Search

Topological defects play a critical role across many fields, mediating phase transitions and macroscopic behaviors as they move through space. Their role as robust information carriers has also generated much attention. However, controlling their motion remains challenging, especially towards achieving motion along well-defined paths which typically require predefined structural patterning. Here we demonstrate the tunable, unidirectional motion of topological defects, specifically magnetic dislocations in a weak magnetic stripe pattern, induced by external magnetic field in a laterally unconfined thin film. This motion is shown to mediate the overall continuous rotation of the stripe pattern. We determine the connection between the unidirectional motion of dislocations and the underlying three-dimensional (3D) magnetic structure by performing 3D magnetic vectorial imaging with in situ magnetic fields. A minimal model for dislocations in stripe patterns that encodes the symmetry breaking induced by the external magnetic field reproduces the motion of dislocations that facilitate the 2D rotation of the stripes, highlighting the universality of the phenomenon. This work establishes a framework for studying the field-driven behavior of topological textures and designing materials that enable well defined, controlled motion of defects in unconfined systems, paving the way to manipulate information carriers in higher-dimensional systems., Comment: 18 pages, 5 figures

Topological spin textures in magnetic materials beyond two-dimensional skyrmions have attracted attention for electronics beyond CMOS technologies. In particular, three-dimensional (3D) topological spin textures are promising due to the expected complex non-linear dynamics as well as high static and dynamic thermal stability. In multilayer heterostructures, a hybrid chiral skyrmion tube is a well-known example of a 3D topological spin texture, exhibiting an intriguing chirality transition along the thickness direction. This transition progresses from left-handed to right-handed N\'eel-type chirality, passing through a Bloch-type intermediate state. Such an exotic spin configuration potentially exhibits distinctly different dynamics from that of the common skyrmion tube that exhibits a homogeneous chirality; yet these dynamics have not been ascertained so far. Here we reveal the distinct features of current-induced dynamics that result from the hybrid chiral skyrmion tube structure in synthetic antiferromagnetic (SyAFM) multilayers. Strikingly, the SyAFM hybrid chiral skyrmion tubes exhibit a non-reciprocal skyrmion Hall effect in the flow regime. The non-reciprocity can even be tuned by the degree of magnetic compensation in the SyAFM systems. Our theoretical modeling qualitatively corroborates that the non-reciprocity stems from the dynamic oscillation of skyrmion helicity during its current-induced motion. The findings highlight the critical role of the internal degrees of freedom of these complex skyrmion tubes for their current-induced dynamics.

The dynamics of domain walls in a square of permalloy (Ni$_{81}$Fe$_{19}$; Py) upon excitation with an oscillating magnetic field of 4 mT amplitude were recorded by pump-probe ptychography with X-ray magnetic circular dichroism (XMCD) at the Ni L$_3$-edge. The 2.5 $\mu$m Py square of 160 nm thickness forms a vortex flux-closure pattern with domain walls that fall into alternating out-of-plane magnetization states due to the interplay of in-plane shape and growth-induced perpendicular anisotropies. Dynamic modes of the domain wall structure were excitable along with the vortex core gyration with frequencies of 500 MHz and 1 GHz. Micromagnetic simulations served to corroborate the imaged domain wall motion.

The ferroelectric domain structure of a freestanding BiFeO$_3$ film was visualized by ptychographic dichroic imaging with linearly polarized X-rays at the O K-edge around 530 eV. The dichroic contrast is maximized at the energy of the hybridization of the O 2p state and the Fe 3d orbitals, which is split by the octahedral crystal field of the perovskite structure. The microscopy images thus obtained complement the ptychographic imaging of the antiferromagnetic contribution at the Fe L$_3$-edge. The approach can be extended to the separation of different ferroic contributions in other multiferroic oxides.

