Resonant generation of propagating second-harmonic spin waves in nano-waveguides.

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field of magnonics, which considers the use of spin waves in magnetic nanostructures to implement wave-based signal processing and computing. However, due to the strong frequency dependence of the phase velocity of spin waves, resonant phase-matched generation of second-harmonic spin waves has not yet been achieved in practice. Here, we show experimentally that such a process can be realized using a combination of different modes of nano-sized spin-wave waveguides based on low-damping magnetic insulators. We demonstrate that our approach enables efficient spatially-extended energy transfer between interacting waves, which can be controlled by the intensity of the initial wave and the static magnetic field.

True amplification of spin waves in magnonic nano-waveguides.

Magnonic nano-devices exploit magnons - quanta of spin waves - to transmit and process information within a single integrated platform that has the potential to outperform traditional semiconductor-based electronics. The main missing cornerstone of this information nanotechnology is an efficient scheme for the amplification of propagating spin waves. The recent discovery of spin-orbit torque provided an elegant mechanism for propagation losses compensation. While partial compensation of the spin-wave losses has been achieved, true amplification - the exponential increase in the spin-wave intensity during propagation - has so far remained elusive. Here we evidence the operating conditions to achieve unambiguous amplification using clocked nanoseconds-long spin-orbit torque pulses in magnonic nano-waveguides, where the effective magnetization has been engineered to be close to zero to suppress the detrimental magnon scattering. We achieve an exponential increase in the intensity of propagating spin waves up to 500% at a propagation distance of several micrometers.

Giant nonlinear self-phase modulation of large-amplitude spin waves in microscopic YIG waveguides.

Nonlinear self-phase modulation is a universal phenomenon responsible, for example, for the formation of propagating dynamic solitons. It has been reported for waves of different physical nature. However its direct experimental observation for spin waves has been challenging. Here we show that exceptionally strong phase modulation can be achieved for spin waves in microscopic waveguides fabricated from nanometer-thick films of magnetic insulator, which support propagation of spin waves with large amplitudes corresponding to angles of magnetization precession exceeding 10°. At these amplitudes, the nonstationary nonlinear dynamic response of the spin system causes an extreme broadening of the spectrum of spin-wave pulses resulting in a strong spatial variation of the spin-wave wavelength and a temporal variation of the spin-wave phase across the pulse. Our findings demonstrate great complexity of nonlinear wave processes in microscopic magnetic structures and importance of their understanding for technical applications of spin waves in integrated devices.

Evidence for spin current driven Bose-Einstein condensation of magnons.

The quanta of magnetic excitations - magnons - are known for their unique ability to undergo Bose-Einstein condensation at room temperature. This fascinating phenomenon reveals itself as a spontaneous formation of a coherent state under the influence of incoherent stimuli. Spin currents have been predicted to offer electronic control of Bose-Einstein condensates, but this phenomenon has not been experimentally evidenced up to now. Here we show that current-driven Bose-Einstein condensation can be achieved in nanometer-thick films of magnetic insulators with tailored nonlinearities and minimized magnon interactions. We demonstrate that, above a certain threshold, magnons injected by the spin current overpopulate the lowest-energy level forming a highly coherent spatially extended state. We quantify the chemical potential of the driven magnon gas and show that, at the critical current, it reaches the energy of the lowest magnon level. Our results pave the way for implementation of integrated microscopic quantum magnonic and spintronic devices.

The 2021 Magnonics Roadmap.

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

Spatial separation of degenerate components of magnon Bose-Einstein condensate by using a local acceleration potential.

Bose-Einstein condensation (BEC) of magnons is one of the few macroscopic quantum phenomena observable at room temperature. Due to the competition of the exchange and the magnetic dipole interactions, the minimum-energy magnon state is doubly degenerate and corresponds to two antiparallel non-zero wavevectors. Correspondingly, the room-temperature magnon BEC differs essentially from other condensates, since it takes place simultaneously at ± kmin. The degeneracy of BEC and interaction between its two components have significant impact on condensate properties. Phase locking of the two condensates causes formation of a standing wave of the condensate density and quantized vortices. Additionally, interaction between the two components is believed to be important for stabilization of the condensate with respect to a real-space collapse. Thus, the possibility to create a non-degenerate, single-component condensate is decisive for understanding of underlying physics of magnon BEC. Here, we experimentally demonstrate an approach, which allows one to accomplish this challenging task. We show that this can be achieved by using a separation of the two components of the degenerate condensate in the real space by applying a local pulsed magnetic field, which causes their motion in the opposite directions. Thus, after a certain delay, the two clouds corresponding to different components become well separated in the real space. We find that motion of the clouds can be described well based on the peculiarities of magnon dispersion characteristics. Additionally, we show that, during the motion, the condensate cloud harvests non-condensed magnons, which results in a partial compensation of condensate depletion.

Direct evidence of spatial stability of Bose-Einstein condensate of magnons.

