Accurate calculation of the transverse anisotropy in perpendicularly magnetized multilayers

The transverse anisotropy constant and the related D\"oring mass density are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. So far, no general framework is available to determine these quantities from static characterizations such as magnetometry measurements. Here, we derive a universal analytical expression to calculate the transverse anisotropy constant for the important class of perpendicular magnetic multilayers. All the required input parameters of the model, such as the number of repeats, the thickness of a single magnetic layer, and the layer periodicity, as well as the effective perpendicular anisotropy, the saturation magnetization, an…

Imaging Spin Dynamics on the Nanoscale Using X-Ray Microscopy

The dynamics of emergent magnetic quasiparticles, such as vortices, domain walls and bubbles are studied by scanning transmission X-ray microscopy (STXM), combining magnetic (XMCD) contrast with about 25 nm lateral resolution as well as 70 ps time resolution. Essential progress in the understanding of magnetic vortex dynamics is achieved by vortex core reversal observed by sub-GHz excitation of the vortex gyromode, either by ac magnetic fields or spin transfer torque. The basic switching scheme for this vortex core reversal is the generation of a vortex-antivortex pair. Much faster vortex core reversal is obtained by exciting azimuthal spin wave modes with (multi-GHz) rotating magnetic fiel…

Multiscale simulations of topological transformations in magnetic-skyrmion spin structures

Magnetic Skyrmions belong to the most interesting spin structures for the development of future information technology as they have been predicted to be topologically protected. To quantify their stability, we use an innovative multiscale approach to simulating spin dynamics based on the Landau-Lifshitz-Gilbert equation. The multiscale approach overcomes the micromagnetic limitations that have hindered realistic studies using conventional techniques. We first demonstrate how the stability of a Skyrmion is influenced by the refinement of the computational mesh and reveal that conventionally employed traditional micromagnetic simulations are inadequate for this task. Furthermore, we determine…

Multiscale simulations of topological transformations in magnetic Skyrmions

Magnetic Skyrmions belong to the most interesting spin structures for the development of future information technology as they have been predicted to be topologically protected. To quantify their stability, we use an innovative multiscale approach to simulating spin dynamics based on the Landau-Lifshitz-Gilbert equation. The multiscale approach overcomes the micromagnetic limitations that have hindered realistic studies using conventional techniques. We first demonstrate how the stability of a Skyrmion is influenced by the refinement of the computational mesh and reveal that conventionally employed traditional micromagnetic simulations are inadequate for this task. Furthermore, we determine…

Domain wall transformations and hopping in La0.7Sr0.3MnO3nanostructures imaged with high resolution x-ray magnetic microscopy

We investigate the effect of electric current pulse injection on domain walls in La(0.7)Sr(0.3)MnO(3) (LSMO) half-ring nanostructures by high resolution x-ray magnetic microscopy at room temperature. Due to the easily accessible Curie temperature of LSMO, we can employ reasonable current densities to induce the Joule heating necessary to observe effects such as hopping of the domain walls between different pinning sites and nucleation/annihilation events. Such effects are the dominant features close to the Curie temperature, while spin torque is found to play a small role close to room temperature. We are also able to observe thermally activated domain wall transformations and we find that,…

A magnetic skyrmion as a non-linear resistive element - a potential building block for reservoir computing

Inspired by the human brain, there is a strong effort to find alternative models of information processing capable of imitating the high energy efficiency of neuromorphic information processing. One possible realization of cognitive computing are reservoir computing networks. These networks are built out of non-linear resistive elements which are recursively connected. We propose that a skyrmion network embedded in frustrated magnetic films may provide a suitable physical implementation for reservoir computing applications. The significant key ingredient of such a network is a two-terminal device with non-linear voltage characteristics originating from single-layer magnetoresistive effects,…

Switching by Domain-Wall Automotion in Asymmetric Ferromagnetic Rings

A ring-shaped magnetic logic device offers two vortex states (clockwise and counterclockwise) to encode bits, with relative stability against external magnetic fields. The dynamics of magnetization switching in such structures, though, still need unraveling. The authors present direct experimental visualization of reproducible, robust switching in magnetic rings via domain-wall automotion, which does not require an applied field. Simulations reveal that annihilation of domain walls through automotion always occurs, with the detailed topology of the walls only influencing the dynamics locally, in line with the experimental results.

