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.

A possibility for surface magnon–plasmon–polaritons (SMPPs)–coupled microwave oscillations of magnetization, electron density, and electromagnetic field–to exist in real ferromagnetic metal–insulator–ideal non-magnetic metal structures has been analyzed theoretically. The developed theory predicts that the effective formation of SMPPs is possible only at certain values of the external dc magnetic field and must be accompanied by a shift in the characteristic frequency of the resonance plasmon-polariton systems. A theoretical estimation of the frequency shift for SMPPs in the structure “surface electromagnetic wave resonator made of permalloy–vacuum–ideal metal” gives a value of ±45 MHz for a resonator with a characteristic frequency of 10 GHz, which seems sufficient for this effect to be observed experimentally.

Droplet solitons are strongly nonlinear, dynamic structures in ferromagnets with perpendicular magnetic anisotropy. For experimental observation of such structures a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping is utilized. We analyze eigenmode of this droplet excitations in a simplest case of conservative droplet solitons, when both Gilbert damping in magnetic films and energy gain due to spin-polarized current can be neglected. As a result of such analysis eigenmode frequencies of conservative droplet are obtained. Among main features of conservative droplet eigenmode is azimuthal degeneration of mods and localization of mode frequencies in a finite region. (C) 2017 Elsevier B.V. All rights reserved.

The damping of spin waves parametrically excited in the magnetic insulator Yttrium Iron Garnet (YIG) is controlled by a dc current passed through an adjacent normal-metal film. The experiment is performed on a macroscopically sized YIG(100 nm)/Pt(10 nm) bilayer of 4 × 2 mm2 lateral dimensions. The spin-wave relaxation frequency is determined via the threshold of the parametric instability measured by Brillouin light scattering spectroscopy. The application of a dc current to the Pt film leads to the formation of a spin-polarized electron current normal to the film plane due to the spin Hall effect. This spin current exerts a spin transfer torque in the YIG film and, thus, changes the spin-wave damping. Depending on the polarity of the applied dc current with respect to the magnetization direction, the damping can be increased or decreased. The magnitude of its variation is proportional to the applied current. A variation in the relaxation frequency of ±7.5% is achieved for an applied dc current density of 5 × 1010 A/m2.

Magnetization reversal in finite chains and square arrays of closely packed cylindrical magnetic dots, having vortex ground state in the absence of the external bias field, has been studied experimentally by measuring static hysteresis loops, and also analyzed theoretically. It has been shown that the field Bn of a vortex nucleation in a dot as a function of the finite number N of dots in the array's side may exhibit a monotonic or an oscillatory behavior depending on the array geometry and the direction of the external bias magnetic field. The oscillations in the dependence Bn(N) are shown to be caused by the quantization of the collective soft spin wave mode, which corresponds to the vortex nucleation in a finite array of dots. These oscillations are directly related to the form and symmetry of the dispersion law of the soft SW mode: the oscillation could appear only if the minimum of the soft mode spectrum is not located at any of the symmetric points inside the first Brillouin zone of the array's lattice. Thus, the purely static measurements of the hysteresis loops in finite arrays of coupled magnetic dots can yield important information about the properties of the collective spin wave excitations in these arrays.

Thermalization of a parametrically driven magnon gas leading to the formation of a Bose-Einstein condensate at the bottom of a spin-wave spectrum was studied by time- and wavevector-resolved Brillouin light scattering spectroscopy. It has been found that the condensation is preceded by the conversion of initially pumped magnons into a second group of frequency degenerated magnons, which appear due to parametrically stimulated scattering of the initial magnons to a short-wavelength spectral region. In contrast to the first magnon group, which wavevectors are orthogonal to the wavevectors of the magnons at the lowest energy states, the secondary magnons can effectively scatter to the bottom of the spectrum and condense there.

Abstract This chapter discusses the room-temperature kinetics and thermodynamics of the magnon gas in yttrium iron garnet films driven by a parametric microwave pumping. It shows that for high enough pumping powers, the thermalization of the driven gas results in a quasi-equilibrium state described by the Bose–Einstein statistics with a non-zero chemical potential. Further increase of the pumping power causes a Bose–Einstein condensation documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the Brillouin light scattering spectroscopy to the coherence degree of the scattering magnons, the chapter demonstrates the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, which occurs if their density exceeds a critical value.

When the in-plane bias magnetic field acting on a flat circular magnetic dot is smaller than the saturation field, there are two stable competing magnetization configurations of the dot: the vortex and the quasi-uniform (C-state). We measured microwave absorption properties in an array of non-interacting permalloy dots in the frequency range 1–8 GHz when the in-plane bias magnetic field was varied in the region of the dot magnetization state bi-stability. We found that the microwave absorption properties in the vortex and quasi-uniform stable states are substantially different, so that switching between these states in a fixed bias field can be used for the development of reconfigurable microwave magnetic materials.

Processes that take place in permalloy nanodots under external electromagnetic pumping are considered. It is shown that in such system similar to bulk samples Suhl and kinetic instability processes are possible. Using micromagnetic simulations approach key features of mode excitation with an external pumping power increase were revealed. Results of the simulations were compared with published experimental data dedicated to investigation of magnetic nanodotes in nonlinear regime.

We present spatially resolved measurements of the magnon temperature in a magnetic insulator subject to a thermal gradient. Our data reveal an unexpectedly close correspondence between the spatial dependencies of the exchange magnon and phonon temperatures. These results indicate that if--as is currently thought--the transverse spin Seebeck effect is caused by a temperature difference between the magnon and phonon baths, it must be the case that the magnon temperature is spectrally nonuniform and that the effect is driven by the sparsely populated dipolar region of the magnon spectrum.

