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, which covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with the Boolean digital data, unconventional approaches, such as neuromorphic computing, and the progress toward magnon-based quantum computing. This 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.

Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing attention from the perspective of novel magnon-based data processing applications. For short wavelengths needed in small-scale devices, the group velocity is directly proportional to the spin-wave exchange stiffness constant $\lambda_\mathrm{ex}$. Using wave vector resolved Brillouin Light Scattering (BLS) spectroscopy, we directly measure $\lambda_\mathrm{ex}$ in Ga-substituted YIG thin films and show that it is about three times larger than for pure YIG. Consequently, the spin-wave group velocity overcomes the one in pure YIG for wavenumbers $k > 4$ rad/$\mu$m, and the ratio between the velocities reaches a constant value of around 3.4 for all $k > 20$ rad/$\mu$m. As revealed by vibrating-sample magnetometry (VSM) and ferromagnetic resonance (FMR) spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert damping ($\alpha < 10^{-3}$), a decreased saturation magnetization $\mu_0 M_\mathrm{S}~\approx~20~$mT and a pronounced out-of-plane uniaxial anisotropy of about $\mu_0 H_{\textrm{u1}} \approx 95 $ mT which leads to an out-of-plane easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport for all wavelengths in nano-scale systems independently of dipolar effects.

Spin-wave dynamics were studied in an extended thin film of single-crystalline yttrium iron garnet using time-resolved scanning transmission x-ray microscopy. A combination of mechanical grinding and focused ion beam milling has been utilized to achieve a soft x-ray transparent thickness of the underlying bulk gadolinium gallium garnet substrate. Damon-Eshbach type spin waves down to about 100 nm wavelength have been directly imaged in real space for varying frequencies and external magnetic fields. The dispersion relation extracted from the experimental data agreed well with theoretical predictions. A significant influence of the ion milling process on the local magnetic properties was not detected.

We investigate the temperature dependent microwave absorption spectrum of an yttrium iron garnet sphere as a function of temperature (5 K to 300 K) and frequency (3 GHz to 43.5 GHz). At temperatures above 100 K, the magnetic resonance linewidth increases linearly with temperature and shows a Gilbert-like linear frequency dependence. At lower temperatures, the temperature dependence of the resonance linewidth at constant external magnetic fields exhibits a characteristic peak which coincides with a non-Gilbert-like frequency dependence. The complete temperature and frequency evolution of the linewidth can be modeled by the phenomenology of slowly relaxing rare-earth impurities and either the Kasuya-LeCraw mechanism or the scattering with optical magnons. Furthermore, we extract the temperature dependence of the saturation magnetization, the magnetic anisotropy and the g-factor.

The magnetostatic mode (MSM) spectrum of a 300 μm diameter single crystalline sphere of yttrium iron garnet is investigated using broadband ferromagnetic resonance (FMR). The individual MSMs are identified via their characteristic dispersion relations, and the corresponding mode number tuples (nmr) are assigned. Taking FMR data over a broad frequency and magnetic field range allows one to analyze both the Gilbert damping parameter α and the inhomogeneous line broadening contribution to the total linewidth of the MSMs separately. The linewidth analysis shows that all MSMs share the same Gilbert damping parameter α = 2.7(5) × 10−5 irrespective of their mode index. In contrast, the inhomogeneous line broadening shows a pronounced mode dependence. This observation is modeled in terms of two-magnon scattering processes of the MSMs into the spin-wave manifold, mediated by surface and volume defects.

Measurements of the exchange stiffness D and the exchange constant A of Yttrium Iron Garnet (YIG) films are presented. YIG films with thicknesses from 0.9 to 2.6 mu m were investigated with a microwave setup in a wide frequency range from 5 to 40 GHz. The measurements were performed with the external static magnetic field applied in-plane and out-of-plane. The method of Schreiber and Frait (1996 Phys. Rev. B 54 6473), based on the analysis of the perpendicular standing spin wave mode frequency dependence on the applied out-of-plane magnetic field, was used to obtain the exchange stiffness D. This method was modified to avoid the influence of internal magnetic fields during the determination of the exchange stiffness. Furthermore, the method was also adapted for in-plane measurements. The results obtained using all methods are compared and values of D between (5.18 +/- 0.01). 10(-17) T. m(2) and (5.40 +/- 0.02). 10(-17) T. m(2) were obtained for different thicknesses. From this, the exchange constant was calculated to be A = (3.7 +/- 0.4) pJ.m(-1).