Understanding the magnetic and ferroelectric ordering of magnetoelectric multiferroic materials at the nanoscale necessitates a versatile imaging method with high spatial resolution. Here, soft X-ray ptychography is employed to simultaneously image the ferroelectric and antiferromagnetic domains in an 80 nm thin freestanding film of the room-temperature multiferroic BiFeO$_3$ (BFO). The antiferromagnetic spin cycloid of period 64 nm is resolved by reconstructing the corresponding resonant elastic X-ray scattering in real space and visualized together with mosaic-like ferroelectric domains in a linear dichroic contrast image at the Fe L$_3$ edge. The measurements reveal a near perfect coupling between the antiferromagnetic and ferroelectric ordering by which the propagation direction of the spin cycloid is locked orthogonally to the ferroelectric polarization. In addition, the study evinces both a preference for in-plane propagation of the spin cycloid and changes of the ferroelectric polarization by 71{\deg} between multiferroic domains in the epitaxial strain-free, freestanding BFO film. The results provide a direct visualization of the strong magnetoelectric coupling in BFO and of its fine multiferroic domain structure, emphasizing the potential of ptychographic imaging for the study of multiferroics and non-collinear magnetic materials with soft X-rays., Comment: Supporting information available with published version: https://doi.org/10.1002/adma.202311157

Spin waves are collective perturbations in the orientation of the magnetic moments in magnetically ordered materials. Their rich phenomenology is intrinsically three-dimensional; however, the three-dimensional imaging of spin waves has so far not been possible. Here, we image the three-dimensional dynamics of spin waves excited in a synthetic antiferromagnet, with nanoscale spatial resolution and sub-ns temporal resolution, using time-resolved magnetic laminography. In this way, we map the distribution of the spin-wave modes throughout the volume of the structure, revealing unexpected depth-dependent profiles originating from the interlayer dipolar interaction. We experimentally demonstrate the existence of complex three-dimensional interference patterns and analyze them via micromagnetic modelling. We find that these patterns are generated by the superposition of spin waves with non-uniform amplitude profiles, and that their features can be controlled by tuning the composition and structure of the magnetic system. Our results open unforeseen possibilities for the study and manipulation of complex spin-wave modes within nanostructures and magnonic devices., Comment: 18 pages, 4 figures

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number describing the rotation of spins across the skyrmion. However, in real systems with a finite thickness of the material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography we reconstruct with about 20nm spatial (voxel) resolution the full three-dimensional spin texture of a skyrmion in an 800 nm diameter and 95 nm thin disk patterned into a trilayer [Ir/Co/Pt] thin film structure. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number and the chirality is non-uniform across the thickness of the disk. Estimates of local micromagnetic energy densities suggest that the changes in topological profile are related to non-uniform competing energetic interactions. Theoretical calculations and micromagnetic simulations are consistent with the experimental findings. Our results provide the foundation for nanoscale magnetic metrology for future tailored spintronics devices using topology as a design parameter, and have the potential to reverse-engineer a spin Hamiltonian from macroscopic data, tying theory more closely to experiment., Comment: 18 pages, 4 figures

Antiferromagnets hosting real-space topological spin textures are promising platforms to model fundamental ultrafast phenomena and explore spintronics. However, to date, they have only been fabricated epitaxially on specific symmetry-matched crystalline substrates, to preserve their intrinsic magneto-crystalline order. This curtails their integration with dissimilar supports, markedly restricting the scope of fundamental and applied investigations. Here, we circumvent this limitation by designing detachable crystalline antiferromagnetic nanomembranes of $\alpha$-Fe$_{2}$O$_{3}$, that can be transferred onto other desirable supports after growth. We develop transmission-based antiferromagnetic vector-mapping to show that these nanomembranes harbour rich topological phenomenology at room temperature. Moreover, we exploit their extreme flexibility to demonstrate three-dimensional reconfiguration of antiferromagnetic properties, driven locally via flexure-induced strains. This allows us to spatially design antiferromagnetic states outside their typical thermal stability window. Integration of such freestanding antiferromagnetic layers with flat or curved nanostructures could enable spin texture designs tailored by magnetoelastic-/geometric-effects in the quasi-static and dynamical regimes, opening new explorations into curvilinear antiferromagnetism and unconventional computing., Comment: 17 pages, 4 figures

