Stimulated Amplification of Propagating Spin Waves.

Spin-wave amplification techniques are key to the realization of magnon-based computing concepts. We introduce a novel mechanism to amplify spin waves in magnonic nanostructures. Using the technique of rapid cooling, we create a nonequilibrium state in excess of high-energy magnons and demonstrate the stimulated amplification of an externally seeded, propagating spin wave. Using an extended kinetic model, we qualitatively show that the amplification is mediated by an effective energy flux of high energy magnons into the low energy propagating mode, driven by a nonequilibrium magnon distribution.

Excitation of Whispering Gallery Magnons in a Magnetic Vortex.

We present the generation of whispering gallery magnons with unprecedented high wave vectors via nonlinear 3-magnon scattering in a µm-sized magnetic Ni_{81}Fe_{19} disc which is in the vortex state. These modes exhibit a strong localization at the perimeter of the disc and practically zero amplitude in an extended area around the vortex core. They originate from the splitting of the fundamental radial magnon modes, which can be resonantly excited in a vortex texture by an out-of-plane microwave field. We shed light on the basics of this nonlinear scattering mechanism from an experimental and theoretical point of view. Using Brillouin light scattering microscopy, we investigated the frequency and power dependence of the 3-magnon splitting. The spatially resolved mode profiles give evidence for the localization at the boundaries of the disc and allow for a direct determination of the modes wave number.

Coherent Excitation of Heterosymmetric Spin Waves with Ultrashort Wavelengths.

In the emerging field of magnonics, spin waves are foreseen as signal carriers for future spintronic information processing and communication devices, owing to both the very low power losses and a high device miniaturization potential predicted for short-wavelength spin waves. Yet, the efficient excitation and controlled propagation of nanoscale spin waves remains a severe challenge. Here, we report the observation of high-amplitude, ultrashort dipole-exchange spin waves (down to 80 nm wavelength at 10 GHz frequency) in a ferromagnetic single layer system, coherently excited by the driven dynamics of a spin vortex core. We used time-resolved x-ray microscopy to directly image such propagating spin waves and their excitation over a wide range of frequencies. By further analysis, we found that these waves exhibit a heterosymmetric mode profile, involving regions with anti-Larmor precession sense and purely linear magnetic oscillation. In particular, this mode profile consists of dynamic vortices with laterally alternating helicity, leading to a partial magnetic flux closure over the film thickness, which is explained by a strong and unexpected mode hybridization. This spin-wave phenomenon observed is a general effect inherent to the dynamics of sufficiently thick ferromagnetic single layer films, independent of the specific excitation method employed.

Oscillatory energy exchange between waves coupled by a dynamic artificial crystal.

We describe a general mechanism of controllable energy exchange between waves propagating in a dynamic artificial crystal. We show that if a spatial periodicity is temporarily imposed on the transmission properties of a wave-carrying medium while a wave is inside, this wave is coupled to a secondary counterpropagating wave and energy oscillates between the two. The oscillation frequency is determined by the width of the spectral band gap created by the periodicity and the frequency difference between the coupled waves. The effect is demonstrated with spin waves in a dynamic magnonic crystal.

Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping.

Bose-Einstein condensation is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle density exceeds a critical value. To achieve Bose-Einstein condensation, one can either decrease the temperature or increase the density of bosons. It has been predicted that a quasi-equilibrium system of bosons could undergo Bose-Einstein condensation even at relatively high temperatures, if the flow rate of energy pumped into the system exceeds a critical value. Here we report the observation of Bose-Einstein condensation in a gas of magnons at room temperature. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equilibrium, they can be described by Bose-Einstein statistics with zero chemical potential and a temperature-dependent density. In the experiments presented here, we show that by using a technique of microwave pumping it is possible to excite additional magnons and to create a gas of quasi-equilibrium magnons with a non-zero chemical potential. With increasing pumping intensity, the chemical potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.

Nondiffractive subwavelength wave beams in a medium with externally controlled anisotropy.

We predict and experimentally demonstrate that in a medium with externally induced anisotropy, a wave source of a sufficiently small size can excite practically nondiffractive wave beams with stable subwavelength transverse aperture. The direction of beam propagation is controlled by rotating the induced anisotropy axis. Nondiffractive wave beam propagation, reflection, and scattering, as well as beam steering have been directly observed by optically probing dipolar spin waves in yttrium iron garnet films, where the uniaxial anisotropy was created by an in-plane bias magnetic field.

Direct current control of three magnon scattering processes in spin-valve nanocontacts.