We present an experimental study of spin-wave excitation and propagation in microstructured waveguides consisting of a 100 nm thick yttrium iron garnet/platinum (Pt) bilayer. The life time of the spin waves is found to be more than an order of magnitude higher than in comparably sized metallic structures, despite the fact that the Pt capping enhances the Gilbert damping. Utilizing microfocus Brillouin light scattering spectroscopy, we reveal the spin-wave mode structure for different excitation frequencies. An exponential spin-wave amplitude decay length of 31 μm is observed which is a significant step towards low damping, insulator based micro-magnonics.

Foils filled with conductive and magnetic materials are developed for absorption of microwaves. The foils have a thickness of 0.5 - 1.5 mm and a basic composition of 25 wt.% polyethylene, 9 wt.% carbon, and 66 wt.% inorganic filler of very different nature. The absorbed power is determined from measurements of reflection and transmission with a closed coaxial measuring technique in the frequency range of 40 MHz to 1 GHz. Transmission measurements are carried out from 700 MHz - 18 GHz and 50 - 75 GHz. Foils with thicknesses of about 1 mm absorb more than 30% of the incident power.

Results on an established batch process preparing melt-textured YBCO in high quality and quantity will be reported. We used a standard composition Y1.5Ba2Cu3O7-X + 1 wt% CeO2 without further doping to fabricate single-domain YBCO monoliths in different sizes and shapes (cylindrical, quadratic) as well as rectangular multi-seeded YBCO monoliths. Up to 2-3 kg melt-textured YBCO blocks are grown reproducibly in one box furnace run. Top seeding by self-made SmBCO was improved and rationalized. Optimization of oxygen annealing treatment leads to macro-crack free YBCO monoliths. Each YBCO monolith was characterized by integral levitation force and field mapping. In a single-domain quadratic monolith with an edge length of 38 mm a maximum induction of 1.44 T at 77 K and a distance of 0.5 mm was frozen. The reproducibility of the batch process is guaranteed. Mean maximum induction from 1.1 to 1.2 T at 77 K per batch was reached. A trapped magnetic field of 2.5 T was achieved between two single-domain monoliths in a gap of 1.5 mm at 77 K.Depending on the application function, elements with different sizes, designs and more or less complex geometry are constructed in several working steps by cutting, machining, bonding and passivation. Selected function elements were checked with field mapping at 77 K. Results of our function. elements in HTSC reluctance motors using single-domain material are shown. We will report on a fly-wheel system and a system to levitate persons.

Results on an established batch process preparing melt-textured YBCO of high quality and in large quantities are reported. We used a standard composition Y1.5Ba2Cu3O7-x + 1 wt% CeO2 without further doping to fabricate single domain YBCO monoliths in different sizes and shapes (cylindrical, quadratic) as well as rectangular multi-seeded YBCO monoliths. Up to 2-3 kg of melt-textured YBCO blocks were grown, reproducible in one box furnace run. Top seeding by a self-made SmBCO was improved and rationalized. Optimization of an oxygen annealing treatment led to macro-crack free YBCO monoliths. Each YBCO monolith was characterized by integral levitation force and field mapping. In a single domain, a quadratic monolith with a edge length of 38 mm, a maximum induction of 1.44 T at 77 K and a distance of 0.5 mm was frozen. The reproducibility of the batch process is guaranteed. Mean maximum induction from 1.1 to 1.2 T at 77 K per batch was reached. A trapped magnetic field of 2.5 T was achieved between two single domain monoliths in a gap of 1.5 mm at 77 K.Depending on the application, function elements with different sizes, designs and more or less complex geometry are constructed in several working steps by cutting, machining, bonding and passivation. Selected function elements were checked with field mapping at 77 K. The results of our function elements in HTSC reluctance motors with an output power of up to 200 kW using single domain material are shown. We report on a fly wheel system DYNASTORE and a system to levitate people.