The current-driven motion of magnetic domain walls (DWs) is the working principle of magnetic racetrack memories. In this type of spintronic technology, high current densities are used to propel DW motion in magnetic nanowires, causing significant wire heating. Synthetic antiferromagnets are known to show very fast DW motion at high current densities, but lower current densities around onset of motion have received less attention. Here we use scanning transmission x-ray microscopy to study the response of DWs in a SAF multilayer to currents. We observe that the DWs depin at $\sim 3 \times 10^{11}$~A/m$^2$ and move more quickly in response to 5~ns duration current pulses than in comparable conventional multilayers. The results suggest that DWs in SAF structures are superior to conventional N\'{e}el DWs for low energy consumption racetrack technologies.

Superfluidity and superconductivity are macroscopic manifestations of quantum mechanics, which have fascinated scientists since their discoveries roughly a century ago. Ever since the initial theories of such quantum fluids were formulated, there has been speculation as to the possibility of multi-component quantum order. A particularly simple multi-component condensate is built from particles occupying different quantum states, or bands, prior to condensation. The particles in one or both bands may undergo condensation, as seen for certain solids and anticipated for certain cold atom systems. For bulk solids, the different bands always order simultaneously, with conventional pairing characterized by complex order parameters describing the condensates in each band. Another type of condensate, notably occurring at room temperature, has been identified for magnons, the magnetic analogue of lattice vibrations, injected by microwaves into yttrium iron garnet. Here we show that magnon quantization for thin samples results in a new multi-band magnon condensate. We establish a phase diagram, as a function of microwave drive power and frequency relative to the magnon bands, revealing both single and multi-band condensation. The most stable multi-band condensate is found in a narrow regime favoured on account of a resonance in the scattering between two bands. Our discovery introduces a flexible non-equilibrium platform operating at room temperature for a well-characterised material, exploiting a Feshbach-like resonance, for examining multi-band phenomena. It points to qualitatively new ways to engineer and control condensates and superconducting states in multiband systems and potential devices containing multiple interacting condensates.

The imaging of magneto-dynamical processes has been, so far, mostly a two-dimensional business, due to the constraints of the available experimental techniques. In this manuscript, building on the recent developments of soft X-ray magnetic laminography, we present an experimental setup where magneto-dynamical processes can be resolved in all three spatial dimensions and in time, with the possibility to freely tune the frequency of the dynamical process. We then employ this setup to investigate the three-dimensional dynamics of two resonant magneto-dynamical modes in a CoFeB microstructure occurring at different frequencies, namely the fundamental vortex gyration mode and a magnetic field-induced domain wall excitation mode. This new technique provides much needed capabilities for the experimental investigation of the magnetization dynamics of three-dimensional magnetic systems.

Magnetic skyrmions are topological spin textures that hold great promise as nanoscale information carriers in non-volatile memory and logic devices. While room-temperature magnetic skyrmions and their current-induced manipulation were recently demonstrated, the stray field resulting from their finite magnetization as well as their topological charge limit their minimum size and reliable motion in tracks. Antiferromagnetic (AF) skyrmions allow these limitations to be lifted owing to their vanishing magnetization and net zero topological charge, promising room-temperature, ultrasmall skyrmions, fast dynamics, and insensitivity to external magnetic fields. While room-temperature AF spin textures have been recently demonstrated, the observation and controlled nucleation of AF skyrmions operable at room temperature in industry-compatible synthetic antiferromagnetic (SAF) material systems is still lacking. Here we demonstrate that isolated skyrmions can be stabilized at zero field and room temperature in a fully compensated SAF. Using X-ray microscopy techniques, we are able to observe the skyrmions in the different SAF layers and demonstrate their antiparallel alignment. The results are substantiated by micromagnetic simulations and analytical models using experimental parameters, which confirm the chiral SAF skyrmion spin texture and allow the identification of the physical mechanisms that control the SAF skyrmion size and stability. We also demonstrate the local nucleation of SAF skyrmions via local current injection as well as ultrafast laser excitations at zero field. These results will enable the utilization of SAF skyrmions in skyrmion-based devices.

