Magnonics is a research field that has gained an increasing interest in both the fundamental and applied sciences in recent years. This field aims to explore and functionalize collective spin excitations in magnetically ordered materials for modern information technologies, sensing applications and advanced computational schemes. Spin waves, also known as magnons, carry spin angular momenta that allow for the transmission, storage and processing of information without moving charges. In integrated circuits, magnons enable on-chip data processing at ultrahigh frequencies without the Joule heating, which currently limits clock frequencies in conventional data processors to a few GHz. Recent developments in the field indicate that functional magnonic building blocks for in-memory computation, neural networks and Ising machines are within reach. At the same time, the miniaturization of magnonic circuits advances continuously as the synergy of materials science, electrical engineering and nanotechnology allows for novel on-chip excitation and detection schemes. Such circuits can already enable magnon wavelengths of 50 nm at microwave frequencies in a 5G frequency band. Research into non-charge-based technologies is urgently needed in view of the rapid growth of machine learning and artificial intelligence applications, which consume substantial energy when implemented on conventional data processing units. In its first part, the 2024 Magnonics Roadmap provides an update on the recent developments and achievements in the field of nano-magnonics while defining its future avenues and challenges. In its second part, the Roadmap addresses the rapidly growing research endeavors on hybrid structures and magnonics-enabled quantum engineering. We anticipate that these directions will continue to attract researchers to the field and, in addition to showcasing intriguing science, will enable unprecedented functionalities that enhance the efficiency of alternative information technologies and computational schemes.

We demonstrate the nonlinear generation of spin-wave edge modes with half the frequency of the applied oscillating field in a Co25Fe75 ferro- magnetic stripe through micromagnetic simulations and experiments. The generation of half-frequency modes depends on the simultaneous presence of resonances near both the driving frequency and the half-frequency in different regions of the material. The half-frequency genera- tion occurs in a system that is thin enough that typical three-magnon decay would not be allowed in a ferromagnetic resonance experiment in an extended film. We find that a limited range of driving frequencies will produce a half-frequency for a given set of system parameters. This range can be tuned by the strength of the oscillating field and the strength of the static external field. Our experimental results agree well with the findings from the simulations.

Time-resolved x-ray microscopy is used in a low-alpha synchrotron operation mode to image spin dynamics at an unprecedented combination of temporal and spatial resolution. Thereby, nanoscale spin waves with wavelengths down to 70 nm and frequencies up to 30 GHz are directly observed in ferromagnetic thin film microelements with spin vortex ground states. In an antiparallel ferromagnetic bilayer system, we detect the propagation
of both optic and acoustic modes; the latter exhibiting even a strong non-reciprocity. In single layer systems, quasi-uniform spin waves are observed together with modes of higher order (up to the 4th order), bearing precessional nodes over the thickness of the film. Furthermore, the effects from magnetic material properties, film thickness and magnetic fields on the spin-wave spectrum are experimentally determined. Our experimental results were found to be consistent with those from numerically solving an analytic micromagnetic theory even on these so-far unexplored time- and length scales.

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow a suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by utilizing wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Non-reciprocal wave propagation arises in systems with broken time-reversal symmetry and is key to the functionality of devices, such as isolators or circulators, in microwave, photonic and acoustic applications. In magnetic systems, collective wave excitations known as magnon quasiparticles so far yielded moderate non-reciprocities, mainly observed by means of incoherent thermal magnon spectra, while their occurrence as coherent spin waves (magnon ensembles with identical phase) is yet to be demonstrated. Here, we report the direct observation of strongly non-reciprocal propagating coherent spin waves in a patterned element of a ferromagnetic bilayer stack with antiparallel magnetic orientations. We use time-resolved scanning transmission x-ray microscopy (TR-STXM) to directly image the layer-collective dynamics of spin waves with wavelengths ranging from 5 µm down to 100 nm emergent at frequencies between 500 MHz and 5 GHz. The experimentally observed non-reciprocity factor of these counter-propagating waves is greater than 10 with respect to both group velocities and specific wavelengths. Our experimental findings are supported by the results from an analytic theory and their peculiarities are further discussed in terms of caustic spin-wave focusing.

The efficient excitation of spin waves is a key challenge in the realization of magnonic devices. We demonstrate the current-driven generation of spin waves in antiferromagnetically coupled magnetic vortices. We employ time-resolved scanning transmission X-ray microscopy (TR-STXM) to directly image the emission of spin waves upon the application of an alternating current flowing directly through the magnetic stack. Micromagnetic simulations allow us to identify the origin of the excitation to be the current-driven Oersted field, which in the present system proves to be orders of magnitude more efficient than the commonly used excitation via stripline antennas. Our numerical studies also reveal that the spin-transfer torque can lead to the emission of spin waves as well, yet only at much higher current amplitudes. By using magnetostrictive materials, we futhermore demonstrate that the direction of the magnon propagation can be steered by increasing the excitation amplitude, which modifies the underlying magnetization profile through an additional anisotropy in the magnetic layers. The demonstrated methods allow for the efficient and tunable excitation of spin waves, marking a significant advance in the generation and control of spin waves in magnonic devices.