HTSC bulk material which has been developed during the last ten years is now prepared in increasing quantities and used in demonstrators or prototypes of several applications, e.g., flywheels and motors. The quality control of large amounts of samples requires a method which is fast and provides essential information about the sample quality. In particular, the critical current density and its inhomogeneity should be determined. In this contribution we report about a trapped field measurement technique using pulsed field magnetization and field detection by a Hall-array. With this arrangement the required time of measurement is in the order of a few minutes per sample. The software which controls the devices contains also an analyzing procedure for the calculation of an effective critical current density as well as parameters describing the homogeneity of the samples.

Bulk melt-textured High Temperature Superconductors (HTS) can be applied in electric motors, magnetic bearings or other power applications. We prepare melt-textured YBCO in a batch process. Field mapping and levitation force measurements are performed as quality control. Differences between the evidence of these methods can be seen. Trapped fields higher than 1 T at 77 K were achieved in standard material, e.g. cuboids with an edge size of 3.5 cm. We prepare function elements from this material by assembling plates for electric motors, rings for magnetic bearings, or other elements defined by the application. Plates for electric motors up to 200 kW were constructed. Superconducting joining was successfully performed on a superconducting ring.

Function elements can be constructed by cutting, machining and bonding of batch processed melt-textured YBCO. Depending on the application structures with different complex geometry can be fabricated. They consist of several monoliths, e.g. rings, bars and plates, and may be passivated, if necessary. Melt-textured YBCO monoliths with different shape and a maximum size of 60 mm can be reproducible prepared in a batch process. Seeding by self-made SmBa2Cu3Ox leads to single domain material. Zero field cooled levitation forces at 77 K higher than 80 N were achieved. In single domain cylinders with a diameter of 30 mm and in quadratic shaped monoliths with an edge length of 35 mm maximum inductions of 1.3 and 1.2 T are frozen at 77 K. The trapped magnetic field of our function elements, e.g. plates and bars, are checked at 77 K. Results of our function elements in HTSC reluctance motors using single domain material are shown. Also, we will report about a fly wheel system, called “Dynastore” and a system to levitate persons.

Several applications of bulk high temperature superconductors are in discussion at the temperature of liquid hydrogen (21K). Here also MgB2 with its critical temperature of about 38K might be a usable material. In this work we present the preparation of bulk MgB2 and its magnetic properties. Thermal analysis and X-ray investigations on commercial MgB2 and sintered material will be reported. Sintering was performed in air and vacuum. A critical temperature of 37K was determined by ac-susceptibility. Critical current densities of 25.000 A/cm(2) at 10K and the irreversibility fields were obtained by VSM measurements. In addition we present data from high pressure prepared material.

Melt-textured bulk samples of YBa2Cu3O7−δ which have a high potential for magnetic applications are usually characterized by trapped field measurements. In this paper we present a fitting procedure which allows to eliminate the influence of different geometric parameters of the sample and the set-up and to calculate an effective value of the critical current density. A more general fitting procedure allows to calculate the spatial distribution of the critical current density jc.

Melt-textured Y-Ba-Cu-O (YBCO) is prepared in a batch process with reproducible material properties, Functional models of magnetic bearings and electric motors were equipped with this material. From the tests of these models the requirements on further material development can be derived. The quality of a magnetic bearing can be improved by increasing the size of the superconducting domains, The current density should be in the order of 200 - 400 A/mm(2). Reluctance motors with output powers up to 38 kW at 77K were constructed. Further improvements can be achieved using large superconducting domains with higher current density.

In this contribution we present a systematic approach to the calculation of levitation forces in plane-parallel (infinitely extended in one direction) arrangements of permanent magnets and superconductors. Starting from an extremely idealized geometry with a very simple expression for the levitation force, we go step by step to more realistic arrangements and present the corrections in the force equations. In particular, magnet configurations with an increased field gradient which allow a higher stiffness are investigated. Finally, numerical calculations are presented which show the dependance of the levitation force on the size and the critical current density of the superconductor and the effect of magnet-iron combinations instead of magnets without iron. The calculations show that the stiffness can be increased by using magnets which consist of several sections with alternating polarity. However, this improvement can only be used for reduced bearing gaps and increased critical current density. The use of magnet-iron combinations has only little advantages.

Melt-textured yttrium-barium-copper-oxide is suitable for many applications. By testing demonstrators where these elements are used, it can be learned which material properties must be optimized for a specific application field. For example, critical-current density must be increased for use in electric motors. Mechanical properties are very important for trapped-field magnets. Homogeneous properties on large monoliths seem necessary for bearings in fly-wheel systems.