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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 techno

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.

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.

Over the past few decades, extensive research has been conducted on magnetic vortices due to their fundamental physical properties and potential applications as magnetic storage devices or resonators. Information can be encoded in the polarity or gyrotropic motion of the vortex core. Moreover, magnetic vortices offer a versatile spectrum of radial and azimuthal magnon modes, which exhibit interesting linear and nonlinear dynamics. One notable example is three-magnon splitting, where one mode can spontaneously split into two secondary magnon modes when excited above a threshold power. Three-magnon splitting follows specific selection rules, with the split modes having distinct frequencies and mode numbers to fulfill energy and angular momentum conservation [1]. Magnetic vortices offer the potential to stimulate these processes below their intrinsic threshold powers [2, 3], making them promising candidates for novel computing approaches such as reservoir computing. In this study, we demonstrate that the application of in-plane magnetic fields in the order of a few mT can efficiently modify three-magnon splitting [4]. Using micromagntic simulations and Brillouin-light-scattering microscopy, we show that the deformation of the vortex results in additional secondary butterfly modes that follow the same selection rules as the regular modes but exhibit different localization and much lower three-magnon splitting threshold powers. [1] K. Schultheiss et al. PRL 122, 097202 (2019) [2] L. Körber et al. PRL 125, 207203 (2020) [3] L. Körber et al. arXiv 2211.02328 (2022) [4] L. Körber et al. APL 122, 092401 (2023)

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.

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or simply consume too much energy. Moreover, conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, which uses the nonlinearity and recurrence of a physical system to separate patterns of time series data into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized NiFe discs [1] which we learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al. Physical Review Letters 122, 097202 (2019) [2] L. Körber, et al. Physical Review Letters 125, 207203 (2020)

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or simply consume too much energy. Moreover, conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, which uses the nonlinearity and recurrence of a physical system to separate patterns of time series data into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized NiFe discs [1] which we learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al. Physical Review Letters 122, 097202 (2019) [2] L. Körber, et al. Physical Review Letters 125, 207203 (2020)

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or simply consume too much energy. Moreover, conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, which uses the nonlinearity and recurrence of a physical system to separate patterns of time series data into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized NiFe discs [1] which we learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al. Physical Review Letters 122, 097202 (2019) [2] L. Körber, et al. Physical Review Letters 125, 207203 (2020)

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or simply consume too much energy. Moreover, conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, which uses the nonlinearity and recurrence of a physical system to separate patterns of time series data into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized NiFe discs [1] which we learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al. Physical Review Letters 122, 097202 (2019) [2] L. Körber, et al. Physical Review Letters 125, 207203 (2020)

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.

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or simply consume too much energy. Moreover, conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, which uses the nonlinearity and recurrence of a physical system to separate patterns of time series data into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized NiFe discs [1] which we learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al. Physical Review Letters 122, 097202 (2019) [2] L. Körber, et al. Physical Review Letters 125, 207203 (2020)

Conventional electronics use the flow of electric charges and are based on standard semiconductors. Spintronic devices exploit the electrons’ spin to generate and control currents and to combine electric and magnetic signals. Today there is a strong effort worldwide to integrate spintronic devices with standard CMOS technology towards hybrid spin-CMOS chips, offering advantages in terms of power consumption, compactness, and speed. Recent results (from SAMSUNG [1], TSMC [2], etc.) confirm the merit of this approach.

This data publication contains the numerical and experimental data for our paper "Modification of three-magnon splitting in a flexed magnetic vortex" submitted to Applied Physics Letters. The data contains mumax3 recipes, field- and power-dependent frequency spectra and spatial mode profiles of spin waves in a ferromagnetic disk in the vortex state. All files are sorted according to the figures in which they appear in the paper.

This data publication contains the data for our publication "Pattern recognition in reciprocal space with a magnon-scattering reservoir" published in Nature Communications. The dataset is structured in folders corresponding to the different figures in the paper. Folder Fig2 and Fig2 contain the experimental data measured with Brillouin-light-scattering microscopy. The files contain the data integrated for the measurement positions described in the methods section in a csv format. Forlder Fig4 contains the evaluated numerical data presented in the corresponding figure. The raw data generated with micromagnetic simulations is too large for this dataset and is available upon request by the authors.

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.

