When the density of a quasi-equilibrium gas of Bose quasiparticles, such as, polaritons, excitons, or magnons, increases, a macroscopically populated coherent state, the Bose–Einstein condensate (BEC), can form at the bottom of the quasiparticle spectrum. Considering the BEC of magnons, we analytically found an expression for the additional number of magnons that must be created in a magnetic sample to reach the threshold of BEC. This number is determined by the paraprocess, which reduces the number of thermal magnons as the magnetizing bias field increases, and also by the fact that only long-lived dipole-exchange magnons with wavenumbers smaller than 107cm−1 participate in the formation of the BEC. The general results obtained are applied to two particular cases of magnon BEC formation: by parallel parametric pumping in a ferrimagnetic film and by two-magnon scattering processes in a ferrimagnetic sample with a rough surface.

Coherence time is a key property of quantum systems, determining how long quantum information can be preserved. In solid-state platforms, this parameter is closely linked to the lifetime of quasiparticles that can store quantum information. For decades, magnons - quasiparticles arising from collective magnetization dynamics - have exhibited lifetimes below one microsecond at gigahertz frequencies, limiting their viability as quantum information carriers. Here, we report the discovery of short-wavelength magnons with lifetimes exceeding 18 μs at millikelvin temperatures. The experiment was performed on an ultra-pure single-crystal Yttrium Iron Garnet (YIG) sphere over a wide temperature range, from ambient down to 30 mK. These results directly confirm the theoretical prediction that the magnon lifetime in an ideal YIG crystal at zero temperature is infinite, paving the way for the engineering of lossless magnetic systems in which magnons will be employed as long-lived carriers of information for quantum gates and quantum storage.

Since their prediction by Einstein at the dawn of quantum mechanics, Bose-Einstein condensates (BECs), owing to their property to show quantum phenomena on macroscopic scales, are drawing increasing attention across various fields in physics. They are the subject of many fascinating observations in various physical systems, from liquid helium to diluted atomic gases. In addition to real particles like atoms and composite bosons such as Cooper pairs or excitons, this phenomenon is also observed in gases of quasiparticles such as polaritons and magnons - quanta of spin-wave excitations in magnetic media. The fundamental property of the BEC state is its coherence, which is represented by a precisely defined phase of the corresponding wave function, which arises spontaneously and encompasses all particles gathered at the bottom of their spectrum. Until now, the BEC phase was only revealed in phenomena depending on the spatial phase difference, such as interference, second order coherence, and macroscopic BEC motions - supercurrents, superfluidity and Josephson oscillations. Here, we present a method for the direct time-domain measurement of the magnon BEC coherent state phase relative to an outside reference signal. We report the emergence of spontaneous coherence from a freely evolving magnon gas, which manifests as the condensation of magnons into a uniform precession state with minimal energy and a well-defined phase. These findings confirm all postulated fundamental properties of quasiparticle condensates, provide access to a new degree of freedom in such systems, and open up the possibility of information processing using microwave-frequency magnon BECs.

Brillouin Light Scattering (BLS) spectroscopy is widely used for studying collective acoustic and magnetic excitations. In magnetism, it is employed as a versatile tool for measuring the characteristics of magnetic media, visualizing linear and nonlinear spin-wave spatiotemporal dynamics, investigating magnon–phonon interaction effects, and exploring fundamental phenomena such as the Bose–Einstein condensation of magnons. At the same time, magnetic BLS spectroscopy has so far suffered from a lack of possibilities to resolve short-wavelength magnons in arbitrary wavevector directions. Here, we demonstrate two-dimensional thermal magnon and phonon spectra measured in a single-crystal film of Yttrium Iron Garnet (Y3Fe5O12). The wide-range two-dimensional wavevector selectivity is accomplished in the backscattering geometry via independent rotations of the probing beam and the sample plane. The spectra were measured in the range of magnon and phonon wavelengths down to 400nm and are fully consistent with calculations that take into account exchange, dipole, and elastic interactions. Our results open the way to an in-depth study of the magnon, phonon, and magnon–phonon dynamics of solids.