Soft magnetic dots in the form of thin rings have unique topological properties. They can be in a vortex state with no vortex core. Here, we study the magnon modes of such systems both analytically and numerically. In an external magnetic field, magnetic rings are characterized by easy-cone magnetization and shows a giant splitting of doublets for modes with the opposite value of the azimuthal mode quantum number. The effect of the splitting can be refereed as a magnon analog of the topology-induced Aharonov-Bohm effect. For this we develop an analytical theory to describe the non-monotonic dependence of the mode frequencies on the azimuthal mode number, influenced by the balance between the local exchange and non-local dipole interactions.

We use a pure spin current originating from the spin Hall effect to generate a spin-orbit torque strongly reducing the effective damping in an adjacent ferromagnet. Because of additional microwave excitation, large spin-wave amplitudes are achieved exceeding the threshold for four-magnon scattering, thus resulting in additional spin-wave signals at discrete frequencies. Two or more modes are generated below and above the directly pumped mode with equal frequency spacing. It is shown how this nonlinear process can be controlled in magnonic waveguides by the applied dc current and the microwave pumping power. The sudden onset of the nonlinear effect after exceeding the thresholds can be interpreted as a spiking phenomenon, which makes the effect potentially interesting for neuromorphic computing applications. Moreover, we investigated this effect under microwave frequency and external field variation. The appearance of the additional modes was investigated in the time domain, revealing a time delay between the directly excited and the simultaneously generated nonlinear modes. Furthermore, spatially resolved measurements show different spatial decay lengths of the directly pumped mode and nonlinear modes.

We present an experimental and numerical study of three-magnon splitting in a micrometer-sized magnetic disk with the vortex state strongly deformed by static in-plane magnetic fields. Excited with a large enough power at frequency fRF, the primary radial magnon modes of a cylindrical magnetic vortex can decay into secondary azimuthal modes via spontaneous three-magnon splitting. This nonlinear process exhibits selection rules leading to well-defined and distinct frequencies fRF/2±Δf of the secondary modes. Here, we demonstrate that three-magnon splitting in vortices can be significantly modified by deforming the magnetic vortex with in-plane magnetic fields, leading to a much richer three-magnon response. We find that, with increasing field, an additional class of secondary modes is excited which are localized to the highly-flexed regions adjacent to the displaced vortex core. While these modes satisfy the same selection rules of three-magnon splitting, they exhibit a much lower three-magnon threshold power compared to regular secondary modes of a centered vortex. The applied static magnetic fields are small (≃ 10 mT), providing an effective parameter to control the nonlinear spectral response of confined vortices. Our work expands the understanding of nonlinear magnon dynamics in vortices and advertises these for potential neuromorphic applications based on magnons.

1D spin-wave conduits are envisioned as nanoscale components of magnonics-based logic and computing schemes for future generation electronics. A-la-carte methods of versatile control of the local magnetization dynamics in such nanochannels are highly desired for efficient steering of the spin waves in magnonic devices. Here, we present a study of localized dynamical modes in 1-$\mu$m-wide Permalloy conduits probed by microresonator ferromagnetic resonance technique. We clearly observe the lowest-energy edge mode in the microstrip after its edges were finely trimmed by means of focused Ne+ ion irradiation. Furthermore, after milling the microstrip along its long axis by focused ion beams, creating consecutively ~50 and ~100 nm gaps, additional resonances emerge and are attributed to modes localized at the inner edges of the separated strips. To visualize the mode distribution, spatially resolved Brillouin light scattering microscopy was used showing an excellent agreement with the ferromagnetic resonance data and confirming the mode localization at the outer/inner edges of the strips depending on the magnitude of the applied magnetic field. Micromagnetic simulations confirm that the lowest-energy modes are localized within $\sim$15-nm-wide regions at the edges of the strips and their frequencies can be tuned in a wide range (up to 5 GHz) by changing the magnetostatic coupling (i.e. spatial separation) between the microstrips.