Analytic and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from intrinsic Dzyaloshinskii-Moriya interaction or interface-induced anisotropies. In constrast, these chiral effects stem from isotropic exchange or dipole-dipole interaction, present in all magnetic materials, which acquire asymmetric contributions in case of curved geometry of the specimen. As a result, for example, the spin-wave dispersion in round magnetic nanotubes becomes asymmetric, namely spin waves of the same frequency propagating in opposite directions along the nanotube exhibit different wavelenghts. Here, using time-resolved scanning transmission X-ray microscopy experiments, standard micromagntic simulations and a dynamic-matrix approach, we show that the spin-wave spectrum undergoes additional drastic changes when transitioning from a continuous to a discrete rotational symmetry, i.e. from round to hexagonal nanotubes, which are much easier to fabricate. The polygonal shape introduces localization of the modes both to the sharp, highly curved corners and flat edges. Moreover, due to the discrete rotational symmetry, the degenerate nature of the modes with azimuthal wave vectors known from round tubes is partly lifted, resulting in singlet and duplet modes. For comparison with our experiments, we calculate the microwave absorption from the numerically obtained mode profiles which shows that a dedicated antenna design is paramount for magnonic applications in 3D nano-structures. To our knowledge these are the first experiments directly showing real space spin-wave propagation in 3D nano objects.

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 experimental results are in good agreement with modelling when including the interfacial spin-transfer torque, and cannot be reproduced by using the spin-orbit torque alone. We also show that for skyrmion collections the velocity is approximately independent of diameter, in marked contrast to the motion of isolated skyrmions, as the group of skyrmions move together at an average group velocity. Moreover, the calculated skyrmion velocities are comparable to those obtained in experiments when the interfacial spin-transfer torque in included, whilst modelling using the spin-orbit torque alone shows large discrepancies with the experimental data. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which is of similar strength to the spin-orbit torque, and both significantly larger than the bulk spin-transfer torque. Due to the good agreement with experiments, we conclude that the interfacial spin-transfer torque should be included in numerical modelling for correct reproduction of experimental results., Comment: 25pages, 5 figures

We investigate the inversion process of magnetic domain walls (DWs) propagating through synthetic noncollinear magnetic textures, whereby an up/down DW can be transformed into a down/up DW and vice versa. We exploit the lateral coupling between out-of-plane and in-plane magnetic regions induced by the interfacial Dzyaloshinskii-Moriya interaction in Pt/Co/AlOx trilayers to realize both field-driven and current-driven magnetic DW inverters. The inverters consist of narrow in-plane magnetic regions embedded in out-of-plane DW racetracks. Magnetic imaging and micromagnetic simulations provide insight into the DW inversion mechanism, showing that DW inversion proceeds by annihilation of the incoming domain on one side of the in-plane region and nucleation of a reverse domain on the opposite side. By changing the shape of the in-plane magnetic region, we show that the DW inversion efficiency can be tuned by adjusting the ratio between the chiral coupling energy at the inverter boundary and the energy cost of nucleating a reverse domain. Finally, we realize an asymmetric DW inverter that has nonreciprocal inversion properties and demonstrate that such a device can operate as a DW diode. Our results provide input for the versatile manipulation of DWs in magnetic racetracks and the design of efficient DW devices for nonvolatile magnetic logic schemes.