We theoretically demonstrate that adding an easy-axis magnetic anisotropy facilitates magnon condensation in thin yttrium iron garnet (YIG) films. Dipolar interactions in a quasi-equilibrium state stabilize room-temperature magnon condensation in YIG. Even though the out-of-plane easy-axis anisotropy generally competes with the dipolar interactions, we show that adding such magnetic anisotropy may even assist the generation of the magnon condensate electrically via the spin transfer torque mechanism. We use analytical calculations and micromagnetic simulations to illustrate this effect. Our results may explain the recent experiment on Bi-doped YIG and open a pathway toward applying current-driven magnon condensation in quantum spintronics.

The creation of temperature variations in magnetization, and hence in the frequencies of the magnon spectrum in laser-heated regions of magnetic films, is an important method for studying Bose-Einstein condensation of magnons, magnon supercurrents, Bogoliubov waves, and similar phenomena. In our study, we demonstrate analytically, numerically, and experimentally that, in addition to the magnetization variations, it is necessary to consider the connected variations of the demagnetizing field. In case of a heat induced local minimum of the saturation magnetization, the combination of these two effects results in a local increase in the minimum frequency value of the magnon dispersion at which the Bose-Einstein condensate emerges. As a result, a magnon supercurrent directed away from the hot region is formed.

We consider flux equilibrium in dissipative nonlinear wave systems subject to external energy pumping. In such systems, the elementary excitations, or quasiparticles, can create a Bose-Einstein condensate. We develop a theory on the Bose-Einstein condensation of quasiparticles for various regimes of external excitation, ranging from weak and stationary to ultra-strong pumping, enabling us to determine the number of quasiparticles near the bottom of the energy spectrum and their distribution along wave vectors. We identify physical phenomena leading to condensation in each of the regimes. For weak stationary pumping, where the distribution of quasiparticles deviates only slightly from thermodynamic equilibrium, we define a range of pumping parameters where the condensation occurs and estimate the density of the condensate and the fraction of the condensed quasiparticles. As the pumping amplitude increases, a powerful influx of injected quasiparticles is created by the Kolmogorov-Zakharov scattering cascade, leading to their Bose-Einstein condensation. With even stronger pumping, kinetic instability may occur, resulting in a direct transfer of injected quasiparticles to the bottom of the spectrum. For the case of ultra-strong parametric pumping, we have developed a stationary nonlinear theory of kinetic instability. The theory agrees qualitatively with experimental data obtained using Brillouin light scattering spectroscopy during parametric pumping of magnons in room-temperature films of yttrium-iron garnet.

When excited, the magnetization in a magnet precesses around the field in an anticlockwise manner on a timescale governed by viscous magnetization damping, after which any information carried by the initial actuation seems to be lost. This damping appears to be a fundamental bottleneck for the use of magnets in information processing. However, here we demonstrate the recall of the magnetization-precession phase after times that exceed the damping timescale by two orders of magnitude using dedicated two-colour microwave pump–probe experiments for a Y 3 Fe 5 O 12 microstructured film. Time-resolved magnetization state tomography confirms the persistent magnetic coherence by revealing a double-exponential decay of magnetization correlation. We attribute persistent magnetic coherence to a feedback effect, that is, coherent coupling of the uniform precession with long-lived excitations at the minima of the spin-wave dispersion relation. Our finding liberates magnetic systems from the strong damping in nanostructures that has limited their use in coherent information storage and processing.

Nonlinear interactions are crucial in science and engineering. Here, we investigate wave interactions in a highly nonlinear magnetic system driven by parametric pumping leading to Bose-Einstein condensation of spin-wave quanta-magnons. Using Brillouin light scattering spectroscopy in yttrium-iron garnet films, we found and identified a set of nonlinear processes resulting in off-resonant spin-wave excitations-virtual magnons. In particular, we discovered a dynamically strong, correlation-enhanced four-wave interaction process of the magnon condensate with pairs of parametric magnons having opposite wave vectors and fully correlated phases.

