The ferromagnetic resonance modes in a single rectangular Py microstrip were directly imaged using timeresolved STXM-FMR measurements and the findings were corroborated by micromagnetic simulations. The spin wave resonance modes showed a nonstanding character, when the wave-vector is parallel to the external static magnetic field due to the highly inhomogeneous effective field inside the strip. The propagating character is observed for all the observed spin waves. The influence of the edge quality was analyzed using micromagnetic simulations.

The ferromagnetic resonance of a disordered A2 Fe60Al40 of ferromagnetic strip, of dimensions 5 µm × 1 µm x 32 nm, has been observed in two vastly differing surroundings: in the first case, the ferromagnetic region was circumferenced by ordered B2 Fe60Al40, and in the second case it was free standing, adhering only to the oxide substrate. The embedded ferromagnet possesses a periodic magnetic domain structure, which transforms to a single domain structure in the freestanding case. The two cases differ in their dynamic response, for instance, the resonance field for the uniform (k = 0) mode at ~ 14 GHz excitation displays a shift from 209 to 194 mT, respectively for the embedded and freestanding cases, with the external magnetic field applied along the long axis. The resonant behavior of a microscopic ferromagnet can thus be finely tailored via control of its near-interfacial surrounding.

Traditionally, the primary field, where curvature has been at the heart of research, was the theory of general relativity. In recent studies, however, the
impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry and biology to mathematics,
giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors,
superfluidity, optics, two-dimensional van der Waals materials, plasmonics, magnetism and superconductivity. Here, we summarize the state of the art
and outline prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism,
antiferromagnetism and superconductivity. Highlighting the recent developments and current challenges in theory, fabrication and characterization of
curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application
potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention
to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching
novel functionalities. In addition, the perspective should stimulate the development and dissemination of R&D-oriented techniques to facilitate rapid
transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

We experimentally demonstrate the generation of spin-wave frequency combs based on the non-
linear interaction of propagating spin waves in a microstructured waveguide. By means of time- and space-resolved Brillouin light scattering spectroscopy, we show that the simultaneous excita- tion of spin waves with different frequencies leads to a cascade of four-magnon scattering events which ultimately results in well-defined frequency combs. Their spectral weight can be tuned by the choice of amplitude and frequency of the input signals. Furthermore, we introduce a model for stimulated four-magnon scattering which describes the formation of spin-wave frequency combs in the frequency and time domain.
Frequency

Local crystallization of ferromagnetic layers is crucial in the successful realization of miniaturized
tunneling magnetoresistance (TMR) devices. In the case of Co–Fe–B TMR devices, used most
successfully so far in applications and devices, Co–Fe–B layers are initially deposited in an amorphous
state and annealed post-deposition to induce crystallization in Co–Fe, thereby increasing the device
performance. In this work, first direct proof of locally triggered crystallization of 10 nm thick Co–Fe–B
films by laser irradiation is provided by means of X-ray diffraction (XRD) using synchrotron radiation.
A comparison with furnace annealing is performed for benchmarking purposes, covering different
annealing parameters, including temperature and duration in the case of furnace annealing, as
well as laser intensity and scanning speed for the laser annealing. Films of Co–Fe–B with different
stoichiometry sandwiched between a Ru and a Ta or MgO layer were systematically assessed by XRD
and SQUID magnetometry in order to elucidate the crystallization mechanisms. The transformation
of Co–Fe–B films from amorphous to crystalline is revealed by the presence of pronounced CoFe(110)
and/or CoFe(200) reflexes in the XRD θ-2θ scans, depending on the capping layer. For a certain window
of parameters, comparable crystallization yields are obtained with furnace and laser annealing.
Samples with an MgO capping layer required a slightly lower laser intensity to achieve equivalent Co–
Fe crystallization yields, highlighting the potential of laser annealing to locally enhance the TMR ratio.

