Calculations and measurements of polarization-dependent soft X-ray scattering intensity are presented during a magnetic hysteresis cycle. It is confirmed that the dependence of the intensity on the magnetic moment can be linear, quadratic or a combination of both, depending on the polarization of the incident X-ray beam and the direction of the magnetic moment. With a linearly polarized beam, the scattered intensity will have a purely quadratic dependence on the magnetic moment when the magnetic moment is parallel to the scattering plane. However, with the magnetic moment perpendicular to the scattering plane, there is also a linear component. This means that, when measuring the hysteresis with linear polarization during a hysteresis cycle, the intensity will be an even function of the applied field when the change in the magnetic moment (and field) is confined within the scattering plane but becomes more complicated when the magnetic moment is out of the scattering plane. Furthermore, with circular polarization, the dependence of the scattered intensity on the moment is a combination of linear and quadratic. With the moment parallel to the scattering plane, the linear component changes with the helicity of the incident beam. Surprisingly, in stark contrast to absorption studies, even when the magnetic moment is perpendicular to the scattering plane there is still a dependence on the moment with a linear component. This linear component is completely independent of the helicity of the beam, meaning that the hysteresis loops will not be inverted with helicity.

Measuring Hysteresis Curves with Polarised Soft X-ray Reflectivity

The topological surface states (TSSs) in topological insulators (TIs) offer exciting prospects for dissipationless spin transport. Common spin-based devices, such as spin valves, rely on trilayer structures in which a non-magnetic layer is sandwiched between two ferromagnetic (FM) layers. The major disadvantage of using high-quality single-crystalline TI films in this context is that a single pair of spin-momentum locked channels spans across the entire film, meaning that only a very small spin current can be pumped from one FM to the other, along the side walls of the film. On the other hand, using nanocrystalline TI films, in which the grains are large enough to avoid hybridization of the TSSs, will effectively increase the number of spin channels available for spin pumping. Here, we used an element-selective, x-ray based ferromagnetic resonance technique to demonstrate spin pumping from a FM layer at resonance through the TI layer and into the FM spin sink.

Spin pumping through nanocrystalline topological insulators

Magnetic skyrmions (skyrmions hereafter) are magnetization configurations, whose topological robustness and nanoscale size have led to speculation that they could find use as a next-generation information carrier. Skyrmions have been observed in magnetic multilayer materials that are thin compared to the radius of a skyrmion, and chiral cubic single crystals that can be far larger than any characteristic skyrmion scale. In these single crystals, one would expect that skyrmions could exhibit interesting three-dimensional (3D) characteristics. Here, the symmetry of the micromagnetic free energy is investigated. This symmetry permits a complex 3D modulation of a skyrmion string, which we show to be a requirement of a skyrmion coexisting with the conical state. We discuss the implications of this modulation with respect to Thiele’s equation and interskyrmion interactions. Further to this internal modulation, we study theoretically and show experimentally that the strings themselves must contort towards the surfaces of their confining crystals.

Three-dimensional structure of magnetic skyrmions

An escalating challenge in condensed-matter research is the characterization of emergent orderparameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.

Structural chirality of polar skyrmions probed by resonant elastic x-ray scattering

Magnetic diffraction in combination with x-ray detected ferromagnetic resonance (DFMR) is a powerful technique for performing time-resolved measurements on individual spin textures. Here, we study the ferromagnetic resonance (FMR) modes of both the conical and field-polarized phases in the chiral magnet Cu2OSeO3. Following the identification of the FMR modes at different temperatures using broadband vector network analyzer FMR, we use DFMR on the crystalline (001) Bragg peak to reveal the time-dependent spin configurations of the selected FMR modes. By being able to measure both the amplitude and phase response of the spin system across the resonance, a continuous phase advance (of 180◦) in the conical mode and a phase lag (of 180◦) in the field-polarized mode is found. By performing dynamic measurements in the conical phase as a function of the linear polarization angle of the x rays, i.e., successively probing the dynamics of the moments, we find an inversion of the dynamics along the conical axis upon inverting the applied field direction. By allowing for time-resolved measurements of the phase and amplitude of individual magnetic phases, DFMR opens up new opportunities for obtaining a deeper understanding of the complex dynamics of chiral magnets.

Time-resolved measurement of spin excitations in Cu$_2$OSeO$_3$

Resonant soft-x-ray reflectivity and vibrating sample magnetometry have been used to characterize field driven and spin orbit torque driven magnetization reversal in a CoFeTaB/Pt bilayer. Reversal of the magnetization occurs either along the applied field direction or perpendicular to the current flow direction. Magnetometry results show that field driven (current driven) coercivities are reduced by application of a current (field) highlighting the roles played by the two external parameters. In the current switching case, it is demonstrated with soft-x-ray hysteresis loops that only the layers near the interface with Pt switch, possibly highlighting the role of proximity effects of the magnetized Pt. We show how magnetization reversal perpendicular to the beam results in hysteresis behavior in the reflected intensity that is dependent on the magnetization but independent of the helicity of the circular polarization of the incident beam

Spin orbit torque driven magnetization reversal in CoFeTaB/Pt probed by resonant x-ray reflectivity

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO3/SrTiO3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering

Non-collinear spin textures in ferromagnetic ultrathin films are attracting a renewed interest fueled by possible fine engineering of several magnetic interactions, notably the interfacial Dzyaloshinskii-Moriya interaction. This allows for the stabilization of complex chiral spin textures such as chiral magnetic domain walls (DWs), spin spirals, and magnetic skyrmions among others. We report here on the behavior of chiral DWs at ultrashort timescale after optical pumping in perpendicularly magnetized asymmetric multilayers. The magnetization dynamics is probed using time-resolved circular dichroism in x-ray resonant magnetic scattering (CD-XRMS). We observe a picosecond transient reduction of the CD-XRMS, which is attributed to the spin current-induced coherent and incoherent torques within the continuously varying spin texture of the DWs. We argue that a specific demagnetization of the inner structure of the DW induces a flow of spins from the interior of the neighboring magnetic domains. We identify this time-varying change of the DW texture shortly after the laser pulse as a distortion of the homochiral Néel shape toward a transient mixed Bloch-Néel-Bloch texture along a direction transverse to the DW

Ultrafast time-evolution of chiral Néel magnetic domain walls probed by circular dichroism in x-ray resonant magnetic scattering

All-optical switching of magnetization has great potential for use in future ultrafast and energy efficient nanoscale magnetic storage devices. So far, research was almost exclusively focused on rare-earth based materials, which limits device tunability and scalability. Here, we show that a perpendicularly magnetized synthetic ferrimagnet composed of two distinct transition metal ferromagnetic layers, Ni3Pt and Co, can exhibit helicity independent magnetization switching. Switching occurs between two equivalent remanent states with antiparallel alignment of the Ni3Pt and Co magnetic moments, and is observable over a broad temperature range. Time-resolved measurements indicate that the switching is driven by a spin-polarized current passing through the sub-nanometer Ir layer. The magnetic properties of this model system may be tuned continuously via sub-nanoscale changes in the constituent layer thicknesses as well as growth conditions, allowing the underlying mechanisms to be elucidated, and paving the way to a new class of data storage devices.

Transition metal synthetic ferrimagnets: tuneable media for all-optical switching driven by nanoscale spin current

Magnetic skyrmions are vortex-like spin textures, which are usually treated as two-dimensional objects. In their lattice state, they form well-ordered, hexagonal structures, which have been studied in great detail. To obtain a three-dimensional (3D) skyrmion crystal, these planes can be envisaged to be stacked up forming skyrmion strings in the third dimension. Here, we report the observation of a 3D skyrmion phase in Cu2OSeO3 by carrying out reciprocal space mapping in resonant elastic x-ray scattering. We observe regions in the magnetic field-cooling phase diagram in which the skyrmion phase apparently coexists with the conical phase. However, such a coexistence is forbidden due to symmetry arguments. Instead, the skyrmion strings themselves are periodically modulated along their axes, as confirmed by micromagnetic simulations. The periodic modulation is in fact a necessary consequence of the evolution of the skyrmion phase out of the conical state and should therefore be a universal property of skyrmion strings in chiral helimagnets.

Periodically modulated skyrmion strings in Cu$_2$OSeO$_3$

Heterostructures composed of ferromagnetic layers that are mutually interacting through a nonmagnetic spacer are at the core of magnetic sensor and memory devices. In the present study, layer-resolved ferromagnetic resonance was used to investigate the coupling between the magnetic layers of a Co/MgO/Permalloy magnetic tunnel junction. Two magnetic resonance peaks were observed for both magnetic layers, as probed at the Co and Ni L$_3$ x-ray absorption edges, showing a strong interlayer interaction through the insulating MgO barrier. A theoretical model based on the Landau-Lifshitz-Gilbert-Slonczewski equation was developed, including exchange coupling and spin pumping between the magnetic layers. Fits to the experimental data were carried out, both with and without a spin pumping term, and the goodness of the fit was compared using a likelihood ratio test. This rigorous statistical approach provides an unambiguous proof of the existence of interlayer coupling mediated by spin pumping.

Spin-current mediated exchange coupling in MgO-based magnetic tunnel junctions

Synchrotron radiation based techniques provide unique insight into both the element and time resolved magnetization behavior in magnetic spin systems. Here, we highlight the power of two recent developments, utilizing x-ray scattering techniques to reveal the precessional magnetization dynamics of ordered spin structures in the GHz regime, both in diffraction and reflection configurations. Our recently developed diffraction and reflectometry ferromagnetic resonance (DFMR and RFMR) techniques provide novel ways to explore the dynamics of modern magnetic materials, thereby opening up new pathways for the development of spintronic devices. In this paper we provide an overview of these techniques, and discuss the new understanding they provide into the magnetization dynamics in the chiral magnetic structure in Y-type hexaferrite and the depth dependence to the magnetization dynamics in a [CoFeB/MgO/Ta]$_4$ multilayer.