Controlling the phase and amplitude of spin waves in magnetic insulators with an electric field opens the way to fast logic circuits with ultra-low power consumption. One way to achieve such control is to manipulate the magnetization of the medium via magnetoelectric effects. In experiments with magnetostatic spin waves in an yttrium iron garnet film, we have obtained the first evidence of a theoretically predicted phenomenon: The change of the spin-wave phase due to the magnonic Aharonov$-$Casher effect$-$the geometric accumulation of the magnon phase as these quasiparticles propagate through an electric field region.

Since temperature and its spatial, and temporal variations affect a wide range of physical properties of material systems, they can be used to create reconfigurable spatial structures of various types in physical and biological objects. This paper presents an experimental optical setup for creating tunable two-dimensional temperature patterns on a micrometer scale. As an example of its practical application, we have produced temperature-induced magnetization landscapes in ferrimagnetic yttrium iron garnet films and investigated them using micro-focused Brillouin light scattering spectroscopy. It is shown that, due to the temperature dependence of the magnon spectrum, spatial temperature distributions can be visualized even for microscale thermal patterns.

Magnetic nanoelements attract great interest due to their prospects for data storage and signal processing. Spin-wave confinement in these elements implies wave-number quantization, discrete frequency spectra and thus complex resonance patterns, strongly dependent on the elements' geometry and static magnetic configuration. Here we report experimental observation of unconventional single-frequency resonance response of flat circular Permalloy nanodots, which is achieved via the application of a magnetic field at a certain critical angle (theta) over tilde (B) with respect to the dot normal. This observation is explained as the merging of spin-wave eigenmodes under the transition of the spin-wave dispersion from the forward-volume to the backward-volume type, as elucidated by micromagnetic simulations in conjunction with an analytical theory. Our results offer a way for the creation of spin-wave systems with spectrally narrow magnetic noise.

Magnetic heterostructures consisting of single-crystal yttrium iron garnet (YIG) films coated with platinum are widely used in spin-wave experiments related to spintronic phenomena such as the spin-transfer-torque, spin-Hall, and spin-Seebeck effects. However, spin waves in YIG/Pt bilayers experience much stronger attenuation than in bare YIG films. For micrometer-thick YIG films, this effect is caused by microwave eddy currents in the Pt layer. This paper reports that by employing an excitation configuration in which the YIG film faces the metal plate of the microstrip antenna structure, the eddy currents in Pt are shunted and the transmission of the Damon-Eschbach surface spin wave is greatly improved. The reduction in spin-wave attenuation persists even when the Pt coating is separated from the ground plate by a thin dielectric layer. This makes the proposed excitation configuration suitable for injection of an electric current into the Pt layer and thus for application in spintronics devices. The theoretical analysis carried out within the framework of the electrodynamic approach reveals how the platinum nanolayer and the nearby highly conductive metal plate affect the group velocity and the lifetime of the Damon-Eshbach surface wave and how these two wavelength-dependent quantities determine the transmission characteristics of the spin-wave device.

Coherent wave states such as Bose-Einstein condensates (BECs), which spontaneously form in an overpopulated magnon gas even at room temperature, have considerable potential for wave-based computing and information processing at microwave frequencies. The ability to control the transport properties of magnon BECs plays an essential role for their practical use. Here, we demonstrate spatio-temporal control of the BEC density distribution through the excitation of magnon supercurrents in an inhomogeneously magnetized yttrium iron garnet film. The BEC is created by microwave parametric pumping and probed by Brillouin light scattering spectroscopy. The desired magnetization profile is prepared by heating the film with optical patterns projected onto its surface using a phase-based wavefront modulation technique. Specifically, we observe a pronounced spatially localized magnon accumulation caused by magnon supercurrents flowing toward each other originating in two heated regions. This accumulation effect increases the BEC lifetime due to the constant influx of condensed magnons into the confinement region. The shown approach to manipulate coherent waves provides an opportunity to extend the lifetime of freely evolving magnon BECs, create dynamic magnon textures, and study the interaction of magnon condensates formed in different regions of the sample.