The surface spin flop, observed in synthetic antiferromagnets (SAFs) with uniaxial anisotropy and
strong antiferromagnetic (AF) interlayer exchange coupling, can be considered as a laterally homoge-
neous, vertical AF domain wall pushed into the SAF from either the top or the bottom in the presence
of a strong external vertical magnetic field. As a result, the AF domain wall can be described as a one-
dimensional entity. In this work, we present a concept to stabilize laterally homogeneous vertical AF
domain walls by local variation of the perpendicular magnetic anisotropy in Co/Pt-based SAFs. Our
approach not only allows the stabilization of the vertical AF domain wall in the absence of any exter-
nal magnetic field, but furthermore enables a deterministic selection among four different remanent states,
each one stable within a broad external magnetic field range of almost one tesla. We also demonstrate an
extension to our concept by stabilizing two coexisting vertical AF domain walls, thus yielding a system
with a total of six different selectable (and reprogrammable) remanent states. The controlled stabiliza-
tion of noncollinear AF textures in the form of vertical AF domain walls at remanence could be used as
an infrastructure for propagating spin waves within the AF domain wall itself, as well as for tuning the
dynamic behavior of perpendicular standing spin wave modes existing vertically across the SAF.

Two magnetron sputter targets of CoCrFeNi High-Entropy Alloy (HEA), both in equal atomic ratio, were prepared by spark plasma sintering. One of the targets was fabricated from a homogeneous HEA powder produced via gas atomisation; for the second target, a mixture of pure element powders was used. Economic benefits can be achieved by mixing pure powders in the intended ratio in comparison to the gas atomisation of the specific alloy composition. In this work, thin films deposited via magnetron sputtering from both targets are analysed. The surface elemental composition is investigated by X-ray photoelectron spectroscopy, whereas the bulk stoichiometry is measured by X-ray fluorescence spectroscopy. Phase information and surface microstructure are investigated using X-ray diffraction and scanning electron microscopy, respectively. It is demonstrated that the stoichiometry, phase composition and microscopic structure of the as-deposited HEA thin films are almost identical if the same deposition parameters are used.

Despite the numerous reports over the last two decades dedicated to the study of interfacial thermal transport,
physics of thermal transport across nanoscale metallic multilayers is less explored. This is in part due to the relatively
high conductance characteristic of these interfaces, which renders them difficult to characterize.
Interfacial transport in these systems has so far appeared to be diffusive, a surprising behavior when the interface density
increases and the layer thicknesses become comparable with the mean free path of electrons.
To address the limit of diffusive theories describing heat transport across high-density metallic interfaces,
we systematically investigate heat transport in and across Pt/Co multilayers via frequency domain thermoreflectance.
Sensitivity gained from offsetting the laser beam and reducing the laser spot size allows for the
measurement of anisotropic thermal conductivity of the multilayers. By changing the number of interfaces while keeping the overall
thickness of Pt and Co in the multilayer structure constant, the effect of interface density on the multilayers’ effective thermal
conductivity is studied. The extracted Pt/Co interface thermal boundary conductance is then compared to the calculations from the
electronic diffuse mismatch model and experimental data available in the literature. We show that as the multilayer period thickness
becomes much smaller than the electron mean free path, measurements markedly deviate from the diffusive transport theory. We
attribute this deviation to the nondiffusive nature of heat transport in subnanometric scales at interface densities above 1/nm.

Under certain conditions, spin waves can be channeled into a broad angular spectrum of wave vectors, where the direction
of the group velocity becomes independent of those wave vectors. Such highly focused waves are called caustic waves,
whose properties can be manipulated by anisotropies or chiral interactions, like the Dzyaloshinskii-Moriya interaction. In this
paper, we theoretically study the focusing features of the spin waves induced by the dipole-dipole interaction in synthetic
antiferromagnets. For stacked systems, the dipolar interaction causes a noticeable frequency nonreciprocity when the
magnetizations in both films are antiparallelly aligned, and then the focusing properties of the spin waves are enhanced. The
role of thicknesses and magnetic graduation along the film's normal are systematically analyzed. We found that the degree
of focalization of the spin waves can be manipulated by increasing the layers' thickness. Also, we show that the low- and
high-frequency modes exhibit different focalization properties; the low-frequency mode manifests a similar behavior to the
heavy-metal/ferromagnet systems with interfacial Dzyaloshinskii-Moriya interaction, while the high-frequency one tends the
generate almost reciprocal interference patterns along one axis. In the case of magnetization-graded synthetic
antiferromagnets, we demonstrate that the graduation slightly influences the low-frequency mode, while the focusing and
nonreciprocal dynamic properties of the high-frequency ones are notoriously altered. The theoretical calculations are
compared with micromagnetic simulations, where a good agreement is found between both methods. Our results
demonstrate that a synthetic antiferromagnetic system allows for controlling the propagation of spin waves, assisting in the
transfer of angular momentum and energy.