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

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or are simply to energy consuming. Moreover, it is accepted commonly that conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, where the nonlinear response of a physical system is used to separate patterns hidden in a temporal data stream into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized Permalloy discs [1] which we also learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without actually relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al., Physical Review Letters 125, 207203 (2020) [2] K. Schultheiss, et al., Physical Review Letters 122, 097202 (2019)

Within the last decade, spintronics and magnonics have demonstrated an impressive development in the experimental realization of Boolean logic gates. However, the exponential growth of data and the rise of the internet of things are pushing the deterministic Boolean computing of von-Neumann architectures to their limits or are simply to energy consuming. Moreover, it is accepted commonly that conventional Boolean computer architectures are likely to remain inefficient for certain cognitive tasks in which the human brain excels, such as pattern recognition, particularly when incomplete or noisy data are involved. One of the most generic and abstract implementations of brain-inspired computing schemes is reservoir computing, where the nonlinear response of a physical system is used to separate patterns hidden in a temporal data stream into distinct manifolds of a higher dimensional output space. In this presentation, I will demonstrate the experimental realization of pattern recognition based on reservoir computing using magnons. Recently, we reported on the nonlinear scattering of magnons in vortices in micron-sized Permalloy discs [1] which we also learned to control and stimulate by means of other magnons [2]. Now, we utilize these phenomena to employ magnons for pattern recognition without actually relying on magnon transport in real space. I will present a comprehensive overview of experimental results and numerical simulations demonstrating the capabilities and advantages of magnon reservoir computing in reciprocal space. [1] K. Schultheiss, et al., Physical Review Letters 125, 207203 (2020) [2] K. Schultheiss, et al., Physical Review Letters 122, 097202 (2019)

Data were obtained by means of Brillouin light scattering microscopy, micro magnetic simulations in MuMax3 and analytic calculations.

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

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

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 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.

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 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.

Since the 80’s, when Brillouin light scattering emerged as a powerful tool for investigating magnetization dynamics in thin films and multilayers, it developed into a versatile microscopic probe for studying collective spin excitations. Following a short introduction on studies of millimeter-sized films, we will give examples how to investigate individual magnetic structures down to tens of nanometers in dimension. We will introduce the concepts of time- and phase-resolved Brillouin light scattering which give full access to the spatio-temporal evolution of the optically accessible spin-wave spectrum. During our talk, we will provide hands-on demonstrations how to drive spin waves via spin currents and microwave excitations in magnetic nanostructures using the build in dc/ac probe station in our laboratory and show the capabilities of Brillouin light scattering for quantifying spin-wave phenomena. Furthermore, we will highlight similarities and differences to other optical scanning probe techniques such as time-resolved magneto-optical Kerr microscopy and optically detected magnetic resonance based on vacancy centers. We will outline how those techniques can potentially be combined with Brillouin light scattering to access complementary information.

This repository contains the data used to determine the numerical threshold fields for three-magnon scattering in a vortex-state disk used in our paper "Theory of three-magnon interaction in a vortex-state magnetic nanodot" published in Physical Review B.  For different excitation frequencies, we provide: mumax3 simulation file and table containing the time-dependent magnetic energy for simulations where the microwave-field power is decreased over time mumax3 file and resulting power spectrum for a continuous-wave excitation at a given microwave-field power above threshold spatial mode profiles (magnitude/amplitude) to identify the modes taking part in the three-magnon splitting channel

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

One of the fascinating qualities of spin waves (or magnons), which are the elementary excitations in magnetically ordered substances, is their nonlinear behavior at moder- ate excitation powers. This makes spin waves not only an attractive model system to study general nonlinear systems, but it also provides a way to utilize nonlinear dynamics in possible technical applications. In a ferromagnetic nano disk which is magnetized in the vortex state, the spin-wave modes meet strict boundary conditions and therefore inherit a discrete spectrum. When driven with a large enough excitation field, they can decay into other spin-wave modes within well-defined channels due to a nonlinear process called three-magnon scattering [1]. The aim of this project is to explore this phenomenon within nonlinear spin-wave theory and by means of micromagnetic simulations. For this purpose, first the linear dynamics are mapped out and the possible scattering channels are predicted. The stability of these channels with respect to static external fields is studied. Within this context, exotic spin-wave modes which arise in a broken cylindrical symmetry are found. Moreover, a model to predict the temporal evolution of the spin-wave modes is developed within the classical Hamiltonian formalism for nonlinear spin-wave dynamics. Together with micromagnetic simulations, this model is applied in order to study the power-dependence of three-magnon scattering as well as to uncover a phenomenon called stimulated three-magnon scattering, which may allow for an integration of this nonlinear pro- cess in magnonics circuits. The results are compared with Brillouin light-scattering experiments which were conducted prior to this thesis or were motivated by it. Financial support of within DFG programme SCHU 2922/1-1 and KA 5069/1-1 is acknowledged.

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 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 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.