Magnetization dynamics in ordered spin structures revealed by diffractive and reflectometry ferromagnetic resonance

A chiral bobber is a localized three-dimensional magnetization configuration, terminated by a singularity. Chiral bobbers coexist with magnetic skyrmions in chiral magnets, lending themselves to new types of skyrmion-complementary bits of information. However, the on-demand creation of bobbers, as well as their direct observation remained elusive. Here, we introduce a new mechanism for creating a stable chiral bobber lattice state via the proximity of two skyrmion species with comparable size. This effect is experimentally demonstrated in a Cu$_2$2OSeO$_3$/[Ta/CoFeB/MgO]$_4$ heterostructure in which an exotic bobber lattice state emerges in the phase diagram of Cu$_2$OSeO$_3$. To unambiguously reveal the existence of the chiral bobber lattice state, we have developed a novel characterization technique, magnetic truncation rod analysis, which is based on resonant elastic x-ray scattering.

Creation of a chiral bobber lattice in helimagnet-multilayer heterostructures

Microwave and heat-assisted magnetic recordings are two competing technologies that have greatly increased the capacity of hard disk drives. The efficiency of the magnetic recording process can be further improved by employing non-collinear spin structures that combine perpendicular and in-plane magnetic anisotropy. Here, we investigate both microwave and optically excited magnetization dynamics in [Co/Pt]/NiFe exchange spring samples. The resulting canted magnetization within the nanoscale [Co/Pt]/NiFe interfacial region allows for optically stimulated magnetization precession to be observed for an extended magnetic field and frequency range. The results can be explained by formation of an imprinted domain structure, which locks the magnetization orientation and makes the structures more robust against external perturbations. Tuning the canted interfacial domain structure may provide greater control of optically excited magnetization reversal and optically generated spin currents, which are of paramount importance for future ultrafast magnetic recording and spintronic applications.

Optically and Microwave-Induced Magnetization Precession in [Co/Pt]/NiFe Exchange Springs

Magnetic multilayers offer diverse opportunities for the development of ultrafast functional devices through advanced interface and layer engineering. Nevertheless, a method for determining their dynamic properties as a function of depth throughout such stacks has remained elusive. By probing the ferromagnetic resonance modes with element-selective soft x-ray resonant reflectivity, we gain access to the magnetization dynamics as a function of depth. Most notably, using reflectometry ferromagnetic resonance, we find a phase lag between the coupled ferromagnetic layers in [CoFeB/MgO/Ta]$_4$ multilayers that is invisible to other techniques. The use of reflectometry ferromagnetic resonance enables the time-resolved and depth-resolved probing of the complex magnetization dynamics of a wide range of functional magnetic heterostructures with absorption edges in the soft x-ray wavelength regime.

Depth-Resolved Magnetization Dynamics Revealed by X-Ray Reflectometry Ferromagnetic Resonance

The emergence of magnetic skyrmions, topological spin textures, has aroused tremendous interest in studying the rich physics related to their topology. While skyrmions promise high-density and energy-efficient magnetic memory devices for information technology, the manifestation of their nontrivial topology through single skyrmions and ordered and disordered skyrmion lattices could also give rise to many fascinating physical phenomena, such as chiral magnon and skyrmion glass states. Therefore, generating skyrmions at designated locations on a large scale, while controlling the skyrmion patterns, is the key to advancing topological magnetism. Here, a new, yet general, approach to the “printing” of skyrmions with zero-field stability in arbitrary patterns on a massive scale in exchange-biased magnetic multilayers is presented. By exploiting the fact that the antiferromagnetic order can be reconfigured by local thermal excitations, a focused electron beam with a graphic pattern generator to “print” skyrmions is used, which is referred to as skyrmion lithography. This work provides a route to design arbitrary skyrmion patterns, thereby establishing the foundation for further exploration of topological magnetism.

Electron beam lithography of magnetic skyrmions

Insulating antiferromagnets have recently emerged as efficient and robust conductors of spin current. Element-specific and phase-resolved x-ray ferromagnetic resonance has been used to probe the injection and transmission of ac spin current through thin epitaxial NiO(001) layers. The spin current is found to be mediated by coherent evanescent spin waves of GHz frequency, rather than propagating magnons of THz frequency, paving the way towards coherent control of the phase and amplitude of spin currents within an antiferromagnetic insulator at room temperature.

Coherent transfer of spin angular momentum by evanescent spin waves within antiferromagnetic NiO

We investigate the temperature-dependent electronic structure of the van der Waals ferromagnet, CrGeTe$_3$. Using angle-resolved photoemission spectroscopy, we identify atomic- and orbital-specific band shifts upon cooling through $T_C$. From these, together with x-ray absorption spectroscopy and x-ray magnetic circular dichroism measurements, we identify the states created by a covalent bond between the Te $5p$ and the Cr $e_g$ orbitals as the primary driver of the ferromagnetic ordering in this system, while it is the Cr $t_{2g}$ states that carry the majority of the spin moment. The $t_{2g}$ states furthermore exhibit a marked bandwidth increase and a remarkable lifetime enhancement upon entering the ordered phase, pointing to a delicate interplay between localized and itinerant states in this family of layered ferromagnets.

Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of CrGeTe$_3$

As existing CMOS-based nanoelectronics meets fundamental barriers, spintronic devices employing the electron spin in addition to or instead of the electron charge are being developed as an important new approach to continue miniaturization and scaling. In particular, the generation, manipulation, and detection of pure spin currents or spin-polarized charge currents are a key area of fundamental research. Advances in this area strongly rely on the development and optimization of more efficient detection methods. Ferromagnetic resonance (FMR) is a powerful tool for the study of magnetization dynamics. By using microwaves to excite the magnetization into a steady state of precession, insight may be gained into magnetic properties, such as magnetic damping and magnetic anisotropies in ferromagnetic materials, and even spin-orbit torque effects.