The time evolution of the ferromagnetic resonance output signal in the arrays of permalloy circular dots of submicron sizes was measured near the critical fields of the vortex nucleation and annihilation. Surprisingly short times of the transition from the quasiuniform to the vortex magnetization state (several milliseconds) were detected. The observed effects are explained by overcoming the field dependent energy barriers in the process of vortex core nucleation. The energy barrier values found from the time dependences of the ferromagnetic resonance peak intensities were compared with the ones calculated within the rigid vortex model. The rigid vortex model overestimates the nucleation barriers and a more adequate magnetization reversal model is needed. There is a strong dependence of the stable, metastable energy minima and energy barriers on the magnetic field and dot geometrical parameters.

Microwave emission from a parametrically pumped ferrimagnetic film of yttrium iron garnet was studied versus the magnon density evolution, which was detected by Brillouin light scattering spectroscopy. It has been found that the shutdown of external microwave pumping leads to an unexpected effect: The conventional monotonic decrease of the population of parametrically injected magnons is accompanied by an explosive behavior of electromagnetic radiation at the magnon frequency. The developed theory shows that this explosion is caused by a nonlinear energy transfer from parametrically driven short-wavelength dipolar-exchange magnons to a long-wavelength dipolar magnon mode effectively coupled to an electromagnetic wave.

It is known that the spin-transfer torque (STT) effect in magnetic multilayers, theoretically predicted in [1, 2] and experimentally observed in [3-13], provides a new method of manipulation of magnetization in nanoscale objects [14]: magnetization switching [3, 4] and generation of microwave oscillations under the action of a dc electric current [5-11]. According to the STT effect bias dc current traversing magnetic multilayers can transfer angular magnetic moments from one layer to another, which can give rise to the microwave dynamics of magnetization in the layer [1-11]. However, it is clear that an inverse effect is also possible. This inverse effect leads to the so-called spin-torque diode effect [12-13], first originally observed experimentally in 2005. It can be used for the development of practical microwave detectors, so called spin-torque microwave detectors (STMD), and also for quantitatively measuring STT [15, 16].

Nonlinear ferromagnetic resonance (NFMR) at the nanoscale differs from the same phenomenon in bulk magnetic samples due to the nanosize-related discreteness of the spin wave spectrum. Because of the spectrum discreteness, the conservation laws for multiwave parametric interaction processes cannot be fulfilled exactly and become nonresonant. The presence of the nonresonant parametric processes in a strongly driven magnetic nanosystem can be detected experimentally as distortions on the NFMR curve caused by the nonresonant excitation of spin wave modes.

A theoretical model describing a strongly excited magnon system in a magnetic nanodot has been developed. In this system, despite the discreteness of its spectrum, the parametric processes similar to those occurring in massive specimens take place, in particular, the processes of Suhl instability. Owing to a slight mismatch between the frequencies of modes that are engaged in the indicated processes, the threshold of the latter becomes somewhat higher and a non-resonant parametric interaction takes place. It is shown that, at certain power levels in the system, the processes similar to those of the so-called kinetic instability observed in massive specimens can emerge to excite the lowest-frequency mode of a nanoelement.

Spin waves are delocalized excitations of magnetic media that mainly determine their magnetic dynamics and thermodynamics at temperatures far below the critical one. The quantum-mechanical counterparts of spin waves are magnons, which can be considered as a gas of weakly interacting bosonic quasi-particles. Here, we discuss the room-temperature kinetics and thermodynamics of the magnon gas in yttrium iron garnet films driven by parametric microwave pumping. We show that for high enough pumping powers, the thermalization of the driven gas results in a quasi-equilibrium state described by Bose–Einstein statistics with a non-zero chemical potential. Further increases of the pumping power cause a Bose–Einstein condensation documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the Brillouin light scattering spectroscopy to the degree of coherence of the scattering magnons, we confirm the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, occurring if their density exceeds a critical value.

A new technique of the correlation processing of data based on the nonlinear interaction of signals of backward volume magnetostatic waves in yttrium-iron garnet thin films and a corresponding laboratory mock-up of the correlation receiver operating in the 6 cm wavelength range have been presented in this paper. It was proposed to use additional pumping pulse for obtaining a time-reversed signal pulse. The resultant correlation signal occurred during the nonlinear interaction of the delayed signal wave and the pumping-reversed wave. The specificity of the passage of broadband signals through the resonance system of waveguide of spin waves was taken into account. It has been found out that the resonance properties of the correlator affect the efficiency of the desired signal separation from the noise level. The resultant signal-to-noise ratio for the output signal was enhanced by more than 20 dB.

It is demonstrated that non-resonant wave front reversal (WFR) of spin-wave pulses caused by pulsed parametric pumping can be effectively used for microwave signal processing. When the frequency band of signal amplification by pumping is narrower than the spectral width of the signal, the non-resonant WFR can be used for the analysis of the signal spectrum. In the opposite case the non-resonant WFR can be used for active (with amplification) filtering of the input signal.

Nonlinear interactions of dipolar and dipole-exchange spin waves with microwave magnetic field of parametric electromagnetic pumping were studied experimentally in thin permalloy (Py) films. It was demonstrated that parametric pumping in Py films leads to efficient amplification of the "trace" of quasistanding spin waves created due to the two-magnon scattering by the input signal pulse of long-wavelength dipolar spin waves and, then, to suppression of the amplified signal due to the parametric excitation of short-wavelength exchange-dominated spin waves. It was, also, shown that nonlinear interactions of spin waves in Py films can be used for the development of microwave signal processing devices and for the measurement of relaxation characteristics of different spin-wave groups.