Automotive domain wall propagation in ferromagnetic rings

Automotive domain wall propagation is a self-propelling motion utilizing the energy stored in a particular energy reservoir of the spin structure to speed up domain wall beyond its equilibrium value given by external driving force and damping. Such a concept of DW motion is of great interest due to recent development of spintronic devices based on domain walls, where automotion could be used to assist or prevent domain wall pinning at low driving fields1-2. In turn, most of studies so far have been devoted to the automotion invoked by DW transformations from metastable to stable states3-4; appearing at sufficiently high magnetic fields strong and enough to trigger domain wall spin structure…

Effective field analysis using the full angular spin-orbit torque magnetometry dependence

Spin-orbit torques promise ultra-efficient magnetization switching used for advanced devices based on emergent quasi-particles such as domain walls and skyrmions. Recently, the spin structure dynamics, materials and systems with tailored spin-orbit torques are being developed. A method, which allows one to detect the acting torques in a given system as a function of the magnetization direction is the torque-magnetometry method based on a higher harmonics analysis of the anomalous Hall-effect. Here we show that the effective fields acting on magnetic domain walls that govern the efficiency of their dynamics require a sophisticated analysis taking into account the full angular dependence of t…

Multiscale model approach for magnetization dynamics simulations

Simulations of magnetization dynamics in a multiscale environment enable the rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. We have developed a multiscale magnetization dynamics simulation approach that can be applied to large systems with spin structures that vary locally on small length scales. To implement this, the conventional micromagnetic simulation framework has been expanded to include a multiscale solving routine. The software selectively simulates different regions of a ferromagnetic sample according to the spin structures located within in order to employ a suitable discretization…

Topological Defects in Nanostructures—Chiral Domain Walls and Skyrmions

In this chapter, spin structures with particular topologies in confined geometries are presented. Domain walls in nanowires exhibit a spin structure that depends on the material and geometry while in discs Skyrmions can be stabilized by different competing interactions. The topologies of these spin structures can be characterized by a Skyrmion or Winding number that governs the dynamics and stability.

Dynamics and inertia of skyrmionic spin structures

Understanding the motion of magnetic skyrmions is essential if they are to be used as information carriers in devices. It is now shown that topological confinement endows the skyrmions with an unexpectedly large mass, which plays a key role in their dynamics.

Accurate calculation of the transverse anisotropy of a magnetic domain wall in perpendicularly magnetized multilayers

Bloch domain walls are the most common type of transition between two out-of-plane magnetized domains (one magnetized upwards, one downwards) in films with perpendicular magnetic anisotropy. The rotation of the spins of such domain walls in the plane of the film requires energy, which is described by an effective anisotropy, the so-called transverse or hard axis anisotropy ${K}_{\ensuremath{\perp}}$. This anisotropy and the related D\"oring mass density of the domain wall are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. In particular, the critical field strength or current density where oscillatory domain wall motion sets in (Walker breakdown)…

Synchronous precessional motion of multiple domain in a ferromagnetic nanowire by perpendicular field pulses

Magnetic storage and logic devices based on magnetic domain wall motion rely on the precise and synchronous displacement of multiple domain walls. The conventional approach using magnetic fields does not allow for the synchronous motion of multiple domains. As an alternative method, synchronous current-induced domain wall motion was studied, but the required high-current densities prevent widespread use in devices. Here we demonstrate a radically different approach: we use out-of-plane magnetic field pulses to move in-plane domains, thus combining field-induced magnetization dynamics with the ability to move neighbouring domain walls in the same direction. Micromagnetic simulations suggest …

Dynamics and topological mass of skyrmionic spin structures (presentation video)

Skyrmions are topologically protected particle-like configurations, with a topological complexity described by their Skyrmion number. In magnetic systems, they have been numerically predicted to exhibit rich dynamics, such as the gyrotropic and breathing modes, dominated by their topology. Recent experimental advances brought their static manipulation well under control. However, their dynamical behaviour is largely unexplored experimentally. In this work, we provide with the first direct observation of eigenmode skyrmion dynamics. In particular, we present dynamical imaging data with high temporal and spatial resolution to demonstrate the GHz gyrotropic mode of a single skyrmion bubble, as…

Magnetic Anisotropy Engineering in Thin Film Ni Nanostructures by Magnetoelastic Coupling