Element- and time-resolved measurements of spin dynamics using x-ray detected ferromagnetic resonance

Engineering the anomalous Hall effect (AHE) is the key to manipulate the magnetic orders in the emerging magnetic topological insulators (MTIs). In this letter, we synthesize the epitaxial Bi2Te3/MnTe magnetic heterostructures and observe pronounced AHE signals from both layers combined together. The evolution of the resulting hybrid AHE intensity with the top Bi2Te3 layer thickness manifests the presence of an intrinsic ferromagnetic phase induced by the topological surface states at the heterolayer interface. More importantly, by doping the Bi2Te3 layer with Sb, we are able to manipulate the sign of the Berry phase-associated AHE component. Our results demonstrate the unparalleled advantages of MTI heterostructures over magnetically doped TI counterparts in which the tunability of the AHE response can be greatly enhanced. This in turn unveils a new avenue for MTI heterostructure-based multifunctional applications.

Tailoring Hybrid Anomalous Hall Response in Engineered Magnetic Topological Insulator Heterostructures

Magnetic skyrmions are two-dimensional magnetization swirls that stack in the form of tubes in the third dimension and which are proposed as prospective information carriers for nonvolatile memory devices due to their unique topological properties. From resonant elastic X-ray scattering measurements on Cu2OSeO3 with an in-plane magnetic field, we find that a state of perpendicularly ordered skyrmions forms, in stark contrast to the well-studied bulk state. The surface state is stable over a wide temperature range, unlike the bulk state in out-of-plane fields which is confined to a narrow region of the temperature-field phase diagram. In contrast to ordinary skyrmions found in the bulk, the surface state skyrmions result from the presence of magnetic interactions unique to the surface which stabilize them against external perturbations. The surface guiding makes the robust state particular interesting for racetracklike devices, ultimately allowing for much higher storage densities due to the smaller lateral footprint of the perpendicular skyrmions.

Robust Perpendicular Skyrmions and Their Surface-Confinement

Magnetic skyrmions are nanosized magnetization whirls that exhibit topological robustness and nontrivial magnetoelectrical properties, such as emergent electromagnetism and intriguing spin dynamics in the microwave-frequency region. In chiral magnets, skyrmions are usually found at a pocket in the phase diagram in the vicinity of the ordering temperature, wherein they order in the form of a hexagonal skyrmion lattice (SkL). It is generally believed that this equilibrium SkL phase is a uniform, long-range-ordered magnetic structure with a well-defined lattice constant. Here, using high-resolution small-angle resonant elastic x-ray scattering, we study the field and temperature dependence of the skyrmion lattice in FeGe and Cu2OSeO3 membranes. Indeed, Cu2OSeO3 shows the expected rigid skyrmion lattice, known from bulk samples, that is unaffected by tuning field and temperature within the phase pocket. In stark contrast, the lattice constant and skyrmion size in FeGe membranes undergo a continuous evolution within the skyrmion phase pocket, whereby the lattice constant changes by up to 15% and the magnetic scattering intensity varies significantly. Using micromagnetic modeling, it is found that for FeGe the competing energy terms contributing to the formation of the skyrmion lattice fully explain this breathing behavior. In contrast, for Cu2OSeO3 this stabilizing energy balance is less affected by the smaller field variation across the skyrmion pocket, leading to the observed rigid lattice structure.

Field and temperature dependence of the skyrmion lattice phase in chiral magnet membranes

Collective spin excitations of ordered magnetic structures offer great potential for the development of novel spintronic devices. The present approach relies on micromagnetic models to explain the origins of dynamic modes observed by ferromagnetic resonance (FMR) studies, since experimental tools to directly reveal the origins of the complex dynamic behavior are lacking. Here we demonstrate a new approach which combines resonant magnetic X-ray diffraction with FMR, thereby allowing for a reconstruction of the real-space spin dynamics of the system. This new diffractive FMR technique builds on X-ray detected FMR that allows for element-selective dynamic studies, giving unique access to specific wave components of static and dynamic coupling in magnetic heterostructures. In combination with diffraction, FMR is elevated to the level of a modal spectroscopy technique, potentially opening new pathways for the development of spintronic devices.

Mode-resolved detection of magnetization dynamics using diffractive ferromagnetic resonance

A detailed magnetic phase diagram of FeGe membranes with fields applied out-of-plane is determined using small-angle soft x-ray elastic scattering. In addition to the well-established skyrmion and helical phase, we identify an additional ordered phase which partly coexists with the helical phase in a pocket beneath the skyrmion phase. Furthermore, an evolution of the modulation wave vector, q, is observed when traversing the magnetic phase pocket. For the ordinary and the additional helical phase, q only varies with normalized field but not with temperature—in sharp contrast to the skyrmion phase, for which q is both field and temperature dependent. This study of the helical phases in thin FeGe membranes lays the foundation for their use in future magnetic storage and logic devices.