One of the fascinating qualities of spin waves (or magnons), which are the elementary excitations in magnetically ordered substances, is their nonlinear behavior at moder- ate excitation powers. This makes spin waves not only an attractive model system to study general nonlinear systems, but it also provides a way to utilize nonlinear dynamics in possible technical applications. In a ferromagnetic nano disk which is magnetized in the vortex state, the spin-wave modes meet strict boundary conditions and therefore inherit a discrete spectrum. When driven with a large enough excitation field, they can decay into other spin-wave modes within well-defined channels due to a nonlinear process called three-magnon scattering [1]. The aim of this project is to explore this phenomenon within nonlinear spin-wave theory and by means of micromagnetic simulations. For this purpose, first the linear dynamics are mapped out and the possible scattering channels are predicted. The stability of these channels with respect to static external fields is studied. Within this context, exotic spin-wave modes which arise in a broken cylindrical symmetry are found. Moreover, a model to predict the temporal evolution of the spin-wave modes is developed within the classical Hamiltonian formalism for nonlinear spin-wave dynamics. Together with micromagnetic simulations, this model is applied in order to study the power-dependence of three-magnon scattering as well as to uncover a phenomenon called stimulated three-magnon scattering, which may allow for an integration of this nonlinear pro- cess in magnonics circuits. The results are compared with Brillouin light-scattering experiments which were conducted prior to this thesis or were motivated by it. Financial support of within DFG programme SCHU 2922/1-1 and KA 5069/1-1 is acknowledged.

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 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 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. Here, we briefly describe how the archived data for the publication "Nonlocal stimulation of three-magnon splitting in a magnetic vortex", submitted to PRL, is structured. "rate-equations" - theoretical data of the temporal evolution of the spin wave modes in Fig. 4 "micromagnetic-simulation" - MuMax3 simulation recipes (.go files) and sample-layout masks for the simulations performed for Fig. 2(a,b,c). - corresponding power spectra obtained with our "mumax3-pwsp" program - mode profiles for stimulated and spontaneous splitting (Fig. 1(c) and Fig. 2(d)) - dispersion of the spin waves, calculated by micromagetnic simulation, shown in Fig. 1(b) "experiments" - electron beam microscopy image of the sample - intensity spectrum of

We utilized the following methods in order to obtain the presented data: micro focused Brilluoin light scattering (BLS), micromagnetic simulations in MuMax3 and micro focused magneto-optical Kerr effect (MOKE). The experimental data were obtained on the sample which is labeled with: 'CoFe_WMI_6'. On that sample, we investigated the structures 'E1' and 'F1' which are essentially rectangular stripes (5 micrometer x 65 micrometer, thickness: 30 nm) out of Co25Fe75 alloy. The metadata for all measurements (including ALL parameters) are included in the uploaded primary data subdirectories. The references to the directory of the measured data within our local IT infrastructure are given along with the files themselves. All scripts that were used for data analysis (in Python) are included as well with a short description.

When applying a large enough RF field amplitude, spin waves in a magnetic vortex disk can decay into two other spin waves via three-magnon scattering. In order to reach the threshold of this process, the energy flux from the decay of the directly excited mode must overcome the internal losses of the secondary modes. The resulting scattering processes obey certain selection rules which result in the two output frequencies to be distinct from one another. Moreover, three-magnon scattering of the directly excited mode into multiple pairs of secondary modes is possible. However, typically one of these scattering channels has a lower threshold than the others which leads to this channel being activated first and limiting the energy flux in the other possible “silent” channels. Here, we show that three-magnon scattering in such a system can be stimulated below the usual instability threshold by additionaly pumping one of the secondary modes. This is achieved by coupling the magnetic vortex to an adjacent magnonic wave guide. The response to the stimulation is instantaneous and can be used to activate the silent three-magnon channels, as well.

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.

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.

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.

When applying a large enough RF field amplitude, spin waves in a magnetic vortex disk can decay into two other spin waves via three-magnon scattering. In order to reach the threshold of this process, the energy flux from the decay of the directly excited mode must overcome the internal losses of the secondary modes. The resulting scattering processes obey certain selection rules which result in the two output frequencies to be distinct from one another. Moreover, three-magnon scattering of the directly excited mode into multiple pairs of secondary modes is possible. However, typically one of these scattering channels has a lower threshold than the others which leads to this channel being activated first and limiting the energy flux in the other possible “silent” channels. Here, we show that three-magnon scattering in such a system can be stimulated below the usual instability threshold by additionaly pumping one of the secondary modes. This is achieved by coupling the magnetic vortex to an adjacent magnonic wave guide. The response to the stimulation is instantaneous and can be used to activate the silent three-magnon channels, as well.