hopfion. A mechanism is suggested to create the Hopfion from a target Skyrmion by introducing an interfacial perpendicular magnetic anisotropy.
We report the experimental observation of magnetic skyrmion-like states in patterned ferromagnetic nanostructures consisting of perpendicular magnetized Co/Pt multilayer film exchange coupled with Co nanodisks in vortex state. The magnetic force microscopy and micromagnetic simulations show that depending on the magnitude of Co/Pt perpendicular anisotropy in these systems two different modes of skyrmion formation are realized.
Neel skyrmions are of high interest due to their potential applications in a variety of spintronic devices, currently accessible in ultrathin heavy metal/ferromagnetic bilayers and multilayers with a strong Dzyaloshinskii-Moriya interaction. Here we report on the direct imaging of chiral spin structures including skyrmions in an exchange coupled Co/Pd multilayer at room temperature with Lorentz transmission electron microscopy, a high resolution technique previously suggested to exhibit no Neel skyrmion contrast. Phase retrieval methods allow us to map the internal spin structure of the skyrmi…
We show that magnetic skyrmions can be stabilized at room temperature in continuous Ir/Co/Pt multilayers on SiO2/Si substrate without prior application of electric current or magnetic field. While decreasing the Co thickness, tuning of the magnetic anisotropy gives rise to a transition from worm-like domain patterns to long and separate stripes. The skyrmions are clearly imaged in both states using Magnetic Force Microscopy. The density of skyrmions can be significantly enhanced after applying the in-plane field procedure. In addition, we have investigated the phase diagram of a sample deposit…
Magnetic skyrmions are localized, topologically protected spin-structures that have been proposed for storing or processing information due to their intriguing dynamical and transport properties. Important in terms of applications is the recent discovery of interface stabilized skyrmions as evidenced in ultra-thin transition-metal films. However, so far only skyrmions at interfaces with a single atomic layer of a magnetic material were reported, which greatly limits their potential for application in devices. Here, we predict the emergence of skyrmions in [4d/Fe_2/5d]_n multilayers, i.e. struc…
Facing the ever-growing demand for data storage will most probably require a new paradigm. Magnetic skyrmions are anticipated to solve this issue as they are arguably the smallest spin textures in magnetic thin films in nature. We designed cobalt-based multilayered thin films where the cobalt layer is sandwiched between two heavy metals providing additive interfacial Dzyaloshinskii-Moriya interactions, which reach about 2 mJ/m2 in the case of the Ir/Co/Pt multilayers. Using a magnetization-sensitive scanning x-ray transmission microscopy technique, we imaged magnetic bubble-like domains in the…
Facing the ever-growing demand for data storage will most probably require a new paradigm. Nanoscale magnetic skyrmions are anticipated to solve this issue as they are arguably the smallest spin textures in magnetic thin films in nature. We designed cobalt-based multilayered thin films where the cobalt layer is sandwiched between two heavy metals providing additive interfacial Dzyaloshinskii-Moriya interactions, which reach a value close to 2 mJ m-2 in the case of the Ir|Co|Pt asymmetric multilayers. Using a magnetization-sensitive scanning x-ray transmission microscopy technique, we imaged sm…
We report on a general principle using the interlayer exchange coupling to extend the regime of chiral magnetic films in which stable or metastable magnetic skyrmions can appear at zero magnetic field. We verify this concept on the basis of a first-principles model for a Mn monolayer on W(001) substrate, a prototype chiral magnet for which the atomic-scale magnetic texture is determined by the frustration of exchange interactions, impossible to unwind by laboratory magnetic fields. By means of \textit{ab initio} calculations for the Mn/W$_m$/Co$_n$/Pt/W(001) multilayer system we show that for …
We have studied the effects of electrical current pulses on skyrmion formation in a series of Co/Ni/Pt-based multilayers. Transmission X-ray microscopy reveals that by applying electrical current pulses of duration and current density on the order of $τ$=50 $μ$s and j=1.7x10$^1$$^0$ A/m$^2$, respectively, in an applied magnetic field of $μ$$_0$Hz=50 mT, stripe-to-skyrmion transformations are attained. The skyrmions remain stable across a wide range of magnetic fields, including zero field. The skyrmions then remain stable across a wide range of magnetic fields, including zero field. We primari…
By means of systematic first-principles calculations based on density functional theory we search for suitable materials that can host antiferromagnetically coupled skyrmions. We concentrate on fcc-stacked (111)-oriented metallic $Z$/Co/Pt ($Z=4d$ series: Y$-$Pd, the noble metals: Cu, Ag, Au, post noble metals: Zn and Cd) magnetic multilayers of films of monatomic thickness. We present quantitative trends of magnetic properties: Magnetic moments, interlayer exchange coupling, spin-stiffness, Dzyaloshinskii-Moriya interaction, magnetic anisotropy, and the critical temperature. We show that some…
The current driven motion of skyrmions in MnSi and FeGe thinned single crystals could be initiated at current densities of the order of $10^6$ A/m, five orders of magnitude smaller than for magnetic domain walls. The technologically crucial step of replicating these results in thin films has not been successful to date, but the reasons are not clear. Elucidating them requires analyzing system characteristics at scales of few nm where the key Dzyaloshinskii Moriya (DM) interactions vary, and doing so in near application conditions, i.e. oxidation protected systems at room temperature. In this w…