Helical magnetic ordering in thin FeGe membranes

Magnetic topological insulators (TIs) are an ideal playground for the study of novel quantum phenomena building on time-reversal symmetry-broken topological surface states. By combining different magnetic TIs in a heterostructure, their magnetic and electronic properties can be precisely tuned. Recently, we have combined high-moment Dy:Bi2Te3 with high transition temperature Cr:Sb2Te3 in a superlattice, and we found, using x-ray magnetic circular dichroism (XMCD), that long-range magnetic order can be introduced in the Dy:Bi2Te3 layers. Accompanying first-principles calculations indicated that the origin of the long-range magnetic order is a strong antiferromagnetic coupling between Dy and Cr magnetic moments at the interface extending over several layers. However, based on XMCD alone, which is either averaging over the entire thin-film stack or is surface-sensitive, this coupling scenario could not be fully confirmed. Here we use polarized neutron reflectometry, which is ideally suited for the detailed study of superlattices, to retrieve the magnetization in a layer- and interface-resolved way. We find that the magnetization is, in contrast to similar recent studies, homogeneous throughout the individual layers, with no apparent interfacial effects. This finding demonstrates that heterostructure engineering is a powerful way of controlling the magnetic properties of entire layers, with the effects of coupling reaching beyond the interface region.

Magnetic profile of proximity-coupled (Dy,Bi)$_2$Te$_3$/(Cr,Sb)$_2$Te$_3$ topological insulator heterostructures

Chromium telluride compounds are promising ferromagnets for proximity coupling to magnetic topological insulators (MTIs) of the Cr-doped (Bi,Sb)2(Se,Te)3 class of materials as they share the same elements, thus simplifying thin film growth, as well as due to their compatible crystal structure. Recently, it has been demonstrated that high quality (001)-oriented Cr2Te3 thin films with perpendicular magnetic anisotropy can be grown on c-plane sapphire substrate. Here, we present a magnetic and soft x-ray absorption spectroscopy study of the chemical and magnetic properties of Cr2Te3 thin films. X-ray magnetic circular dichroism (XMCD) measured at the Cr L2,3 edges gives information about the local electronic and magnetic structure of the Cr ions. We further demonstrate the overgrowth of Cr2Te3 (001) thin films by high-quality Cr-doped Sb2Te3 films. The magnetic properties of the layers have been characterized and our results provide a starting point for refining the physical models of the complex magnetic ordering in Cr2Te3 thin films, and their integration into advanced MTI heterostructures for quantum device applications.

Cr$_2$Te$_3$ thin films for integration in magnetic topological insulator heterostructures

Room temperature magnetic skyrmions in magnetic multilayers are considered as information carriers for future spintronic applications. Currently, a detailed understanding of the skyrmion stabilization mechanisms is still lacking in these systems. To gain more insight, it is first and foremost essential to determine the full real‐space spin configuration. Here, two advanced X‐ray techniques are applied, based on magnetic circular dichroism, to investigate the spin textures of skyrmions in [Ta/CoFeB/MgO]n multilayers. First, by using ptychography, a high‐resolution diffraction imaging technique, the 2D out‐of‐plane spin profile of skyrmions with a spatial resolution of 10 nm is determined. Second, by performing circular dichroism in resonant elastic X‐ray scattering, it is demonstrated that the chirality of the magnetic structure undergoes a depth‐dependent evolution. This suggests that the skyrmion structure is a complex 3D structure rather than an identical planar texture throughout the layer stack. The analyses of the spin textures confirm the theoretical predictions that the dipole–dipole interactions together with the external magnetic field play an important role in stabilizing sub‐100 nm diameter skyrmions and the hybrid structure of the skyrmion domain wall. This combined X‐ray‐based approach opens the door for in‐depth studies of magnetic skyrmion systems, which allows for precise engineering of optimized skyrmion heterostructures.

Anatomy of skyrmionic textures in magnetic multilayers

How the interacting electronic states and phases of layered transition-metal dichalcogenides evolve when thinned to the single-layer limit is a key open question in the study of two-dimensional materials. Here, we use angle-resolved photoemission to investigate the electronic structure of monolayer VSe2 grown on bilayer graphene/SiC. While the global electronic structure is similar to that of bulk VSe2, we show that, for the monolayer, pronounced energy gaps develop over the entire Fermi surface with decreasing temperature below Tc = 140 ± 5 K, concomitant with the emergence of charge-order superstructures evident in low-energy electron diffraction. These observations point to a charge-density wave instability in the monolayer that is strongly enhanced over that of the bulk. Moreover, our measurements of both the electronic structure and of X-ray magnetic circular dichroism reveal no signatures of a ferromagnetic ordering, in contrast to the results of a recent experimental study as well as expectations from density functional theory. Our study thus points to a delicate balance that can be realized between competing interacting states and phases in monolayer transition-metal dichalcogenides.