Vortex rings are remarkably stable structures occurring in numerous systems: for example in turbulent gases, where they are at the origin of weather phenomena [1]; in fluids with implications for biology [2]; in electromagnetic discharges [3]; and in plasmas [4]. While vortex rings have also been predicted to exist in ferromagnets [5], they have not yet been observed. Using X-ray magnetic nanotomography [6], we imaged three-dimensional structures forming closed loops in a bulk micromagnet, each composed of a vortex-antivortex pair. Based on the magnetic vorticity, a quantity analogous to hydrodynamic vorticity, we identify these configurations as magnetic vortex rings. While such structures have been predicted to exist as transient states in exchange ferromagnets [5], the vortex rings we observe exist as stable, static configurations, whose stability we attribute to the dipolar interaction. In addition, we observe stable vortex loops intersected by magnetic singularities [7], at which the magnetisation within the vortex and antivortex cores reverses. We gain insight into the stability of these states through field and thermal equilibration protocols. These measurements pave the way for the observation of complex three-dimensional solitons in bulk magnets, as well as for the development of applications based on three-dimensional magnetic structures.

Theoretical and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from the intrinsic Dzyaloshinskii-Moriya interaction or surface-induced anisotropies. The origin of these chiral effects is the isotropic exchange or the dipole-dipole interaction present in all magnetic materials but renormalized by the curvature. Here, we demonstrate experimentally that curvature induced effects originating from the dipole-dipole interaction are directly observable by measuring spin-wave propagation in magnetic nanotubes with hexagonal cross section using time resolved scanning transmission X-ray microscopy. We show that the dispersion relation is asymmetric upon reversal of the wave vector when the propagation direction is perpendicular to the static magnetization. Therefore counter-propagating spin waves of the same frequency exhibit different wavelenghts. Hexagonal nanotubes have a complex dispersion, resulting from spin-wave modes localised to the flat facets or to the extremely curved regions between the facets. The dispersion relations obtained experimentally and from micromagnetic simulations are in good agreement. %The asymmetric spin-wave transport is present for all modes, promoting hexagonal nanotubes for magnonic applications. These results show that spin-wave transport is possible in 3D, and that the dipole-dipole induced magneto-chiral effects are significant.

The ability to experimentally map the three-dimensional structure and dynamics in bulk and patterned three-dimensional ferromagnets is essential both for understanding fundamental micromagnetic processes, as well as for investigating technologically-relevant micromagnets whose functions are connected to the presence and dynamics of fundamental micromagnetic structures, such as domain walls and vortices. Here, we demonstrate time-resolved magnetic laminography, a technique which offers access to the temporal evolution of a complex three-dimensional magnetic structure with nanoscale resolution. We image the dynamics of the complex three-dimensional magnetization state in a two-phase bulk magnet with a lateral spatial resolution of 50 nm, mapping the transition between domain wall precession and the dynamics of a uniform magnetic domain that is attributed to variations in the magnetization state across the phase boundary. The capability to probe three-dimensional magnetic structures with temporal resolution paves the way for the experimental investigation of novel functionalities arising from dynamic phenomena in bulk and three-dimensional patterned nanomagnets., Comment: Nat. Nanotechnol. (2020)

Magnetic skyrmions are topologically non-trivial nanoscale objects. Their topology, which originates in their chiral domain wall winding, governs their unique response to a motion-inducing force. When subjected to an electrical current, the chiral winding of the spin texture leads to a deflection of the skyrmion trajectory, characterized by an angle with respect to the applied force direction. This skyrmion Hall angle was believed to be skyrmion diameter-dependent. In contrast, our experimental study finds that within the plastic flow regime the skyrmion Hall angle is diameter-independent. At an average velocity of 6 $\pm$ 1 m/s the average skyrmion Hall angle was measured to be 9{\deg} $\pm$ 2{\deg}. In fact, in the plastic flow regime, the skyrmion dynamics is dominated by the local energy landscape such as materials defects and the local magnetic configuration.