We investigate the frequency non-reciprocity in CoFeB/Ru/CoFeB synthetic antiferromagnets near the spin-flop transition region, where the magnetic moments in the two ferromagnetic layers are non-collinear. Using conventional Brillouin light scattering, we perform systematic measurements of the frequency non-reciprocity as a function of an external magnetic field. For the antiparallel alignment of the magnetic moments in the two layers, we observe a significant frequency non-reciprocity of up to a few GHz, which vanishes when the relative magnetization orientation switches into the parallel configuration at saturation. A non-monotonous dependence of the frequency non-reciprocity is found in the region where the system transitions from the antiparallel to the parallel orientation, with a maximum frequency shift around the spin-flop critical point. This non-trivial dependence of the non-reciprocity is attributed to the non-monotonous dependence of the dynamic dipolar interaction, which is the main factor that causes asymmetry in the dispersion relation. Furthermore, we found that the sign of the frequency shift changes even without switching the polarity of the bias field. These results show that one can precisely control the non-reciprocal propagation of spin waves via field-driven magnetization reorientation.

Magnons are elementary excitations in magnetic materials and undergo nonlinear multimode scattering processes at large input powers. In experiments and simulations, we show that the interaction between magnon modes of a confined magnetic vortex can be harnessed for pattern recognition. We study the magnetic response to signals comprising sine wave pulses with frequencies corresponding to radial mode excitations. Three-magnon scattering results in the excitation of different azimuthal modes, whose amplitudes depend strongly on the input sequences. We show that recognition rates above 95\% can be attained for four-symbol sequences using the scattered modes, with strong performance maintained with the presence of amplitude noise in the inputs.

Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of current challenges and the outlook of further development for each research direction.

A broken interfacial inversion symmetry in ultrathin ferromagnet/heavy metal (FM/HM) bilayers is generally believed to be a prerequisite for accommodating Dzyaloshinskii-Moriya interaction (DMI) and for stabilizing chiral spin textures. By contrast, we present an approach for engineering both the sign and amplitude of DMI in relatively thick films without involving interfacial asymmetry, which is achieved through incorporating the composition gradient-induced bulk magnetic asymmetry (BMA) combined with strong spin-orbit coupling (SOC). The pivotal roles of BMA and SOC are theoretically examined based on the three-site Fert-Lévy model and the first principles calculations. Experimentally, both the sign and amplitude of DMI in films with controllable composition gradients along the growth direction, in the presence/absence of SOC are studied by using a Brillouin light scattering spectroscopy. Our results suggest that the appreciable value of DMI (±0.15 mJ/m2) could be established through combining BMA and SOC into relatively thick films. It is expected that our findings may help to further understand chiral magnetism and to design novel non-collinear spin textures.

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

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.

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.

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.

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.

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.

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 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.

Spin waves have the potential to be used as a next-generation platform for data transfer and processing as they can reach wavelengths in the nanometer range and frequencies in the terahertz range. To realize a spin-wave device, it is essential to be able to manipulate the amplitude as well as the phase of spin waves. Several theoretical and recent experimental works have also shown that the spin-wave phase can be manipulated by the transmission through a domain wall (DW). Here, we study propagation of spin waves through a DW by means of micro-focused Brillouin light scattering microscopy (μBLS). The 2D spin-wave intensity maps reveal that spin-wave transmission through a Néel DW is influenced by a topologically enforced circular Bloch line in the DW center and that the propagation regime depends on the spin-wave frequency. In the first regime, two spin-wave beams propagating around the circular Bloch line are formed, whereas in the second regime, spin waves propagate in a single central beam through the circular Bloch line. Phase-resolved μBLS measurements reveal a phase shift upon transmission through the domain wall for both regimes. Micromagnetic modeling of the transmitted spin waves unveils a distortion of their phase fronts, which needs to be taken into account when interpreting the measurements and designing potential devices. Moreover, we show that, by means of micromagnetic simulations, an external magnetic field can be used to move the circular Bloch line within the DW and to manipulate spin-wave propagation.
The authors thank R. Schäfer and O. Fruchart for the discussions on the DW classification.
This research was supported by the CEITEC Nano+ project (No. CZ.02.1.01/0.0/0.0/16013/0001728) and Austrian Science Fund (FWF) project I1937. M. Staňo acknowledges support by the ESF under the project CZ.02.2.69/0.0/0.0/19_074/0016239. CzechNanoLab project LM2018110 funded by MEYS CR is gratefully acknowledged for the financial support of the measurement and sample fabrication at the CEITEC Nano Research Infrastructure.

Metastable face-centered-cubic Fe78Ni22 thin films are excellent candidates for focused ion beam direct writing of magnonic structures due to their favorable magnetic properties after ion-beam-induced transformation. The focused ion beam transforms the originally nonmagnetic fcc phase into the ferromagnetic bcc phase with additional control over the direction of uniaxial magnetic in-plane anisotropy and saturation magnetization. Local magnetic anisotropy direction control eliminates the need for external magnetic fields, paving the way towards complex magnonic circuits with waveguides pointing in different directions. In the present study, we show that the magnetocrystalline anisotropy in transformed areas is strong enough to stabilize the magnetization in the direction perpendicular to the long axis of narrow waveguides. Therefore, it is possible to propagate spin waves in these waveguides in the favorable Damon-Eshbach geometry without the presence of any external magnetic field. Phase-resolved microfocused Brillouin light scattering yields the dispersion relation of these waveguides in zero as well as in nonzero external magnetic fields.