Electronic structure and enhanced charge-density wave order of monolayer VSe$_2$

Magnetic skyrmions are particle-like, topologically protected magnetisation entities that are promising candidates as information carriers in racetrack memory. The transport of skyrmions in a shift-register-like fashion is crucial for their embodiment in practical devices. Here, we demonstrate that chiral skyrmions in Cu2OSeO3 can be effectively manipulated under the influence of a magnetic field gradient. In a radial field gradient, skyrmions were found to rotate collectively, following a given velocity–radius relationship. As a result of this relationship, and in competition with the elastic properties of the skyrmion lattice, the rotating ensemble disintegrates into a shell-like structure of discrete circular racetracks. Upon reversing the field direction, the rotation sense reverses. Field gradients therefore offer an effective handle for the fine control of skyrmion motion, which is inherently driven by magnon currents. In this scheme, no local electric currents are needed, thus presenting a different approach to shift-register-type operations based on spin transfer torque.

Manipulation of skyrmion motion by magnetic field gradients

The combination of topological properties and magnetic order can lead to new quantum states and exotic physical phenomena, such as the quantum anomalous Hall (QAH) effect. The size of the magnetic gap in the topological surface states, key for the robust observation of the QAH state, scales with the magnetic moment of the doped three-dimensional topological insulator (TI). The pioneering transition-metal doped (Sb,Bi)2(Se,Te)3 thin films only allow for the observation of the QAH effect up to some 100 mK, despite the much higher magnetic ordering temperatures. On the other hand, high magnetic moment materials, such as rare-earth-doped (Sb,Bi)2(Se,Te)3 thin films, show large moments but no long-range magnetic order. Proximity coupling and interfacial effects, multiplied in artificial heterostructures, allow for the engineering of the electronic and magnetic properties. Here, we show the successful growth of high-quality Dy:Bi2Te3/Cr:Sb2Te3 thin film heterostructures. Using x-ray magnetic spectroscopy we demonstrate that high transition temperature Cr:Sb2Te3 can introduce long-range magnetic order in high-moment Dy:Bi2Te3 —up to a temperature of 17 K— in excellent agreement with first-principles calculations, which reveal the origin of the long-range magnetic order in a strong antiferromagnetic coupling between Dy and Cr magnetic moments at the interface extending over several layers. Engineered magnetic TI heterostructures may be an ideal materials platform for observing the QAH effect at liquid He temperatures and above.

Imposing long-range ferromagnetic order in rare-earth-doped magnetic topological-insulator heterostructures

Arrays of non-interacting nanomagnets are widespread in data storage and processing. As current technologies approach fundamental limits on size and thermal stability, enhancing functionality through embracing the strong interactions present at high array densities becomes attractive. In this respect, artificial spin ices are geometrically frustrated magnetic metamaterials that offer vast untapped potential due to their unique microstate landscapes, with intriguing prospects in applications from reconfigurable logic to magnonic devices or hardware neural networks. However, progress in such systems is impeded by the inability to access more than a fraction of the total microstate space. Here, we demonstrate that topological defect-driven magnetic writing—a scanning probe technique—provides access to all of the possible microstates in artificial spin ices and related arrays of nanomagnets. We create previously elusive configurations such as the spin-crystal ground state of artificial kagome dipolar spin ices and high-energy, low-entropy ‘monopole-chain’ states that exhibit negative effective temperatures.

Realization of ground state in artificial kagome spin ice via topological defect-driven magnetic writing

Domain wall propagation dynamics has been studied in nanostructured artificial kagome spin-ice structures. A stripline circuit has been used to provide localized pulsed magnetic fields within the artificial spin-ice (ASI) structure. This provides control of the system through electrically assisted domain wall nucleation events. Synchronization of the pulsed fields with additional global magnetic fields and the use of a focused magneto-optical Kerr effect magnetometer allows our experiments to probe the domain wall transit through an extended ASI structure. We find that the propagation distance depends on the driving field revealing field-driven properties of domain walls below their intrinsic nucleation field.

Dynamic dependence to domain wall propagation through artificial spin ice

The interaction between a magnetic domain wall and a pinning site is explored in a planar nanowire using micromagnetics to reveal perturbations of the pinning energetics for propagating domain walls. Numerical simulations in the high damping ’quasi-static’ and low damping ’dynamic’ regimes are compared and show clear differences in de-pinning fields, indicating that dynamical micromagnetic models, which incorporate precessionally limited magnetization processes, are needed to understand domain wall pinning. Differences in the micromagnetic domain wall structure strongly influence the pinning and show periodic behaviour with increasing applied field associated with Walker breakdown. In the propagating regime pinning is complicated.

Effective pinning energy landscape perturbations for propagating magnetic domain walls

Realising the promise of next-generation magnetic nanotechnologies is contingent on the development of novel methods for controlling magnetic states at the nanoscale. There is currently demand for simple and flexible techniques to access exotic magnetisation states without convoluted fabrication and application processes. 360° domain walls (metastable twists in magnetisation separating two domains with parallel magnetisation) are one such state, which is currently of great interest in data storage and magnonics. Here, we demonstrate a straightforward and powerful process whereby a moving magnetic charge, provided experimentally by a magnetic force microscope tip, can write and manipulate magnetic charge states in ferromagnetic nanowires. The method is applicable to a wide range of nanowire architectures with considerable benefits over existing techniques. We confirm the method’s efficacy via the injection and spatial manipulation of 360° domain walls in Py and Co nanowires. Experimental results are supported by micromagnetic simulations of the tip-nanowire interaction.