Since the discovery of ferromagnetic two-dimensional (2D) van der Waals (vdW) crystals, significant interest on such 2D magnets has emerged, inspired by their appealing properties and integration with other 2D family for unique heterostructures. In known 2D magnets, spin-orbit coupling (SOC) stabilizes perpendicular magnetic anisotropy (PMA). Such a strong SOC could also lift the chiral degeneracy, leading to the formation of topological magnetic textures such as skyrmions through the Dzyaloshinskii-Moriya interaction (DMI). Here, we report the experimental observation of N\'eel-type chiral magnetic skyrmions and their lattice (SkX) formation in a vdW ferromagnet Fe3GeTe2 (FGT). We demonstrate the ability to drive individual skyrmion by short current pulses along a vdW heterostructure, FGT/h-BN, as highly required for any skyrmion-based spintronic device. Using first principle calculations supported by experiments, we unveil the origin of DMI being the interfaces with oxides, which then allows us to engineer vdW heterostructures for desired chiral states. Our finding opens the door to topological spin textures in the 2D vdW magnet and their potential device application., Comment: 26 pages, 5 figures

Since the experimental discovery of magnetic skyrmions achieved one decade ago, there have been significant efforts to bring the virtual particles into all-electrical fully functional devices, inspired by their fascinating physical and topological properties suitable for future low-power electronics. Here, we experimentally demonstrate such a device: electrically-operating skyrmion-based artificial synaptic device designed for neuromorphic computing. We present that controlled current-induced creation, motion, detection and deletion of skyrmions in ferrimagnetic multilayers can be harnessed in a single device at room temperature to imitate the behaviors of biological synapses. Using simulations, we demonstrate that such skyrmion-based synapses could be used to perform neuromorphic pattern-recognition computing using handwritten recognition data set, reaching to the accuracy of ~89 percents, comparable to the software-based training accuracy of ~94 percents. Chip-level simulation then highlights the potential of skyrmion synapse compared to existing technologies. Our findings experimentally illustrate the basic concepts of skyrmion-based fully functional electronic devices while providing a new building block in the emerging field of spintronics-based bio-inspired computing., Comment: 11 pages, 4 figures

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 on the statics and above-ns dynamics have been performed, leaving still many open questions on the dynamics of the nucleation process. Furthermore, the vast majority of the presently existing studies focus on the nucleation from random natural pinning sites, or from patterned constrictions in the magnetic material itself, which limit the functionality of the skyrmion-based device. Those limitations can be overcome by the fabrication of a dedicated injector device on top of the magnetic material. In this study, we investigate the nucleation of magnetic skyrmions from a dedicated nano-engineered injector, demonstrating the reliable magnetic skyrmion nucleation at the remnant state. The sub-ns dynamics of the skyrmion nucleation process were also investigated, allowing us to shine light on the physical processes driving the nucleation.

Integrated optically-inspired wave-based processing is envisioned to outperform digital architectures in specific tasks, such as image processing and speech recognition. In this view, spin-waves represent a promising route due to their nanoscale wavelength in the GHz frequency range and rich phenomenology. Here, we realize a versatile optically-inspired platform using spin-waves, demonstrating the wavefront engineering, focusing, and robust interference of spin-waves with nanoscale wavelength. In particular, we use magnonic nanoantennas based on tailored spin-textures for launching spatially shaped coherent wavefronts, diffraction-limited spin-wave beams, and generating robust multi-beam interference patterns, which spatially extend for several times the spin-wave wavelength. Furthermore, we show that intriguing features, such as resilience to back-reflection, naturally arise from the spin-wave nonreciprocity in synthetic antiferromagnets, preserving the high quality of the interference patterns from spurious counterpropagating modes. This work represents a fundamental step towards the realization of nanoscale optically-inspired devices based on spin-waves.

Ultrafast dynamics are generally investigated using stroboscopic pump-probe measurements, which characterize the sample properties for a single, specific time delay. These measurements are then repeated for a series of discrete time delays to reconstruct the overall time trace of the process. As a consequence, this approach is limited to the investigation of fully reversible phenomena. We recently introduced an off-axis zone plate based X-ray streaking technique, which overcomes this limitation by sampling the relaxation dynamics with a single femtosecond X-ray pulse streaked over a picosecond long time window. In this article we show that the X-ray absorption cross section can be employed as the contrast mechanism in this novel technique. We show that changes of the absorption cross section on the percent level can be resolved with this method. To this end we measure the ultrafast magnetization dynamics in CoDy alloy films. Investigating different chemical compositions and infrared pump fluences, we demonstrate the routine applicability of this technique. Probing in transmission the average magnetization dynamics of the entire film, our experimental findings indicate that the demagnetization time is independent of the specific infrared laser pump fluence. These results pave the way for the investigation of irreversible phenomena in a wide variety of scientific areas., Comment: 9 pages, 5 figures