We present a combined numerical, theoretical and experimental study on stimulated three-magnon splitting in a magnetic disk in the vortex equilibrium state. Our micromagnetic simulations and Brillouin-light-scattering results confirm that three-magnon splitting can be triggered even below threshold by exciting one of the secondary modes by magnons propagating in a waveguide next to the disk. The experiments show that stimulation is possible over an extended range of excitation powers and a wide range of frequencies around the eigenfrequencies of the secondary modes. Rate-equation calculations predict an instantaneous response to stimulation and the possibility to prematurely trigger three-magnon splitting even above threshold in a sustainable manner. These predictions are confirmed experimentally using time-resolved Brillouin-light-scattering measurements and are in a good qualitative agreement with the theoretical results. We believe that the controllable mechanism of stimulated three-magnon splitting could provide a possibility to utilize magnon-based nonlinear networks as hardware for reservoir or neuromorphic computing.

We report on the impact of nonlinear four-magnon scattering on magnon transport in microstructured waveguides with low magnetic damping. Using microfocused Brillouin light scattering, we analyze magnon propagation lengths in a broad range of excitation powers and observe a decrease of the attenuation length at high powers, which is consistent with the onset of nonlinear four-magnon scattering. Hence, when measuring magnon propagation lengths and deriving damping parameters from those results, one needs to be careful to stay in the linear regime. Otherwise, the intrinsic nonlinearity of magnetization dynamics may lead to a misinterpretation of magnon propagation lengths and, thus, to wrong values of the magnetic damping of the system.

We demonstrate a novel type of spin Hall nano-oscillators (SHNOs) that allow for efficient tuning of magnetic auto-oscillations over an extended range of gigahertz frequencies, using bipolar direct currents at constant magnetic fields. This is achieved by stacking two distinct magnetic materials with a platinum layer in between. In this device, the orientation of the spin polarised electrons accumulated at the top and bottom interfaces of platinum is switched upon changing the polarity of the direct current. As a result, the effective anti-damping required to drive large amplitude auto-oscillations can appear either at the top or bottom magnetic layer. Tuning of the auto-oscillation frequencies by several gigahertz can be obtained by combining two materials with suffciently different saturation magnetization. Here we show that the combination of NiFe and CoFeB can result in 3 GHz shifts in the auto-oscillation frequencies. Bipolar SHNOs as such may bring enhanced synchronisation capabilities to neuromorphic applications.

Modern spectroscopic techniques for the investigation of magnetization dynamics in micro- and nano- structures or thin films use mostly microwave antennas which are directly fabricated on the sample by means of electron-beam-lithography (EBL). Following this approach, every magnetic structure on the sample needs its own antenna, resulting in additional EBL steps and layer deposition processes. We demonstrate a new device for magnetization excitation that is suitable for optical and non-optical spectroscopic techniques. By patterning the antenna on a separated flexible glass cantilever and insulating it electrically, we solved the be- fore mentioned issues. Since we use flexible transparent glass as a substrate, optical spectroscopic techniques like Brillouin-light-scattering microscopy (μBLS), time resolved magneto-optical Kerr effect measurements (TRMOKE) or optical detected magnetic resonance (ODMR) measurements can be performed at visible laser wavelengths. As the antenna is detached from the sample it can be freely positioned in all three dimensions to get access to all desired magnetic sample structures, while being brought in close contact with the sample for an effective excitation. We show the functionality of these antennas using μBLS. We compare with thermally excited magnons to show the enhancement of the signal by a factor of about 400 demonstrating the high impact of the magnetization excitation by the antenna. Moreover, we show the possibility to characterize yttrium iron garnet thin films by doing optical ferromagnetic resonance (FMR) experiments allowing for the characterization of magnetic properties spatially resolved. Additionally, we show the spatial excitation profile of the antenna by measuring the magnetization dynamics in two dimensions. Furthermore, injection-locking of spin Hall nano-oscillators could be shown.

Non-collinear antiferromagnets are revealing many unexpected phenomena and they became crucial for the field of antiferromagnetic spintronics. To visualize and prepare a well-defined domain structure is of key importance. The spatial magnetic contrast, however, remains extraordinary difficult to be observed experimentally. Here, we demonstrate a magnetic imaging technique based on a laser induced local thermal gradient combined with detection of the anomalous Nernst effect. We employ this method in one the most actively studied representative of this class of materials - Mn₃Sn. We undoubtedly proof that the observed contrast is of magnetic origin. We further show an algorithm to prepare a well defined domain pattern at room temperature based on heat assisted recording principle. Our study opens a prospect to study spintronics phenomena in non-collinear antiferromagnets with spatial resolution.