A novel method for the injection and manipulation of magnetic charge states in nanostructures

Magnetic skyrmions in chiral magnets are nanoscale, topologically protected magnetization swirls that are promising candidates for spintronics memory carriers. Therefore, observing and manipulating the skyrmion state on the surface level of the materials are of great importance for future applications. Here, we report a controlled way of creating a multidomain skyrmion state near the surface of a Cu2OSeO3 single crystal, observed by soft resonant elastic X-ray scattering. This technique is an ideal tool to probe the magnetic order at the L3 edge of 3d metal compounds giving an average depth sensitivity of ∼50 nm. The single-domain 6-fold-symmetric skyrmion lattice can be broken up into domains, overcoming the propagation directions imposed by the cubic anisotropy by applying the magnetic field in directions deviating from the major cubic axes. Our findings open the door to a new way to manipulate and engineer the skyrmion state locally on the surface or on the level of individual skyrmions, which will enable applications in the future.

Multidomain Skyrmion Lattice State in Cu$_2$OSeO$_3$

The angular dependence of the magnetization reversal in interconnected kagome artificial spin ice structures has been studied through experimental MOKE measurements and micromagnetic simulations. This reversal is mediated by the propagation of magnetic domain walls along the interconnecting bars, which either nucleate at the vertex or arrive following an interaction in a neighboring vertex. The physical differences in these processes show a distinct angular dependence allowing the different contributions to be identified. The configuration of the initial magnetization state, either locally or on a full sublattice of the system, controls the reversal characteristics of the array within a certain field window. This shows how the available magnetization reversal routes can be manipulated and the system can be trained.

Angular-dependent magnetization reversal processes in artificial spin ice

Magnetic charge is carried through nanowire networks by domain walls, and the micromagnetic structure of a domain wall provides an opportunity to manipulate its movement. We have shown previously that magnetic monopole defects exist in artificial spin ice (ASI) and result from two bar switching at a vertex. To create and manipulate monopole defects and indeed magnetic charge in general, path selectivity of the domain wall at a vertex is required. We have recently shown that in connected ASI structures, transverse wall chirality (or topology) determines wall path direction, but a mechanism known as Walker breakdown, where a wall mutates into a wall of opposite chirality partially destroys selectivity. Recently it has been claimed that in isolated Y-shaped junctions that support vortex walls, selectivity is entirely determined by chirality (or topology), the suggestion being that vortex wall chirality is robust in the Walker breakdown process. Here we demonstrate that in Y-shaped junctions, magnetic switching in the important topologically protected regime exists only for a narrow window of field and bar geometry, and that it will be challenging to access this regime in field-driven ASI. This work has implications for the wider field of magnetic charge manipulation for high density memory storage.

Limitations in Artificial Spin Ice path selectivity: the challenges beyond topological control

Understanding domain wall pinning and propagation in nanowires are important for future spintronics and nanoparticle manipulation technologies. Here, the effects of microscopic local modification of the magnetic properties, induced by focused-ion-beam intermixing, in NiFe/Au bilayer nanowires on the pinning behavior of domain walls was investigated. The effects of irradiation dose and the length of the irradiated features were investigated experimentally. The results are considered in the context of detailed quasi-static micromagnetic simulations, where the ion-induced modification was represented as a local reduction of the saturation magnetization. Simulations show that domain wall pinning behavior depends on the magnitude of the magnetization change, the length of the modified region, and the domain wall structure. Comparative analysis indicates that reduced saturation magnetisation is not solely responsible for the experimentally observed pinning behavior.

Control of domain wall pinning by localised focused Ga$^+$ ion irradiation on Au capped NiFe nanowires

The dynamic behavior of magnetic domain walls incident upon a Y-shaped junction between three nanowires is explored. Details in the micromagnetic structure of the domain wall and the local spin texture at a vertex result in a complex interaction which ultimately determines the propagation direction of the domain wall following the vertex. This interaction has been explored through both magneto-optical Kerr effect experiments and micromagnetic simulations on single-vertex structures. Differences in the micromagnetic structure of incident domain walls in the dynamic regime have a significant influence on the interaction. We observe an oscillatory path selection with increasing domain wall propagation distance preceding the vertex. Our analysis shows that this behavior originates from cyclic reversals of the transverse domain wall chirality due to Walker breakdown processes.

Dynamic interaction between domain walls and nanowire vertices

The influence of interfacial intermixing on the picosecond magnetization dynamics of ferromagnetic/non-magnetic thin-film bilayers was studied. Low-dose focused-ion-beam irradiation was used to induce intermixing across the interface between a 10 nm Ni81Fe19 layer and a 2–3 nm capping layer of either Au or Cr. Time-resolved magneto-optical Kerr effect was used to study magnetization dynamics as a function of ion-beam dose. With an Au cap, the damping of the un-irradiated bilayer was comparable with native Ni81Fe19 and increased with increasing ion dose. In contrast, for Ni81Fe19/Cr the damping was higher than that for native Ni81Fe19, but the damping decreased with increasing dose. 
 We gratefully acknowledge financial support from Department of Science and Technology, Government of India, and the British Council for the DST-UKIERI joint project, Grant No. DST/INT/UK/P-44/2012. D.A. also acknowledges EPSRC funding (EP/G010897/1 and Durham Strategic Partnership Award) and UK CRG XMaS beam-line at ESRF.