We report on the time-resolved investigation of current- and field-induced domain wall motion in perpendicularly magnetized microwires exhibiting asymmetric exchange interaction by means of scanning transmission x-ray microscopy using a time step of 200 ps. Dynamical domain wall velocities on the order of 50-100 m s$^{-1}$ were observed. The improvement in the temporal resolution allowed us to observe the absence of incubation times for the motion of the domain wall, together with indications for a negligible inertia. Furthermore, we observed that, for short current and magnetic field pulses, the magnetic domain walls do not exhibit a tilting during its motion, providing a mechanism for the fast, tilt-free, motion of magnetic domain walls.

Moving towards significantly smaller nanostructures, direct structuring techniques such as electron beam lithography approach fundamental limitations in feature size and aspect ratios. Application of nanostructures like diffractive X-ray lenses requires feature sizes of below 10 nm to enter a new regime in high resolution X-raymicroscopy. As such dimensions are difficult to obtain using conventional electron beam lithography, we pursue a line-doubling approach. We demonstrate that thismethod yields structure sizes as small as 6.4 nm. X-ray lenses fabricated in this way are tested for their efficiency and microscopic resolution. In addition, the line-doubling technique is successfully extended to a six-fold scheme, where each line in a template structure written by electron beam lithography evolves into six metal lines.

We demonstrated that thick Permalloy films exhibiting a weak growth-induced perpendicular magnetic anisotropy can be employed as an ideal test system for the investigation of gyration dynamics in topologically trivial and non-trivial magnetic states ranging from an isolated magnetic skyrmion to more complex n$\pi$ spin configurations.

Magnonics is gaining momentum as an emerging technology for information processing. The wave character and Joule heating-free propagation of spin-waves hold promises for highly efficient analog computing platforms, based on integrated magnonic circuits. Miniaturization is a key issue but, so far, only few examples of manipulation of spin-waves in nanostructures have been demonstrated, due to the difficulty of tailoring the nanoscopic magnetic properties with conventional fabrication techniques. In this Letter, we demonstrate an unprecedented degree of control in the manipulation of spin-waves at the nanoscale by using patterned reconfigurable spin-textures. By space and time-resolved scanning transmission X-ray microscopy imaging, we provide direct evidence for the channeling and steering of propagating spin-waves in arbitrarily shaped nanomagnonic waveguides based on patterned domain walls, with no need for external magnetic fields or currents. Furthermore, we demonstrate a prototypic nanomagnonic circuit based on two converging waveguides, allowing for the tunable spatial superposition and interaction of confined spin-waves modes., Comment: 16 pages, 5 figures

The influence of a strain-induced uniaxial magnetoelastic anisotropy on the magnetic vortex core dynamics in microstructured magnetostrictive Co$_{40}$Fe$_{40}$B$_{20}$ elements was investigated with time-resolved scanning transmission x-ray microscopy. The measurements revealed a monotonically decreasing eigenfrequency of the vortex core gyration with the increasing magnetoelastic anisotropy, which follows closely the predictions from micromagnetic modeling.

Magnetic skyrmions are knot-like quasiparticles. They are candidates for non-volatile data storage in which information is moved between fixed read and write terminals. Read-out operation of skyrmion-based spintronic devices will rely upon electrical detection of a single magnetic skyrmion within a nanostructure. Here, we present Pt/Co/Ir nanodiscs which support skyrmions at room temperature. We measured the Hall resistivity whilst simultaneously imaging the spin texture using magnetic scanning transmission x-ray microscopy (STXM). The Hall resistivity is correlated to both the presence and size of the skyrmion. The size-dependent part matches the expected anomalous Hall signal when averaging the magnetisation over the entire disc. We observed a resistivity contribution which only depends on the number and sign of skyrmion-like objects present in the disc. Each skyrmion gives rise to 22$\pm$2 n{\Omega} cm irrespective of its size. This contribution needs to be considered in all-electrical detection schemes applied to skyrmion-based devices., Comment: 13 pages, 3 figures