The magnetization dynamics of individual Fe-filled multiwall carbon-nanotubes (FeCNT), grown by chemical vapor deposition, are investigated by microresonator ferromagnetic resonance (FMR) and Brillouin light scattering (BLS) microscopy and corroborated by micromagnetic simulations. Up to now, only static magnetometry measurements are available. They suggest that the FeCNTs consist of a single-crystalline Fe nanowire throughout the length. The number and structure of the FMR lines and the abrupt decay of the spin-wave transport seen in BLS indicate, however that the Fe filling is not a single straight piece along the length. Therefore a stepwise cutting procedure was applied in order to investigate the evolution of the ferromagnetic resonance lines as a function of the nanowire length. Our results show that the FeCNT is indeed not homogeneous along the full length but is built from 300-400 nm long single-crystalline segments. These segments consist of magnetically high quality Fe nanowires with almost the bulk values of Fe and with a similar small damping in relation to thin films, promoting the FeCNTs as appealing candidates for spin-wave transport in magnonic applications.

We report ultra-low intrinsic magnetic damping in Co25Fe75 heterostructures, reaching the low 10E−4 regime at room temperature. By using a broadband ferromagnetic resonance technique, we extracted the dynamic magnetic properties of several Co25Fe75-based heterostructures with varying ferromagnetic layer thickness. By estimating the eddy current contribution to damping, measuring radiative damping and spin pumping effects, we extrapolated an intrinsic damping of α0 ≤ 3.05 × 10E−4. Furthermore, using Brillouin light scattering microscopy we measured spin-wave propagation lengths of up to (21 ± 1) μm in a 26 nm thick Co25 Fe75 heterostructure at room temperature, which is in excellent agreement with the measured damping.

Bulk and patterned ferromagnets can exhibit various nonlinear phenomena at moderate excitation power, making them a nice test bed for study of nonlinear dynamics. We investigate nonlinear ferromagnetic resonance in magnetic nanostructures with discrete spectra of spin-wave modes in the case of allowed 3-magnon scattering processes. These processes result in the splitting of a directly driven spin-wave mode into two secondary modes if a certain excitation threshold is overcome. The 3-magnon splitting manifests itself as a characteristic distortion of the resonance curve, which can be detected in a simple ferromagnetic resonance experiment. Theoretical results are also compared to the experimental study of nonlinear spin-wave dynamics in a vortex-state magnetic disk, in which 3-magnon splitting is confirmed by direct measurements using Brillouin light scattering microscopy.

We demonstrate a combined frequency and time domain investigation of injection-locked, constriction-based spin Hall nano-oscillators by Brillouin light scattering (BLS) and time-resolved magneto-optical Kerr effect (TR-MOKE). This was achieved by applying an alternating current in the GHz regime in addition to the direct current which drives auto-oscillations in the constriction. In the frequency domain, we analyze the width of the locking range, the increase in intensity and reduction in linewidth as a function of the applied direct current. Then we show that the injection locking of the auto-oscillation allows for its investigation by TR-MOKE measurements, a stroboscopic technique that relies on a phase stable excitation, in this case given by the synchronisation to the microwave current. Field sweeps at different direct currents clearly demonstrate the impact of the spin current on the Kerr amplitude. Two-dimensional TR-MOKE and BLS maps show a strong localization of the auto-oscillation within the constriction, independent of the external locking.

In the last decade, two revolutionary concepts in nanomagnetism emerged from research for storage technologies and advanced information processing. The first suggests the use of magnetic domain walls in ferromagnetic nanowires to permanently store information in domain-wall racetrack memories. The second proposes a hardware realization of neuromorphic computing in nanomagnets using nonlinear magnetic oscillations in the gigahertz range. Both ideas originate from the transfer of angular momentum from conduction electrons to localized spins in ferromagnets, either to push data encoded in domain walls along nanowires or to sustain magnetic oscillations in artificial neurones. Even though both concepts share a common ground, they live on very different timescales which rendered them incompatible so far. Here, we bridge both ideas by demonstrating the excitation of magnetic auto-oscillations inside nanoscale domain walls using pure spin currents. This Letter will shed light on the current characteristic and spatial distribution of the excited auto-oscillations.