We experimentally demonstrate the formation of room-temperature skyrmions with radii of about 25 nm in easy-plane anisotropy multilayers with an interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of individual magnetic skyrmions by magnetic force microscopy and find that the skyrmions are stable in out-of-plane fields up to about 200 mT. We determine the interlayer exchange coupling as well as the strength of the interfacial DMI. Additionally, we investigate the dynamic microwave spin excitations by broadband
magnetic resonance spectroscopy. From the uniform Kittel mode we determine the magnetic anisotropy and lowdamping α < 0.04. We also find clear magnetic resonance signatures in the nonuniform (skyrmion) state. Our findings demonstrate that skyrmions in easy-plane multilayers are promising for spin-dynamical applications.

We report on the controlled switching of domain-wall (DW) magnetization in aligned stripe-domain
structures, stabilized in [Co(0.44 nm)/Pt(0.7 nm)]X (X = 48, 100, 150) multilayers with perpendicular
magnetic anisotropy. The switching process, induced by an external magnetic field, is monitored by measuring the evolution of the in-plane magnetization. We show that the remanent in-plane magnetization originates from the polarization of the Bloch-type DWs. With micromagnetic simulations, we reveal that
the reversal of the DW polarization is the result of the emergence and collapse of horizontal Bloch lines
within the DWs at particular strengths of the external magnetic field, applied opposite to the DW polarization. Our findings are relevant for DW-based magnonics and bubble-skyrmion applications in magnetic multilayers.

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.

Modern problems in magnetization dynamics require more and more the numerical determination of the spin-wave spectra and -dispersion in magnetic systems where analytic theories are not yet available. Micromagnetic simulations can be used to compute the spatial mode profiles and oscillation frequencies of spin-waves in magnetic system with almost arbitrary geometry and different magnetic interactions. Although numerical approaches are very versatile, they often do not give the same insight and physical understanding as analytical theories. For example, it is not always possible to decide whether a certain feature (such as dispersion asymmetry, for example) is governed by one magnetic interaction or the other. Moreover, since numerical approaches typically yield the normal modes of the system, it is not always feasible to disentangle hybridized modes. In this manuscript, we build a bridge between numerics and analytics by presenting a methodology to calculate the individual contributions to general spin-wave dispersions in a fully numerical manner. We discuss the general form of any spin-wave dispersion in terms of the effective (stiffness) fields produced by the modes. Based on a special type of micromagnetic simulation, the numerical dynamic-matrix approach, we show how to calculate each stiffness field in the respective dispersion law, separately for each magnetic interaction. In particular, it becomes possible to disentangle contributions of different magnetic interactions to the dispersion asymmetry in systems where non-reciprocity is present. At the same time, dipolar-hybridized modes can be easily disentangled. Since this methodology is independent of the geometry or the involved magnetic interactions at hand, we believe it is attractive for experimental and theoretical studies of magnetic systems where there are no analytics available yet, but also to aid the development of new analytical theories.

The effects of hydrogen absorption on the effective magnetization (4πM_eff), gyromagnetic ratio (γ), Gilbert damping constant (α_G), and the inhomogeneous linewidth broadening in Py(x)/Y(16 nm)/Pd(15 nm) trilayer films (x = 2, 3, 5, 8, 10, 20, 40 nm) were investigated with ferromagnetic resonance (FMR), transmission electron microscopy, and vibrating sample magnetometry. In the presence of a hydrogen atmosphere, the samples show a reduction of their FMR linewidth which is found to stem purely from a reduction of the inhomogeneous linewidth broadening. This is attributed to a rearrangement of atoms at the Py/Y interface in the presence of hydrogen, making the Py/Y interface more homogeneous. In addition, a reduction of 4πM_eff was seen for all samples in the hydrogen atmosphere which is typical for an increase of the interfacial perpendicular magnetic anisotropy at the Py/Y interface.