Interactions between quasiparticles of different nature, such as magnons and phonons in a magnetic medium, significantly change the spectrum of both types of quasiparticles. In regions where their dispersion curves intersect, forming an avoided crossing, the properties of the two subsystems mix and hybrid states are born, whose characteristics, such as velocity, lifetime and scattering efficiency, are determined by the magnon and phonon portion of their composition. In particular, the influence of the elastic component of quasiparticles allows for the manipulation of the position and even the number of spectral minima of the magnon gas in the wavevector space. Using Brillouin light scattering spectroscopy, we experimentally investigated such a system populated by the parametric pumping of magnons in a film of yttrium iron garnet. We found that the processes of thermalization of exchange and dipole magnons lead to their accumulation in different areas at the bottom of the spin-wave spectrum separated by the magnon–phonon hybridization region. The localization of quasiparticles in the wavevector space eventually leads to their separation in real space.

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.

Advances in quantum computing and telecommunications stimulate the search for classical systems allowing partial implementation of a similar functionality under less stringent environmental conditions. Here, we present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose–Einstein condensate (BEC) formed at opposite wavevectors in a room-temperature yttrium-iron-garnet ferrimagnetic film. Employing micromagnetic numerical simulations, we show the use of wavelength-selective parametric pumping to controllably initialize and manipulate the two-component BEC. Next, by modeling the interaction of this BEC with a pulse- and radio-frequency-driven dynamic magnonic crystal we translate the concept of Rabi-oscillations into the wavevector domain and demonstrate how to manipulate the magnon-BEC system regarding the polar and azimuthal angles in the Bloch sphere representation. We hope that our study provides a significant stimulus on the boundary between qubit functionality and classical systems of interacting BECs, which use a subset of qubit-based algorithms.

We derive and solve quantum kinetic equations describing the accumulation of magnetoelastic bosons in an overpopulated magnon gas realized in a thin film of the magnetic insulator yttrium iron garnet. We show that in the presence of a magnon condensate, there is a non-equilibrium steady state in which incoherent magnetoelastic bosons accumulate in a narrow region in momentum space for energies slightly below the bottom of the magnon spectrum. The results of our calculations agree quite well with Brillouin light scattering measurements of the stationary non-equilibrium state of magnons and magnetoelastic bosons in yttrium iron garnet.

We have recently shown that injection of magnons into a magnetic dielectric via the spin-orbit torque (SOT) effect in the adjacent layer of a heavy metal subjected to the action of short (0.1 $\mu$s) current pulses allows for control of a magnon Bose-Einstein Condensate (BEC). Here, the BEC was formed in the process of rapid cooling (RC), when the electric current heating the sample is abruptly terminated. In the present study, we show that the application of a longer (1.0 $\mu$s) electric current pulse triggers the formation of a nonlinear localized magnonic bullet below the linear magnon spectrum. After pulse termination, the magnon BEC, as before, is formed at the bottom of the linear spectrum, but the nonlinear bullet continues to exist, stabilized for additional 30 ns by the same process of RC-induced magnon condensation. Our results suggest that a stimulated condensation of excess magnons to all highly populated magnonic states occurs.

Interaction between quasiparticles of a different nature, such as magnons and phonons in a magnetic medium, leads to the mixing of their properties and the formation of hybrid states in the areas of intersection of individual spectral branches. We recently reported the discovery of a new phenomenon mediated by the magnon-phonon interaction: the spontaneous bottleneck accumulation of magneto-elastic bosons under electromagnetic pumping of pure magnons into a ferrimagnetic yttrium iron garnet film. Here, by studying the transport properties of the accumulated magneto-elastic bosons, we reveal that such accumulation occurs in two frequency-distant groups of quasiparticles: quasi-phonons and quasi-magnons. They propagate with different speeds in different directions relative to the magnetization field. The theoretical model we propose qualitatively describes the double accumulation effect, and the analysis of the two-dimensional spectrum of quasiparticles in the hybridization region allows us to determine the wavevectors and frequencies of each of the groups.