We present the generation of whispering gallery magnons with unprecedented high wave vectors via nonlinear 3-magnon scattering in a μm-sized magnetic vortex state disc. These modes exhibit a strong localisation at the perimeter of the disc and practically zero amplitude in an extended area around the vortex core. They originate from the splitting of the fundamental radial magnon modes, which can be resonantly excited in a vortex texture by an out-of-plane microwave field. We shed light on the basics of this non-linear scattering mechanism from experimental and theoretical point of view. Using Brillouin light scattering (BLS) microscopy, we investigated the frequency and power dependence of the 3-magnon splitting. The spatially resolved mode
profiles give evidence for the localisation at the boundaries of the disc and allow for a direct determination of the modes wavenumber.

Spin Hall oscillators (SHO) are promising candidates for the generation, detection and amplification of high frequency signals, that are tunable through a wide range of operating frequencies. They offer to be read out electrically, magnetically and optically in combination with a simple bilayer design. Here, we experimentally study the spatial dependence and spectral properties of auto-oscillations in SHO devices based on Pt(7 nm)/ Ni80Fe20(5nm) tapered nanowires. Using Brillouin light scattering microscopy, we observe two individual self- localized spin-wave bullets that oscillate at two distinct frequencies (5.2 GHz and 5.45 GHz) and are localized at different positions separated by about 750 nm within the SHO. This state of a tapered SHO has been predicted by a Ginzburg-Landau auto-oscillator model, but not yet been directly confirmed experimentally. We demonstrate that the observed bullets can be individually synchronized to external microwave signals, leading to a frequency entrainment, linewidth reduction and increase in oscillation amplitude for the bullet that is selected by the microwave frequency. At the same time, the amplitude of other parasitic modes decreases, which promotes the single-mode operation of the SHO. Finally, the synchronization of the spin-wave bullets is studied as a function of the microwave power. We believe that our findings promote the realization of extended spin Hall oscillators accomodating several distinct spin-wave bullets, that jointly cover an extended range of tunability.

The curvature of a magnetic membrane was presented as a means of inducing nonreciprocities in the spin-wave (SW) dispersion relation [see Otalora et al. Phys. Rev. Lett. 117, 227203 (2017) and Otalora et al. Phys. Rev. B 95, 184415 (2017)], thereby expanding the toolbox for controlling SWs. In this paper, we further complement this toolbox by analytically showing that the membrane curvature is also manifested in the absorption of SWs, leading to a difference in the frequency linewidth (or lifetime) of counterpropagating magnons. Herein, we studied the nanotubular case, predicting changes of approximately greater than 10% and up to 20% in the frequency linewidth of counterpropagating SWs for a wide range of nanotube radii ranging from 30 nm to 260 nm and with a thickness of 10 nm. These percentages are comparable to those that can be extracted from experiments on heavy metal/magnetic metal sandwiches, wherein linewidth asymmetry results from an interfacial Dzyaloshinskii-Moriya interaction (DMI). We also show that the interplay between the frequency linewidth and group velocity leads to asymmetries in the SW decay length, presenting changes between 10% and 22% for counterpropagating SWs in the frequency range of 2-10 GHz. For the case of the SW dispersion relation, the predicted effects are identified as the classical dipole-dipole interaction, and the analytical expression of the frequency linewidth has the same mathematical form as in thin films with the DMI. Furthermore, we present limiting cases of a tubular geometry with negligible curvature such that our analytical model converges to the case of a planar thin film known from the literature. Our findings represent a step forward toward the realization of three-dimensional curvilinear magnonic devices.

We study the correlation between the magnetic reversal and the anisotropic magnetoresistance (AMR) response in magnetic hybrid structures that were created by local modification of magnetic properties induced by ion implantation. The stripe pattern have been investigated simultaneously by dual-wavelength Kerr microscopy and magnetoresistance measurements. We observe that the switching of the stripe pattern introduces an additional AMR maximum. The domain wall in between the stripes provides a positive resistance contribution, whereas domains at the stripe edges lead to an asymmetric AMR response. A method for calculating the AMR response from the quantitative Kerr micrographs is demonstrated that allows the reconstruction of the AMR value within a region of interest only.

The reciprocity of spin-wave propagation in 180° Néel walls and surrounding domains is studied. For this, the dispersion relation, phase fronts and spin-wave intensities are analyzed via micromagnetic simulations. Despite the in-plane curling of the magnetization, the domain wall itself acts as a reciprocal channel, whereas non-reciprocal spin-wave propagation is found within the domains. Since the spin-wave localization depends on the selected frequency, this may allow to control the degree of propagation asymmetry.

Spin waves (SW) are the excitation of the spin system in a ferromagnetic condensed matter body. They are collective excitations of the electron system and, from a quasi-classical point of view, can be understood as a coherent precession of the electrons' spins. Analogous to photons, they are also referred to as magnons indicating their quasi-particle character. The collective nature of SWs is established by the short-range exchange interaction as well as the non-local magnetic dipolar interaction, resulting in coherence of SWs from mesoscopic to even macroscopic length scales. As one consequence of this collective interaction, SWs are 'charge current free' and, therefore, less subject to dissipation caused by scattering with impurities on the atomic level. This is a clear advantage over diffusive transport in spintronics that not only uses the charge of an electron but also its spin degree of freedom. Any (spin) current naturally involves motion and, thus, scattering of electrons leading to excessive heating as well as losses. This renders SWs a promising alternative to electric (spin) currents for the transport of spin information—one of the grand challenges of condensed matter physics.