In this paper, using micromagnetic simulations, we investigate the stress-induced frequency tunability of double-vortex nano-oscillators comprising magnetostrictive and non-magnetostrictive ferromagnetic layers separated vertically by a non-magnetic spacer. We show that the relative orientations of the vortex core polarities p1 and p2 have a strong impact on the eigen-frequencies of the dynamic modes. When the two vortices with antiparallel polarities have different eigen-frequencies and the magnetostatic coupling between them is sufficiently strong, the stress-induced magnetoelastic anisotropy can lead to the single-frequency resonant gyration mode of the two vortex cores. Additionally, for the case of parallel polarities, we demonstrate that for sufficiently strong magnetostatic coupling, the magnetoelastic anisotropy leads to the coupled vortex gyration in the chaotic regime and to the lateral separation of the vortex core trajectories. These findings offer a path for achieving a fine control over gyration frequencies and trajectories in vortex-based oscillators via adjustable elastic stress, which can be easily generated and tuned electrically, mechanically or optically.

We study layered synthetic antiferromagnets (SAFs) with out-of-plane interface anisotropy, where the layer-wise antiferromagnetic (AF)
alignment is induced by interlayer exchange coupling (IEC). By applying low energy He+ focused ion beam irradiation to the SAF, a depth-dependent
reduction of the IEC and anisotropy can be achieved due to layer intermixing. As a consequence, after irradiation, a specific field
reversal sequence of the SAF is energetically preferred. When tuning the pristine SAF to exhibit an inverted field reversal, we are thus able to
create AF domains in the irradiated regions. When irradiated with a fluence gradient, these AF domains can be further deterministically
manipulated by an external magnetic field. Among other applications, this could be utilized for engineering a controllable and local magnetic
stray field landscape, for example, at AF domain walls, within the otherwise stray field free environment provided by the SAF.

Spin waves with nanoscale wavelengths can transfer information free of electron transport and hence are promising for wave-based computing technologies with low-power consumption as a solution to the severe energy losses in modern electronics. Logic circuits based on the interference of spin waves have been proposed for more than a decade. However, spin-wave interference at the nanoscale has yet been realized. Here, we demonstrate experimentally the interference of spin waves with wavelengths down to 50 nm in a low-damping magnetic insulator. The constructive and destructive interference of spin waves is detected in the frequency domain using propagating spin-wave spectroscopy, which is further confirmed by the Brillouin light scattering. The interference pattern is found to be highly sensitive to the distance between two magnetic nanowires acting as spin-wave emitters. By controlling the magnetic configuration of the double-wire system, one can switch the spin-wave interferometer on and off. The observed phenomena are theoretically accounted for by the interlayer magnon-magnon coupling. Our demonstrations are thus key to the realization of spin-wave computing system based on non-volatile nanomagnets at the GHz frequencies.

Spin waves (SWs) in magnetic nanotubes have shown interesting nonreciprocal properties in their dispersion relation, group velocity, frequency linewidth, and attenuation lengths. The reported chiral effects are similar to those induced by the Dzyaloshinskii–Moriya interaction but originating from the dipole–dipole interaction. Here, we show that the isotropic-exchange interaction can also induce chiral effects in the SW transport; the so-called Berry phase of SWs. We demonstrate that with the application of magnetic fields, the nonreciprocity of the different SW modes can be tuned between the fully dipolar governed and the fully exchange governed cases, as they are directly related to the underlying equilibrium state. In the helical state, due to the combined action of the two effects, every single sign combination of the azimuthal and axial wave vectors leads to different dispersions, allowing for a very sophisticated tuning of the SW transport. A disentangle- ment of the dipole–dipole and exchange contributions so far was not reported for the SW transport in nanotubes. Furthermore, we propose a device based on coplanar waveguides that would allow to selectively measure the exchange or dipole induced SW nonreciprocities. In the context of magnonic applications, our results might encourage further developments in the emerging field of 3D magnonic devices using curved magnetic membranes.