Current-induced spin-orbit torques (SOTs) represent one of the most effective ways to manipulate the magnetization in spintronic devices. The orthogonal torque-magnetization geometry, the strong damping, and the large domain wall velocities inherent to materials with strong spin-orbit coupling make SOTs especially appealing for fast switching applications in nonvolatile memory and logic units. So far, however, the timescale and evolution of the magnetization during the switching process have remained undetected. Here, we report the direct observation of SOT-driven magnetization dynamics in Pt/Co/AlO$_x$ dots during current pulse injection. Time-resolved x-ray images with 25 nm spatial and 100 ps temporal resolution reveal that switching is achieved within the duration of a sub-ns current pulse by the fast nucleation of an inverted domain at the edge of the dot and propagation of a tilted domain wall across the dot. The nucleation point is deterministic and alternates between the four dot quadrants depending on the sign of the magnetization, current, and external field. Our measurements reveal how the magnetic symmetry is broken by the concerted action of both damping-like and field-like SOT and show that reproducible switching events can be obtained for over $10^{12}$ reversal cycles.

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 the thermal stability and interaction of skyrmions with intrinsic and/or artificial defects. It should be emphasized that imaging magnetic skyrmionic structures forms the basis for all the planned subsequent material optimization, electrical transport experiments and devices preparation in the MAGicSky research program. In particular, imaging is paramount as a technique since it enables us to unequivocally demonstrate chiral magnetic skyrmions by directly imaging i) the effects of engineering multilayer samples with large DMis and ii) the skyrmionic structure and properties. In order to get complementary physical insight on the properties of magnetic skyrmions and to corroborate our research results, we utilise a plethora of key state-of-the-art advanced magnetic imaging techniques, namely: i) Spin-polarised Scanning Tunnelling Microscopy (SP-STM), Scanning Transmission X-ray Microscopy (STXM) Lorentz Transmission Electron Microscopy (Lorentz TEM) as well as, Magnetic Force Microscopy (MFM). These imaging experiments can therefore stand as the base for all the other objectives in WP1 as well as WP2 that will study Dynamic properties: nucleation, propagation and detection of skyrmions. Imaging has been aimed to test and get feedback from the theoretical and numerical investigations of skyrmion systems of WP3. Finally, for WP4: Towards skyrmion based devices for information storage and processing, some of the techniques detailed here in D1.1 will enable us to image and test the first devices and their functionality. In short, the MAGicSky consortium research results in D1.1 constitute a major milestone that acts as a stepping-stone to every other experimental effort and we have achieved it. The results relevant to the D1.1 deliverable were presented in 5 publications and several invited talks at international workshop and conferences

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 small magnetic domains at very low field in these multilayers. The study of their behavior in perpendicular magnetic field allows us to conclude that they are actually magnetic skyrmions stabilized by the large Dzyaloshinskii-Moriya interaction. This discovery of stable sub-100 nm individual skyrmions at room temperature in a technologically relevant material opens the way for device applications in a near future.

Imaging the magnetic structure of a material is essential to understanding the influence of the physical and chemical microstructure on its magnetic properties. Magnetic imaging techniques, however, have up to now been unable to probe 3D micrometer-sized systems with nanoscale resolution. Here we present the imaging of the magnetic domain configuration of a micrometre-thick FeGd multilayer with hard X-ray dichroic ptychography at energies spanning both the Gd L3 edge and the Fe K edge, providing a high spatial resolution spectroscopic analysis of the complex X-ray magnetic circular dichroism. With a spatial resolution reaching 45 nm, this advance in hard X-ray magnetic imaging is the first step towards the investigation of buried magnetic structures and extended three-dimensional magnetic systems at the nanoscale.