We present a detailed analytical derivation of the spin wave (SW) dispersion relation in magnetic nanotubes with magnetization along the azimuthal direction. The obtained formula can be used to calculate the dispersion relation for any longitudinal and azimuthal mode. The obtained dispersion is asymmetric for all azimuthal modes traveling along the axial direction. As reported in our recent publication [Phys. Rev. Lett. 117, 227203 (2016)], the asymmetry is a curvature-induced effect originating from the dipole-dipole interaction. Here, we discuss the asymmetry of the dispersion for azimuthal modes by analyzing the SW asymmetry deltaf (kz) = fn(kz) − fn(−kz), where fn(kz) is the eigenfrequency of a magnon with a longitudinal and azimuthal wave vectors, kz and n, respectively; and the dependence of the maximum asymmetry with the nanotube radius R. The analytical results are in perfect agreement with micromagnetic simulations. Furthermore, we show that the dispersion relation simplifies to the thin-film dispersion relation with in-plane magnetization when analyzing the three limiting cases: (i) kz = 0, (ii) kz>>1/R, and (iii) kz<<1/R. In the first case, for the zeroth-order modes the thin-film Kittel formula is obtained. For modeswith higher order the dispersion relation for the Backward-Volume geometry is recovered. In the second case, for the zeroth-order mode the exchange dominated dispersion relation for SW in Damon-Esbach configuration is obtained. For the case kz<<1/R, we find that the dispersion relation can be reduced to a formula similar to the Kalinikos-Slavin [J. Phys. C: Sol. State Phys. 19, 7013 (1986)] type.

Erstmals konnten Forscher experimentell das Brechungsgesetz für Spinwellen direkt nachweisen.

In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates, and good packaging in magnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asymmetric regarding the sign of the wave vector. It is a purely curvature-induced effect and its fundamental origin is identified to be the classical dipole-dipole interaction. The analytical expression of the dispersion relation has the same mathematical form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore, this curvatureinduced effect can be seen as a “dipole-induced Dzyalonshiinsky-Moriya-like” effect.

In the research field of magnonics, it is envisaged that spin waves will be used as information carriers, promoting operation based on their wave properties. However, the field still faces major challenges. To become fully competitive, novel schemes for energy-efficient control of spin-wave propagation in two dimensions have to be realized on much smaller length scales than used before. In this Letter, we address these challenges with the experimental realization of a novel approach to guide spin waves in reconfigurable, nano-sized magnonic waveguides. For this purpose, we make use of two inherent characteristics of magnetism: the non-volatility of magnetic remanence states and the nanometre dimensions of domain walls formed within these magnetic configurations. We present the experi- mental observation and micromagnetic simulations of spin- wave propagation inside nano-sized domain walls and realize a first step towards a reconfigurable domain-wall-based magnonic nanocircuitry.

In this work, high-resolution gamma-ray computed tomography (HireCT) was applied for the first time on a viscous coupling to visualize the internal operating fluid distribution. The HireCT measurement system comprises a 137Cs isotopic source and a gamma-ray detector arc operated in single photon counting mode and is able to produce cross-sectional images of dense objects with a spatial resolution of about 2 mm. To scan fast rotating parts rotation-synchronized CT scanning mode was employed in these experiments. The analyzed viscous coupling (Visco® clutch of MAHLE Behr) mainly consists of a driven primary disc and a secondary housing with an engine cooling fan mounted on it and is assembled within an experimental rig. The viscous coupling’s primary and secondary parts are axially assembled and a coupling liquid is pumped into engaged radial ring profiles to provide a defined torque transfer. The internal ring channel width, where the coupling liquid is to be observed, is considerably lower than one millimeter. Although the HireCT measurement system is not able to resolve these micro-channels, the coupling liquid can be successfully visualized via its contrast. Investigations have been performed at different filling levels corresponding to different transmission slips of the test coupling. Moreover, both radial and tangential liquid distributions for different operational steady states could be determined. The obtained experimental data were compared to results from computational fluid dynamics (CFD) simulations in some operating points and are in good agreement.

Spin waves constitute an important part of research in the field of magnetization dynamics. Spin waves are the elementary excitations of the spin system in a magnetically ordered material state and magnons are their quasi particles. In the following article, we will discuss the optical method of Brillouin light scattering (BLS) spectroscopy which is a now a well established tool for the characterization of spin waves. BLS is the inelastic scattering of light from spin waves and confers several benefits: the ability to map the spin wave intensity distribution with spatial resolution and high sensitivity as well as the potential to simultaneously measure the frequency and the wave vector and, therefore, the dispersion properties.