Magnetization switching using in-plane charge current recently has been widely investigated in heavy metal/ferromagnet bilayers with the switching mechanism usually attributed to the action of the spin-orbit coupling. Here we study in-plane current induced magnetization switching in model epitaxial bilayers that consist of Au(001) and Fe(001) grown on MgO(001). We use the planar Hall effect combined with magnetooptical Kerr effect (MOKE) microscopy to investigate magnetic properties of the bilayers and current-induced switching. We show that a current density beyond 1.4×10^7 A/cm can be employed for reproducible electrical switching of the magnetization between multiple stable states that correspond to different arrangements of magnetic domains with magnetization direction along one of the in-plane easy magnetization axes of the Fe(001) film. Lower current densities result in stable intermediate transversal resistances which are interpreted based on MOKE-microscopy investigations as resulting from the current-induced magnetic domain structure that is formed in the area of the Hall cross. We find that the physical mechanism of the current-induced magnetization switching of the Au/Fe/MgO(001) system at room temperature can be fully explained by the Oersted field, which is generated by the charge current flowing mostly through the Au layer.

We investigate the evolution of spin polarization, spontaneous Hall angle (SHA), saturation magnetization and Curie temperature of B2-ordered Fe60Al40 thin films under varying antisite disorder, induced by Ne+-ion irradiation. The spin polarization increases monotonically as a function of ion fluence. A relatively high polarization of 46 % and the SHA of 3.1 % are achieved on 40 nm thick films irradiated with 2 ⋅ 1016 ions/cm2 at 30 keV. An interesting divergence in the trends of the magnetization and SHA is observed for low disorder concentrations. The high spin polarization and its broad tunability range make ion-irradiated Fe60Al40 a promising material for application in spin electronic devices.

We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally invariant along the waveguide. Our method is based on the propagating-wave dynamic-matrix approach by Henry et al. and extends it to arbitrary cross sections using a finite-element method. We solve the linearized equation of motion of the magnetization only in a single waveguide cross section which drastically reduces computational effort compared to common three-dimensional micromagnetic simulations. In order to numerically obtain the dipolar potential of individual spin-wave modes, we present a plane-wave version of the hybrid finite-element/boundary-element method by Frekdin and Koehler which, for the first time, we extend to a modified version of the Poisson equation. Our method is applied to several important examples of magnonic waveguides including systems with surface curvature, such as magnetic nanotubes, where the curvature leads to an asymmetric spin-wave dispersion. In all cases, the validity of our approach is confirmed by other methods. Our method is of particular interest for the study of curvature-induced or magnetochiral effects on spin-wave transport but also serves as an efficient tool to investigate standard magnonic problems.

We investigate the temporal response of constriction-based spin Hall nano-oscillators driven by pulsed stimuli using time-resolved Brillouin light scattering microscopy. The growth rate of the magnetization auto-oscillations, enabled by spin Hall effect and spin orbit torque, is found to vary with the amplitude of the input voltage pulses, as well as the synchronization frequency set by an external microwave input. The combination of voltage and microwave pulses allows to generate auto-oscillation signals with multi-level amplitude and frequency in the time-domain. Our findings suggest that the lead time of processes such as synchronization and logic using spin Hall nano-oscillators can be reduced to the nanosecond time-scale.

Thin ferromagnetic [Co/Pt] multilayers with perpendicular magnetic anisotropy exhibit a variety of nanoscopic magnetic domain patternsat remanence, from long interlaced stripes to lattices of bubbles, depending on the multilayer structure but also on the magnetic historyof the sample. For optimized structural parameters, stripe-bubble transitions accompanied by drastic increases in domain density havebeen observed when the magnitude of the previously applied perpendicular fieldHmis finely tuned throughout the hysteresis loop. Here, we investigate the robustness of these morphological transitions against field sequencing and field cycling. We conducted this study on[Co(x)/Pt(7Å)]N=50where x varies from 4 to 60 Å. We mapped the morphological transition withHmvarying from 0 to 9 T, following bothan ascending sequence (0→9 T) and a descending sequence (9 T→0). We found that the optimal fieldHm=H∗at which the domain densityis maximized and its associated maximal density n∗ are not significantly affected by the field sequencing direction. We have also investigatedpossible pumping effects when cycling the applied field at the value H∗. We found that n∗ remains relatively stable through field cycling, andmuch more stable in the bubble state, compared to longer stripe states. The observed robustness of these morphological transitions againstfield sequencing and field cycling is of crucial importance for potential magnetic recording applications.