Bose-Einstein condensation of magnons is one of few macroscopic quantum phenomena observed at room temperature. Since its discovery, it became an object of intense research, which led to the observation of many exciting phenomena such as quantized vortices, second sound, and Bogolyubov waves. However, it remained unclear what physical mechanisms can be responsible for the spatial stability of the magnon condensate. Indeed, since magnons are believed to exhibit attractive interaction, it is generally expected that the condensate is unstable with respect to the real-space collapse, contrarily to experimental findings. Here, we provide direct experimental evidence that magnons in a condensate exhibit repulsive interaction resulting in the condensate stabilization and propose a mechanism, which is responsible for this interaction. Our experimental conclusions are additionally supported by the theoretical model based on the Gross-Pitaevskii equation. Our findings solve a long-standing problem, providing a new insight into the physics of magnon Bose-Einstein condensates.

Excitation of coherent second sound waves in a dense magnon gas.

Second sound is a quantum mechanical effect manifesting itself as a wave-like (in contrast with diffusion) heat transfer, or energy propagation, in a gas of quasi-particles. So far, this phenomenon has been observed only in an equilibrium gas of phonons existing in liquid/solid helium, or in dielectric crystals (Bi, NaF) at low temperatures. Here, we report observation of a room-temperature magnonic second sound, or a wave-like transport of both energy and spin angular momentum, in a quasi-equilibrium gas of magnons undergoing Bose-Einstein condensation (BEC) in a ferrite film. Due to the contact of the magnon gas with pumping photons and phonons, dispersion of the magnonic second sound differ qualitatively from the phononic case, as there is no diffusion regime, and the second sound velocity remains finite at low wavenumbers. Formation of BEC in the gas of magnons modifies the second sound properties by creating an additional channel of energy relaxation.

Spin Hall-induced auto-oscillations in ultrathin YIG grown on Pt.

We experimentally study nanowire-shaped spin-Hall nano-oscillators based on nanometer-thick epitaxial films of Yttrium Iron Garnet grown on top of a layer of Pt. We show that, although these films are characterized by significantly larger magnetic damping in comparison with the films grown directly on Gadolinium Gallium Garnet, they allow one to achieve spin current-driven auto-oscillations at comparable current densities, which can be an indication of the better transparency of the interface to the spin current. These observations suggest a route for improvement of the flexibility of insulator-based spintronic devices and their compatibility with semiconductor technology.

Chemical potential of quasi-equilibrium magnon gas driven by pure spin current.

Pure spin currents provide the possibility to control the magnetization state of conducting and insulating magnetic materials. They allow one to increase or reduce the density of magnons, and achieve coherent dynamic states of magnetization reminiscent of the Bose-Einstein condensation. However, until now there was no direct evidence that the state of the magnon gas subjected to spin current can be treated thermodynamically. Here, we show experimentally that the spin current generated by the spin-Hall effect drives the magnon gas into a quasi-equilibrium state that can be described by the Bose-Einstein statistics. The magnon population function is characterized either by an increased effective chemical potential or by a reduced effective temperature, depending on the spin current polarization. In the former case, the chemical potential can closely approach, at large driving currents, the lowest-energy magnon state, indicating the possibility of spin current-driven Bose-Einstein condensation.

Direct observation of dynamic modes excited in a magnetic insulator by pure spin current.

Excitation of magnetization dynamics by pure spin currents has been recently recognized as an enabling mechanism for spintronics and magnonics, which allows implementation of spin-torque devices based on low-damping insulating magnetic materials. Here we report the first spatially-resolved study of the dynamic modes excited by pure spin current in nanometer-thick microscopic insulating Yttrium Iron Garnet disks. We show that these modes exhibit nonlinear self-broadening preventing the formation of the self-localized magnetic bullet, which plays a crucial role in the stabilization of the single-mode magnetization oscillations in all-metallic systems. This peculiarity associated with the efficient nonlinear mode coupling in low-damping materials can be among the main factors governing the interaction of pure spin currents with the dynamic magnetization in high-quality magnetic insulators.

Generation of coherent spin-wave modes in yttrium iron garnet microdiscs by spin-orbit torque.

In recent years, spin-orbit effects have been widely used to produce and detect spin currents in spintronic devices. The peculiar symmetry of the spin Hall effect allows creation of a spin accumulation at the interface between a metal with strong spin-orbit interaction and a magnetic insulator, which can lead to a net pure spin current flowing from the metal into the insulator. This spin current applies a torque on the magnetization, which can eventually be driven into steady motion. Tailoring this experiment on extended films has proven to be elusive, probably due to mode competition. This requires the reduction of both the thickness and lateral size to reach full damping compensation. Here we show clear evidence of coherent spin-orbit torque-induced auto-oscillation in micron-sized yttrium iron garnet discs of thickness 20 nm. Our results emphasize the key role of quasi-degenerate spin-wave modes, which increase the threshold current.

Spin-current nano-oscillator based on nonlocal spin injection.