Noncollinear spin textures in ferromagnetic ultrathin films are currently the subject of renewed interest since the discovery of the interfacial Dzyaloshinskii-Moriya interaction (DMI). This antisymmetric exchange interaction selects a given chirality for the spin textures and allows stabilising configurations with nontrivial topology. Moreover, it has many crucial consequences on the dynamical properties of these topological structures, including chiral domain walls (DWs) and magnetic skyrmions. In the recent years the study of noncollinear spin textures has been extended from single ultrathi…
Magnetic skyrmions form in chiral multilayers from the shrinking or fission of elongated stripe textures. Here we report an experimental and theoretical study of the temperature dependence of this stripe-to-skyrmion transition in Co/Pt-based multilayers. Field-reversal magnetometry and Lorentz microscopy experiments over 100 - 350 K establish the increased efficacy of stripe-to-skyrmion fission at higher temperatures - driven primarily by the thermal evolution of key magnetic interactions - thereby enhancing skyrmion density. Atomistic calculations elucidate that the energy barrier to fission …
Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Mori…
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…
Competing interactions produce finite-size textures in myriad condensed matter systems, typically forming elongated stripe or round bubble domains. Transitions between stripe and bubble phases, driven by field or temperature, are expected to be reversible in nature. Here we report on the distinct character of the analogous transition for nanoscale spin textures in chiral Co/Pt-based multilayer films, known to host Néel skyrmions, using microscopy, magnetometry, and micromagnetic simulations. Upon increasing field, individual stripes fission into multiple skyrmions, and this transition exhibits…
We experimentally demonstrate the formation of room-temperature skyrmions with radii of about 25\,nm in easy-plane anisotropy multilayers with interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of individual magnetic skyrmions by magnetic force microscopy and find that the skyrmions are stable in out-of-plane fields up to about 200 mT. We determine the interlayer exchange coupling as well as the strength of the interfacial DMI. Additionally, we investigate the dynamic microwave spin excitations by broadband magnetic resonance spectroscopy. From the uniform Kittel mode…
Magnetic skyrmions are nanoscale topological spin structures offering great promise for next-generation information storage technologies. The recent discovery of sub-100 nm room temperature (RT) skyrmions in several multilayer films has triggered vigorous efforts to modulate their physical properties for their use in devices. Here we present a tunable RT skyrmion platform based on multilayer stacks of Ir/Fe/Co/Pt, which we study using X-ray microscopy, magnetic force microscopy and Hall transport techniques. By varying the ferromagnetic layer composition, we can tailor the magnetic interaction…
The transport response of dipole skyrmions in amorphous centrosymmetric Fe/Gd multilayer is investigated by temperature and field-dependent resistivity measurements collected in three current and magnetic field configurations. It is shown that a dipole skyrmion lattice phase may form at certain temperatures leading to a unique signature of the polar longitudinal resistivity. This signature differs from the conventional field-varying parabolic response associated with stripe phases, which transition to a disordered skyrmion phase under applied fields. Transport measurements under different fiel…
We present an analytical theory to describe three-dimensional magnetic textures in perpendicularly magnetized magnetic multilayers that arise in the presence of magnetostatic interactions and the Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that domain walls in multilayers develop a complex twisted structure, which persists even for films with strong DMI. The origin of this twist is surface-volume stray field interactions that manifest as a depth-dependent effective field whose form mimics the DMI effective field. We find that the wall twist has a minor impact on the equilibrium sky…
The proposal that very small Néel skyrmions can form in SrRuO$_3$/SrIrO$_3$ epitaxial bilayers and that the electric field-effect can be used to manipulate these skyrmions in gated devices strongly stimulated the recent research of SrRuO$_3$ heterostructures. A strong interfacial Dzyaloshinskii-Moriya interaction, combined with the breaking of inversion symmetry, was considered as the driving force for the formation of skyrmions in SrRuO$_3$/SrIrO$_3$ bilayers. Here, we investigated nominally symmetric heterostructures in which an ultrathin ferromagnetic SrRuO$_3$ layer is sandwiched between l…
Magnetic skyrmions are nanoscale spin structures recently discovered at room temperature (RT) in multilayer films. Employing their novel topological properties towards exciting technological prospects requires a mechanistic understanding of the excitation and relaxation mechanisms governing their stability and dynamics. Here we report on the magnetization dynamics of RT Néel skyrmions in Ir/Fe/Co/Pt multilayer films. We observe a ubiquitous excitation mode in the microwave absorption spectrum, arising from the gyrotropic resonance of topological skyrmions, and robust over a wide range of tempe…