The phenomenon of magnetic resonance and its detection via microwave spectroscopy provide direct insight into the magnetization dynamics of bulk or thin film materials. This allows for direct access to fundamental properties, such as the effective magnetization, g-factor, magnetic anisotropy and the various damping (relaxation) channels that govern the decay of magnetic excitations. Cavity-based and broadband ferromagnetic resonance techniques that detect the microwave absorption of spin systems require a minimum magnetic volume to obtain a sufficient signal-to-noise ratio (S/N). Therefore, conventional techniques typically do not offer the sensitivity to detect individual micro- or nanostructures. A solution to this sensitivity problem is the so-called planar microresonator, which is able to detect even the tiniest absorption signals of magnetic nanostructures, including spin-wave or edge resonance modes. As an example, we describe the microresonator-based detection of spin-wave modes within microscopic strips of ferromagnetic A2 Fe60Al40 that are imprinted into a paramagnetic B2 Fe60Al40-matrix via focused ion-beam irradiation. While microresonators operate at a fixed microwave frequency, a reliable quantification of the key magnetic parameters like the g-factor or spin relaxation times requires investigations within a broad range of frequencies. In this study, we introduce and describe the step from microresonators towards a broadband microantenna approach. It allows for performing broadband magnetic resonance experiments on single nanostructured magnetic objects in a frequency range of 2-18 GHz. We employ this detection scheme to explore the influence of lateral structuring on the magnetization dynamics of a Permalloy strip.

We use vector Hamiltonian formalism (VHF) to study theoretically three-magnon parametric interaction (or three-wave splitting) in a magnetic disk existing in a magnetic vortex ground state. The three-wave splitting in a disk is found to obey two selection rules: (i) conservation of the total azimuthal number of the resultant spin-wave modes, and (ii) inequality for the radial numbers of interacting modes, if the mode directly excited by the driving field is radially symmetric (i.e. if the azimuthal number of the directly excited mode is m=0). The selection rule (ii), however, is relaxed in the "small" magnetic disks, due to the influence of the vortex core. We also found, that the efficiency of the three-wave interaction of the directly excited mode strongly depends on the azimuthal and radial mode numbers of the resultant modes, that becomes determinative in the case when several splitting channels (several pairs of resultant modes) simultaneously approximately satisfy the resonance condition for the splitting. The good agreement of the VHF analytic calculations with the experiment and micromagnetic simulations proves the capability of the VHF formalism to predict the actual splitting channels and the magnitudes of the driving field thresholds for the three-wave splitting.

Magnonics is a rather young physics research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. After several papers and review articles published in the last decade, with a steadily increase in the number of citations, we are presenting the first Roadmap on Magnonics. This a collection of 22 sections written by leading experts in this field who review and discuss the current status but also present their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and the interconnections to standard electronics. In this respect, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This Roadmap represents a milestone for future emerging research directions in magnonics and hopefully it will be followed by a series of articles on the same topic.