Local control of domain wall dynamics in ferromagnetic rings

Ferromagnetic nanorings are of great interest due to prospective applications in memory and logic devices based on domain wall (DW) motion.1-3A key-prerequisite for their realization is a reproducible domain wall spin structure with a well-controllable wall velocity. We have found that DW propagation in magnetic ring is characterized by non-constant vortex DW velocity even below Walker breakdown4 (as opposed to straight wires). Several studies have been devoted to the optimization of ring reversal on a global scale using out-of plane field5 or flux charges emanating from neighboring rings if placed in close proximity6. However, these methods involve DW pinning and vortex nucleation processe…

Magnetic configurations in nanostructured Co2MnGa thin film elements

The magnetic configuration of nanostructured elements fabricated from thin films of the Heusler compound Co2MnGa was determined by high-resolution x-ray magnetic microscopy, and the magnetic properties of continuous Co2MnGa thin films were determined by magnetometry measurements. A four-fold magnetic anisotropy with an anisotropy constant of kJ m−3 was deduced, and x-ray microscopy measurements have shown that the nanostructured Co2MnGa elements exhibit reproducible magnetic states dominated by shape anisotropy, with a minor contribution from the magneto-crystalline anisotropy, showing that the spin structure can be tailored by judiciously choosing the geometry.

Local Domain-Wall Velocity Engineering via Tailored Potential Landscapes in Ferromagnetic Rings

One vein of spintronics research seeks to harness propagating magnetic domain walls for information processing. The authors engineer a potential landscape via local variations in a ring geometry, and image the motion of domain walls in rotating magnetic fields to quantify the contribution of the spatially varying potential to wall dynamics. Domain-wall velocity depends on ring width, being highest where the ring is widest, and such a potential thus could be selected to synchronize velocities and enable applications.

Localized domain wall nucleation dynamics in asymmetric ferromagnetic rings revealed by direct time-resolved magnetic imaging

We report time-resolved observations of field-induced domain wall nucleation in asymmetric ferromagnetic rings using single direction field pulses and rotating fields. We show that the asymmetric geometry of a ring allows for controlling the position of nucleation events, when a domain wall is nucleated by a rotating magnetic field. Direct observation by scanning transmission x-ray microscopy (STXM) reveals that the nucleation of domain walls occurs through the creation of transient ripplelike structures. This magnetization state is found to exhibit a surprisingly high reproducibility even at room temperature and we determine the combinations of field strengths and field directions that all…

Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy

Magnetic skyrmions are highly promising candidates for future spintronic applications such as skyrmion racetrack memories and logic devices. They exhibit exotic and complex dynamics governed by topology and are less influenced by defects, such as edge roughness, than conventionally used domain walls. In particular, their finite topological charge leads to a predicted "skyrmion Hall effect", in which current-driven skyrmions acquire a transverse velocity component analogous to charged particles in the conventional Hall effect. Here, we present nanoscale pump-probe imaging that for the first time reveals the real-time dynamics of skyrmions driven by current-induced spin orbit torque (SOT). We…

Nonadiabatic spin-transfer torque of magnetic vortex structures in a permalloy square

The stationary displacement of a magnetic vortex core in a permalloy square caused by an ultrahigh direct current has been measured utilizing scanning electron microscopy with polarization analysis. Data have been analyzed for three different generic states of the Landau structure and up to a current density of $3\ifmmode\times\else\texttimes\fi{}{10}^{11}\mathrm{A}/{\mathrm{m}}^{2}$. This procedure allows for separating the effects caused by the Oersted field, the nonadiabatic, and the adiabatic spin-transfer torque. In addition, the spin polarization of the driving current $P=(65\ifmmode\pm\else\textpm\fi{}4)%$ is independently determined from the spin drift velocity of ${v}_{j}=(4.79\ifm…

Domain Wall Spin Structures in Mesoscopic Fe Rings probed by High Resolution SEMPA

We present a combined theoretical and experimental study of the energetic stability and accessibility of different domain wall spin configurations in mesoscopic magnetic iron rings. The evolution is investigated as a function of the width and thickness in a regime of relevance to devices, while Fe is chosen as a material due to its simple growth in combination with attractive magnetic properties including high saturation magnetization and low intrinsic anisotropy. Micromagnetic simulations are performed to predict the lowest energy states of the domain walls, which can be either the transverse or vortex wall spin structure, in good agreement with analytical models, with further simulations …