Three-dimensional (3D) topological spin textures emerge as promising quasi-particles for encoding information in future spintronic devices. The third dimension provides more malleability regarding their magnetic properties as well as more flexibility for potential applications. However, the stabilization and characterization of such quasi-particles in easily implementable systems remain a work in progress. Here we observe a new type of 3D magnetic textures that we called skyrmionic cocoons that sits in the interior of magnetic thin films multilayers and possesses a characteristic ellipsoidal s…
Skyrmions and antiskyrmions are topologically protected spin structures with opposite topological charge. Particularly in coexisting phases, these two types of magnetic quasi-particles may show fascinating physics and potential for spintronic devices. While skyrmions are observed in a wide range of materials, until now antiskyrmions were exclusive to materials with D2d symmetry. In this work, we show first and second-order antiskyrmions stabilized by magnetic dipole-dipole interaction in Fe/Gd-based multilayers. We modify the magnetic properties of the multilayers by Ir insertion layers. Using…
We report a study of the magnetization reversals and skyrmion configurations in two systems - Pt/Co/MgO and Ir/Fe/Co/Pt multilayers, where magnetic skyrmions are stabilized by a combination of dipolar and Dzyaloshinskii-Moriya interactions (DMI). First Order Reversal Curve (FORC) diagrams of low-DMI Pt/Co/MgO and high-DMI Ir/Fe/Co/Pt exhibit stark differences, which are identified by micromagnetic simulations to be indicative of hybrid and pure Néel skyrmions, respectively. Tracking the evolution of FORC features in multilayers with dipolar interactions and DMI, we find that the negative FORC …
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…
Magnetic skyrmions are nanoscale spin textures touted as next-generation computing elements. When subjected to lateral currents, skyrmions move at considerable speeds. Their topological charge results in an additional transverse deflection known as the skyrmion Hall effect (SkHE). While promising, their dynamic phenomenology with current, skyrmion size, geometric effects and disorder remain to be established. Here we report on the ensemble dynamics of individual skyrmions forming dense arrays in Pt/Co/MgO wires by examining over 20,000 instances of motion across currents and fields. The skyrmi…
Observation by SANS and PNR of pure Néel-type domain wall profiles and skyrmion suppression below room temperature in magnetic [Pt/CoFeB/Ru]$_{10}$ multilayers
The dynamic response of dipole skyrmions in Fe/Gd multilayer films is investigated by ferromagnetic resonance measurements and compared to micromagnetic simulations. We detail thickness and temperature dependent studies of the observed modes as well as the effects of magnetic field history on the resonant spectra. Correlation between the modes and the magnetic phase maps constructed from real-space imaging and scattering patterns allows us to conclude the resonant modes arise from local topological features such as dipole skyrmions but does not depend on the collective response of a closed pac…
The spectral signatures of magnetic skyrmions under microwave field excitation are of fundamental interest and can be an asset for high frequency applications. These topological solitons can be tailored in multilayered thin films, but the experimental observation of their spin wave dynamics remains elusive, in particular due to large damping. Here, we study Pt/FeCoB/AlO$_x$ multilayers hosting dense and robust skyrmion lattices at room temperature with Gilbert damping of $\sim 0.02$. We use magnetic force microscopy to characterise their static magnetic phases and broadband ferromagnetic reson…
Magnetic skyrmions have attracted considerable interest, especially after their recent experimental demonstration at room temperature in multilayers. The robustness, nanoscale size and non-volatility of skyrmions have triggered a substantial amount of research on skyrmion-based low-power, ultra-dense nanocomputing and neuromorphic systems such as artificial synapses. Room-temperature operation is required to integrate skyrmionic synapses in practical future devices. Here, we numerically propose a nanoscale skyrmionic synapse composed of magnetic multilayers that enables room-temperature device…
Deliverable 1.1 is a report on imaging of individual skyrmions of MML systems made by different techniques. This deliverable falls within work package 1 (WP1:Static equilibrium properties of interface induced skyrmions in magnetic films and multilayers) of the MAGicSky research proposal whose objectives are: the growth of magnetic multilayer systems with large interfacial chiral interaction, the determination of the amplitude of the Dzyaloshinskii--Moriya interactions (DMi), the detailed structural and magnetic characterization of interfaces, the magnetic imaging of individual skyrmions and th…
Non-collinear magnets exhibit a rich array of dynamic properties at microwave frequencies. They can host nanometre-scale topological textures known as skyrmions, whose spin resonances are expected to be highly sensitive to their local magnetic environment. Here, we report a magnetic resonance study of an [Ir/Fe/Co/Pt] multilayer hosting Néel skyrmions at room temperature. Experiments reveal two distinct resonances of the skyrmion phase during in-plane ac excitation, with frequencies between 6-12 GHz. Complementary micromagnetic simulations indicate that the net magnetic dipole moment rotates c…