Antiferromagnets (AFMs) with zero net magnetization are proposed as active elements in future spintronic devices. Depending on the critical thickness of the AFM thin films and the measurement temperature, bimetallic Mn-based alloys and transition metal oxide-based AFMs can host various coexisting ordered, disordered, and frustrated AFM phases. Such coexisting phases in the exchange coupled ferromagnetic (FM)/AFM-based heterostructures can result in unusual magnetic and magnetotransport phenomena. Here, we integrate chemically disordered AFM γ-IrMn3 thin films with coexisting AFM phases into complex exchange coupled MgO(001)/γ-Ni3Fe/γ-IrMn3/γ-Ni3Fe/CoO heterostructures and study the structural, magnetic, and magnetotransport properties in various magnetic field cooling states. In particular, we unveil the impact of rotating the relative orientation of the disordered and reversible AFM moments with respect to the irreversible AFM moments on the magnetic and magnetoresistance properties of the exchange coupled heterostructures. We further found that the persistence of AFM grains with thermally disordered and reversible AFM order is crucial for achieving highly tunable magnetic properties and multi-level magnetoresistance states. We anticipate that the introduced approach and the heterostructure architecture can be utilized in future spintronic devices to manipulate the thermally disordered and reversible AFM order at the nanoscale.

We present a frequency and magnetic field dependent investigation of ordered arrangements of 20 nm mag-netic nanoparticles (MNPs) consisting of magnetite (Fe3O4) by employing micro Brillouin light scatteringmicroscopy. We utilized electron beam lithography to prepare hexagonally arranged, circularly shaped MNP-assemblies consisting of a single layer of MNPs using a variant of the Langmuir-Blodgett technique. Bycomparing the results with non-structured, layered superlattices of MNPs, further insight into the influenceof size and geometry of the arrangement on the collective properties is obtained. We show that at low staticexternal field strengths, two signals occur in frequency dependent measurements for both non-structured andstructured assemblies. Enlarging the static external field strength leads to a sharpening of the main signal,while the satellite signal decreases in its intensity and increases in its linewidth. The occurrence of multiplesignals at low external field strengths is also confirmed by sweeping the static external field and keeping theexcitation frequency constant. Micromagnetic simulations unravel the origin of the different signals and theirdependence on the static external field strength, enabling an interpretation of the observed characteristics interms of different local environments of an MNPs forming the MNP assembly.

Artificial spin ices are periodic arrangements of interacting nanomagnets that have been successfully used to investigate emergent phenomena in the presence of geometric frustration. Recently, it has become clear that artificial spin ices equally have the potential to be used as building blocks for creating functional materials, such as magnonic crystals and ratchets, in addition to supporting a large number of programmable magnetic states. In this context, we investigate the magnetization dynamics in a system exhibiting asymmetric magnetostatic interactions owing to locally broken structural symmetry. We find that this gives rise to a rich spectrum that can be tuned through an external field. We also determine the evolution of the observed excitation modes, starting with building blocks and evolving into larger arrays, highlighting the role of symmetry breaking in defining the mode spectrum of the system. Concurrently, the increasing complexity of the spectrum leads to the existence of a large number of modes over a narrow range of frequencies. These results contribute to the understanding of magnetization dynamics in spin ice systems beyond the kagome and square ice geometries with a view towards the realization of reconfigurable magnonic crystals based on spin ices.

The spontaneous magnetic orders arising in ferro-, ferri- and antiferromagnets stem from various magnetic interactions. Depending on the interplay and competition among the Heisenberg exchange interaction, Dzyaloshinskii-Moriya exchange interaction, magnetic dipolar interaction and crystal anisotropies, a great variety of magnetic textures may be stabilized, such as magnetic domain walls, vortices, Skyrmions and spiral helical structures. While each of these spin textures responds to external forces in a specific manner with characteristic resonance frequencies, they also interact with magnons, the fundamental collective excitation of the magnetic order, which can propagate in magnetic materials free of charge transport and therefore with low energy dissipation. Recent theories and experiments found that the interplay between spin waves and magnetic textures is particularly interesting and rich in physics. In this review, we introduce and discuss the theoretical framework of magnons living on a magnetic texture background, as well as recent experimental progress in the manipulation of magnons via magnetic textures. The flexibility and reconfigurability of magnetic textures are discussed regarding the potential for applications in information processing schemes based on magnons.