Nonlocal spin injection has been recognized as an efficient mechanism for creation of pure spin currents not tied to the electrical charge transfer. Here we demonstrate experimentally that it can induce coherent magnetization dynamics, which can be utilized for the implementation of novel microwave nano-sources for spintronic and magnonic applications. We show that such sources exhibit a small oscillation linewidth and are tunable over a wide frequency range by the static magnetic field. Spatially resolved measurements of the dynamical magnetization indicate a relatively large oscillation area, resulting in a high stability of the oscillation with respect to thermal fluctuations. We propose a simple quasilinear dynamical model that reproduces well the oscillation characteristics.

Full control of the spin-wave damping in a magnetic insulator using spin-orbit torque.

It is demonstrated that the threshold current for damping compensation can be reached in a 5 µm diameter YIG(20 nm)|Pt(7 nm) disk. The demonstration rests upon the measurement of the ferromagnetic resonance linewidth as a function of I(dc) using a magnetic resonance force microscope (MRFM). It is shown that the magnetic losses of spin-wave modes existing in the magnetic insulator can be reduced or enhanced by at least a factor of 5 depending on the polarity and intensity of an in-plane dc current I(dc) flowing through the adjacent normal metal with strong spin-orbit interaction. Complete compensation of the damping of the fundamental mode by spin-orbit torque is reached for a current density of ∼3×10(11) A·m(-2), in agreement with theoretical predictions. At this critical threshold the MRFM detects a small change of static magnetization, a behavior consistent with the onset of an auto-oscillation regime.

Nanomagnonic devices based on the spin-transfer torque.

Magnonics is based on signal transmission and processing by spin waves (or their quanta, called magnons) propagating in a magnetic medium. In the same way as nanoplasmonics makes use of metallic nanostructures to confine and guide optical-frequency plasmon-polaritons, nanomagnonics uses nanoscale magnetic waveguides to control the propagation of spin waves. Recent advances in the physics of nanomagnetism, such as the discovery of spin-transfer torque, have created possibilities for nanomagnonics. In particular, it was recently demonstrated that nanocontact spin-torque devices can radiate spin waves, serving as local nanoscale sources of signals for magnonic applications. However, the integration of spin-torque sources with nanoscale magnetic waveguides, which is necessary for the implementation of integrated spin-torque magnonic circuits, has not been achieved to date. Here, we suggest and experimentally demonstrate a new approach to this integration, utilizing dipolar field-induced magnonic nanowaveguides. The waveguides exhibit good spectral matching with spin-torque nano-oscillators and enable efficient directional transmission of spin waves. Our results provide a practical route for the implementation of integrated magnonic circuits utilizing spin transfer.

Synchronization of spin Hall nano-oscillators to external microwave signals.

Recently, a novel type of spin-torque nano-oscillators driven by pure spin current generated via the spin Hall effect was demonstrated. Here we report the study of the effects of external microwave signals on these oscillators. Our results show that they can be efficiently synchronized by applying a microwave signal at approximately twice the frequency of the auto-oscillation, which opens additional possibilities for the development of novel spintronic devices. We find that the synchronization exhibits a threshold determined by magnetic fluctuations pumped above their thermal level by the spin current, and is significantly influenced by the nonlinear self-localized nature of the auto-oscillatory mode.

Spatially non-uniform ground state and quantized vortices in a two-component Bose-Einstein condensate of magnons.

A gas of magnons in magnetic films differs from all other known systems demonstrating Bose-Einstein condensation (BEC), since it possesses two energetically degenerate lowest-energy quantum states with non-zero wave vectors ±k(BEC). Therefore, BEC in this system results in a spontaneously formed two-component Bose-Einstein condensate described by a linear combination of two spatially non-uniform wave-functions ∝exp(±ik(BEC)z), while condensates found in other physical systems are characterized by spatially uniform wave-functions. Here we report a study of BEC of magnons with sub-micrometer spatial resolution. We experimentally confirm the existence of the two wave-functions and show that their interference results in a non-uniform ground state of the condensate with the density oscillating in space. Additionally, we observe stable topological defects in the condensate. By comparing the experimental results with predictions of a theoretical model based on the Ginzburg-Landau equation, we identify these defects as quantized vortices.

Control of magnetic fluctuations by spin current.

We use microfocus Brillouin light scattering spectroscopy to study the interaction of spin current with magnetic fluctuations in a Permalloy microdisk located on top of a Pt strip carrying an electric current. We show that the fluctuations can be efficiently suppressed or enhanced by different directions of the electric current. Additionally, we find that the effect of spin current on magnetic fluctuations is strongly influenced by nonlinear magnon-magnon interactions. The observed phenomena can be used for controllable reduction of thermal noise in spintronic nanodevices.

Bose-Einstein condensation of spin wave quanta at room temperature.

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.

Nonlinear hybridization of the fundamental eigenmodes of microscopic ferromagnetic ellipses.

We have studied experimentally with high spatial resolution the nonlinear eigenmodes of microscopic Permalloy elliptical elements. We show that the nonlinearity affects the frequencies of the edge and the center modes in an essentially different way. This leads to repulsion of corresponding resonances and to nonlinear mode hybridization resulting in qualitative modifications of the spatial characteristics of the modes. We find that the nonlinear counterparts of the edge and the center modes simultaneously exhibit features specific for both their linear analogues.