For several decades, the field of spin waves gained huge interest by the scientific community due to its relevance regarding fundamental issues of spindynamics in the field of solid states physics. The ongoing research in recent years has put emphasis on the high potential of spin waves regarding information technology. In the emerging field of \textit{magnonics}, several concepts for a spin-wave based logic have been proposed and realized. Opposed to charge-based schemes in conventional electronics and spintronics, magnons are charge-free currents of angular momentum, and, therefore, less subject to scattering processes that lead to heating and dissipation. This fact is highlighted by the possibility to utilize spin waves as information carriers in electrically insulating materials. These developments have propelled the quest for ways and mechanisms to guide and manipulate spin-wave transport. In particular, a lot of effort is put into the miniaturization of spin-wave waveguides and the excitation of spin waves in structures with sub-micrometer dimensions.

For the further development of potential spin-wave-based devices, the ability to directly observe spin-wave propagation with spatial resolution is crucial. As an optical technique BLS does not only allow to map the spin-wave intensity in general, but it, in particular, enables the realization of sub-micron space resolution. Focusing of the laser beam to a sub-micrometer spot size can be realized by implementing a microscope objective into the optical setup. Over the last decade, this micro-focus BLS technique has become an established method for the investigation of spin waves in microstructured magnetic elements and proved its value in particular regarding magnonics.

In this article, we will discuss the basic principles of the BLS process and illustrate the experimental optical setup. Particular emphasis will be put on the implementation of the high spatial resolution of the BLS microscope and the consequences this has for the experimental realization. In addition, the outline of a computer based operation principle and automated sample positioning will be given. Owing to these improvements in ease of use as well as experimental applicability, the BLS technique has maintained its relevance for investigations of today's research on spin waves in miniaturized magnetic structures. A selection of experiments in this field will be described.

Magnetic interactions give rise to a surprising amount of complexity due to the fact that both static and dynamic magnetic properties are governed by competing short-range exchange interactions and long-range dipolar coupling. Even though the underlying dynamical equations are well established, the connection of magnetization dynamics to other degrees of freedom, such as optical excitations, charge and heat flow, or mechanical motion, make magnetism a mesoscale research problem that is still wide open for exploration. Synthesizing magnetic materials and heterostructures with tailored properties will allow to take advantage of magnetic interactions spanning many length-scales, which can be probed with advanced spectroscopy and microscopy and modeled with multi-scale simulations. This review highlights some of the current basic research topics in mesoscale magnetism, which beyond their fundamental science impact are also expected to influence applications ranging from information technologies to magnetism based energy conversion.

Magnetization reversal processes were investigated in iron-aluminum (Fe60Al40) alloy films of 40 nm thickness by employing magnetometry and magnetic domain imaging using magneto-optical longitudinal and polar effects. The films were initially chemically ordered and weakly ferromagnetic, and a large increase in the saturation magnetization was induced due to disorder magnetization induced by Ne+-ion irradiation. Three different sample geometries were investigated; a) continuous film; b) homogenously irradiated wire; and c) magnetic stripe-patterned wire. Specific magnetization reversal mechanism were identified for the different sample geometries.

Recent developments in the field of spin dynamics—like the interaction of charge and heat currents with magnons, the quasi-particles of spin waves—opens the perspective for novel information processing concepts and potential applications purely based on magnons without the need of charge transport. The challenges related to the realization of advanced concepts are the spin-wave transport in two-dimensional structures and the transfer of existing demonstrators to the micro- or even nanoscale. Here we present the experimental realization of a microstructured spin-wave multiplexer as a fundamental building block of a magnon-based logic. Our concept relies on the generation of local Oersted fields to control the magnetization configuration as well as the spin-wave dispersion relation to steer the spin-wave propagation in a Y-shaped structure. Thus, the present work illustrates unique features of magnonic transport as well as their possible utilization for potential technical applications.

We demonstrate all-optical magnetic switching (AOS) in an amorphous Tb30Fe70 thin film, triggered by a 5.1 MHz laser oscillator. The magnetic layer is grown on a SiO2/Si substrate. An identical magnetic film deposited on a microscope glass slide shows no AOS and only exhibits thermally induced demagnetization. This effect is due to heat accumulation by multiple laser pulses because of the low thermal conductivity of the glass substrate. In contrast, the use of a proper heat sink (e.g. SiO2/Si) abolishes need for low repetitive laser amplifier systems to induce AOS and paves the way for a cheap and easy to use technological implementation with conventional laser oscillators.