We present an experimental study of time refraction of spin waves propagating in microscopic waveguides under the influence of time-varying magnetic fields. Using space- and time-resolved Brillouin light scattering microscopy, we demonstrate that the broken translational symmetry along the time coordinate can be used to in- or decrease the energy of spin waves during their propagation. This allows for a broadband and controllable shift of the spin-wave frequency. Using an integrated design of spin-wave waveguide and microscopic current line for the generation of strong, nanosecond-long, magnetic field pulses, a conversion efficiency up to 39% of the carrier spin-wave frequency is achieved, significantly larger compared to photonic systems. Given the strength of the magnetic field pulses and its strong impact on the spin-wave dispersion relation, the effect of time refraction can be quantified on a length scale comparable to the spin-wave wavelength. Furthermore, we utilize time refraction to excite spin-wave bursts with pulse durations in the nanosecond range and a frequency shift depending on the pulse polarity.

We present a numerical approach to obtain the Ferromagnetic Resonance (FMR) spectra of micrometer- and nano-sized magnetic elements by micromagnetic simulations. Mimicking common experimental conditions, a static magnetic field is applied and a linearly polarized oscillating magnetic field is used to excite magnetization dynamics. A continuous single-frequency excitation is utilized, which permits to study the steady-state dynamics in space- and time-domain. This gives direct access to resonance fields, line widths and relative amplitudes as observed in the experiments, which is not easily accessible in pulsed schemes and allows for a one-to-one identification between simulation and experiment. Similar to numerical approaches using pulsed excitations the phases, ellipticity and spatial mode profiles of the spin-wave excitations may also be accessed. Using large excitation powers we then showcase that one can additionally study nonlinear responses by this method such as the nonlinear shift of the resonance fields and the fold-over of the absorption lines. Since the dynamic susceptibility is directly determined from standard outputs of common micromagnetic codes, the presented method is robust, efficient and easy-to-use, adding to its practical importance.

We report the use of optically addressable spin qubits in SiC to probe the static magnetic stray fields generated by a ferromagnetic microstructure lithographically patterned on the surface of a SiC crystal. The stray fields cause shifts in the resonance frequency of the spin centers. The spin resonance is driven by a micrometer-sized microwave antenna patterned adjacent to the magnetic element. The patterning of the antenna is done to ensure that the driving microwave fields are delivered locally and more efficiently compared to conventional, millimeter-sized circuits. A clear difference in the resonance frequency of the spin centers in SiC is observed at various distances to the magnetic element, for two different magnetic states. Our results offer a wafer-scale platform to develop hybrid magnon-quantum applications by deploying local microwave fields and the stray field landscape at the micrometer lengthscale.

Topological spin textures such as skyrmions, merons, and vortices in antiferromagnetic (AFM)/ ferromagnetic (FM) materials are actively explored for utilization in future data storage and signal processing devices. An emergent half-integer spin texture such as a magnetic vortex can be stabilized in a soft magnetic NiFe disk structure. Due to the topological nature, the unwinding of the magnetic vortex phase is mediated by the dynamic creation and subsequent annihilation of magnetic singularities, such as Bloch points. This process enables the formation of intermediate topological phases such as vortex-antivortex (V-AV) pairs and edge states. Interfacial interactions between an AFM and a topologically non-trivial spin structure of a FM can stabilize and extend the lifetime of V-AV phases, which are typically considered intrinsic and dynamic are imaged using high-resolution in-field magnetic force microscopy. Additionally, these interactions are used to protect the emerged chirality in an otherwise degenerate chiral spin system, rather than to introduce a preferred chirality.

The understanding of how spins move at pico- and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data storage. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.6 THz. This allows us to evince that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

Long-range spin transport in magnetic systems can be achieved by means of exchange-mediated spin textures with robust topological winding - a phenomenon referred to as spin superfluidity. Its experimental signatures have been discussed in antiferromagnets which are nearly free of dipolar interaction. In ferromagnets, which present with non-negligible dipole fields, however, realization of such spin transport has remained a challenge. Using micromagnetic simulations, we investigate exchange-mediated spin transport in extended thin ferromagnetic films. We uncover a two-fluidstate, in which the long-range spin transport by spin textures co-exists with and is stabilized by spin waves, as well as a soliton-screened spin transport regime at high spin injection biases. Both states are associated with distinct spin texture reconstructions near the spin injection region and sustain spin transport over large distances.