Local Control of Magnetic Damping in Ferromagnetic/Non-magnetic Bilayers by Interfacial Intermixing induced by Focused Ion-Beam Irradiation

Modification of the magnetic properties in a thin-film ferromagnetic/non-magnetic bilayer system by low-dose focused ion-beam (FIB) induced intermixing is demonstrated. The highly localized capability of FIB may be used to locally control magnetic behaviour at the nanoscale. The magnetic, electronic and structural properties of NiFe/Au bilayers were investigated as a function of the interfacial structure that was actively modified using focused Ga+ ion irradiation. Experimental work used MOKE, SQUID, XMCD as well as magnetoresistance measurements to determine the magnetic behavior and grazing incidence x-ray reflectivity to elucidate the interfacial structure. Interfacial intermixing, induced by low-dose irradiation, is shown to lead to complex changes in the magnetic behavior that are associated with monotonic structural evolution of the interface. This behavior may be explained by changes in the local atomic environment within the interface region resulting in a combination of processes including the loss of moment on Ni and Fe, an induced moment on Au and modifications to the spin-orbit coupling between Au and NiFe.

Focused-ion-beam induced interfacial intermixing of magnetic bilayers for nanoscale control of magnetic properties

The magnetization reversal processes in ferromagnetic nanowires with sinusoidally modulated edges were investigated as a function of modulation amplitude and wavelength. The reversal processes were studied in two regimes: nucleation controlled reversal and magnetization reversal mediated by domain-wall propagation. In the latter case, domain walls were introduced using both nucleation-pad structures and local pulsed-field injection techniques. The reversal behavior shows that competing effects govern the switching fields in these structures, giving a minimum as a function of modulation wavelength, showing promising results for improved control of domain-wall propagation behavior. The experimental results were interpreted with detailed micromagnetic simulations and an analytical model, based on the demagnetization effects of the modulation upon the spin structure of the wire. The analysis highlights consistent trends in the reversal behavior resulting from modulation, and, significantly, the switching behavior is found to be scalable in relation to the amplitude and wavelength.

Magnetization switching and domain-wall propagation behavior in edge-modulated ferromagnetic nanowire structures

The control of individual magnetic domain walls has potential for future spintronic memory and data processing applications. The speed and reliability of such devices are determined by the dynamic properties of the domain walls. Typically, spin precession limitations lead to Walker breakdown, limiting wall velocity resulting in low mobility. Here, we show the suppression of Walker breakdown by the careful design of small amplitude periodic nanowire structuring to match the periodicity of domain wall spin structure transformations. This opens up a channel for energy dissipation via spin wave emission, allowing a domain wall to maintain its spin structure during propagation.

Suppression of Walker breakdown in magnetic domain wall propagation through structural control of spin wave emission

A detailed analysis of the structural and compositional changes in NiFe/Au bilayers induced by a focused ion beam (FIB) is presented. NiFe/Au bilayers with different thickness were irradiated with a focused 30 keV Ga+ ion beam, and the evaluation of the individual layers and interfaces were investigated systematically as a function of a broad range of irradiation fluence using grazing incidence x ray reflectivity (GIXRR) and angular dependent x ray fluorescence (ADXRF) techniques carried out at synchrotron radiation sources. Experimental data were collected from 1.3 mm × 4.5 mm structures, and irradiation of such a broad areas with a 100-nm-wide focused ion beam is a challenging task. Two irradiation regimes were identified: For Ga+ fluences < 15.6 × 1014 ion/cm2 (low dose regime), the main influence of the focused ion beam is on the interface and, beyond this dose (high dose regime), sputtering effects and ion implantation becomes significant, eventually causing amorphization of the bilayer system. The broadening of the NiFe/Au interface occurs even at the lowest dose, and above a critical fluence (Φ = 1.56 × 1014 ion/cm2) can be represented by an interfacial-intermixed layer (NixFeyAu(1-x-y); x = 0.5-0.6, y = 0.1-0.15) formed between the NiFe and Au layers. The thickness of this layer increases with irradiation fluence in the low dose regime. A linear relationship is found between the squared intermixing length and irradiation fluence, indicating that FIB-induced mixing is diffusion controlled. The ballistic model fails to describe FIB-induced intermixing, indicating that thermodynamical factors, which might be originated from FIB specific features, should be taken into account. Despite the complexity of the chemical and structural formation, good agreement between the experiment and theory highlights the functionality of the combined GIXRR and ADXRF techniques for studying intermixing in high resolution.

Study of focused-ion-beam induced structural and compositional modifications in nanoscale bilayer systems by combined grazing incidence x ray reflectivity and fluorescence

The magnetization behavior of a Permalloy thin-film (nominally Ni81Fe19) was investigated as a function of combined quasistatic and pulsed magnetic fields measured using magneto-optic Kerr effect magnetometry. We observed complex field dependent switching behavior that depends on the relative contributions to the total field of the quasistatic and pulsed fields. As the pulsed field amplitude was increased, complex switching behavior occurs for total fields in excess of the coercive field. A simple phenomenological domain wall propagation model suggests a qualitative understanding of this complex behavior based on Walker breakdown of the domain wall motion occurring in the Permalloy thin-film.

Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of CrGeTe3

Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of CrGeTe₃