We have investigated the generation of spin waves in the free layer of an extended spin-valve structure with a nanoscaled point contact driven by both microwave and direct electric current using Brillouin light scattering microscopy. Simultaneously with the directly excited spin waves, strong nonlinear effects are observed, namely, the generation of eigenmodes with integer multiple frequencies (2f, 3f, 4f) and modes with noninteger factors (0.5f, 1.5f) with respect to the excitation frequency f. The origin of these nonlinear modes is traced back to three-magnon-scattering processes. The direct current influence on the generation of the fundamental mode at frequency f is related to the spin-transfer torque, while the efficiency of three-magnon-scattering processes is controlled by the Oersted field as an additional effect of the direct current.

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.

Probing arrays of circular magnetic microdots by ferromagnetic resonance.

X-band ferromagnetic resonance (FMR) was used to characterize in-plane magnetic anisotropies in rectangular and square arrays of circular nickel and Permalloy microdots. In the case of a rectangular lattice, as interdot distances in one direction decrease, the in-plane uniaxial anisotropy field increases, in good agreement with a simple theory of magnetostatically interacting uniformly magnetized dots. In the case of a square lattice a four-fold anisotropy of the in-plane FMR field H(r) was found when the interdot distance a gets comparable to the dot diameter D. This anisotropy, not expected in the case of uniformly magnetized dots, was explained by a non-uniform magnetization m(r) in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variation procedure. In the case of perpendicular magnetization multiple sharp resonance peaks were observed below the main FMR peak in all the samples, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra was given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account. It was demonstrated that ferromagnetic resonance force microscopy (FMRFM) can be used to determine both local and global properties of patterned submicron ferromagnetic samples. Local spectroscopy together with the possibility to vary the tip-sample spacing enables the separation of those two contributions to a FMRFM spectrum. The global FMR properties of circular submicron dots determined using magnetic resonance force microscopy are in a good agreement with results obtained using conventional FMR and with theoretical descriptions.

Discrete modes of a ferromagnetic stripe dipolarly coupled to a ferromagnetic film: a Brillouin light scattering study.

Spin wave excitations in a magnetic structure consisting of a series of long permalloy stripes of a rectangular cross section magnetized along the stripe length and situated above a continuous permalloy film are studied both experimentally and theoretically. Stripes and continuous film are coupled by dipole-dipole interaction across 10 nm thick Cu spacers. Experimental measurements made using the Brillouin light scattering technique (with the light wavevector oriented along the stripe width) provide evidence for one dispersive spin wave mode associated with the continuous film and several discrete non-dispersive modes resonating within the finite width of the stripes.To interpret the experimental spectra, an analytic theory based on the spin wave formalism for finite-width magnetic stripes has been developed, achieving a good qualitative and partly quantitative description of the experimentally observed spin wave spectrum of the system. In particular, it is explained why the presence of a continuous magnetic film near the magnetic stripe leads to a substantial decrease of the frequencies of the discrete dipolar spin wave modes localized within the stripes. A more quantitative description of the measured frequencies and of the spatial profiles of the spin wave eigenmodes has been obtained by numerical calculations performed using a finite element method.

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.

Nonadiabatic interaction of a propagating wave packet with localized parametric pumping.

The interaction of a propagating wave packet (carrier frequency omega, wave number k) with nonadiabatic parametric pumping, localized in a region of size the order of the carrier wavelength L approximately lambda=2pi/k, is studied experimentally in a system of dipolar spin waves in a ferrite film. It is shown that the three-wave parametric interaction omega+omega(')=omega(p) leads to the formation of both contrapropagating (k(')=-k) and copropagating (k(')=k) idle wave packets of carrier frequency omega('). A system of equations derived for the packet envelopes gives a quantitative description of the observed random modulation of the output signal caused by the interference of the input and copropagating idle wave packets.

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.

From chaos to selective ordering of vortex cores in interacting mesomagnets.

A spin vortex consists of an in-plane curling magnetization and a small core region (~10 nm) with out-of-plane magnetization. An oscillating field or current induce gyrotropic precession of the spin vortex. Dipole-dipole and exchange coupling between the interacting vortices may lead to excitation of collective modes whose frequencies depend on the core polarities. Here we demonstrate an effective method for controlling the relative core polarities in a model system of overlapping Ni(80)Fe(20) dots. This is achieved by driving the system to a chaotic regime of continuous core reversals and subsequently relaxing the cores to steady-state motion. It is shown that any particular core polarity combination (and therefore the spectral response of the entire system) can be deterministically preselected by tuning the excitation frequency or external magnetic field. We anticipate that this work would benefit the future development of magnonic crystals, spin-torque oscillators, magnetic storage and logic elements.

Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk.

Microwave spectroscopy of individual vortex-state magnetic nanodisks in a perpendicular bias magnetic field H is performed using a magnetic resonance force microscope. It reveals the splitting induced by H on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field Hr, at which the core polarity is reversed. The difference between the frequencies of the two stable rotational modes corresponding to each core polarity is proportional to H and to the ratio of the disk thickness to its radius. Simple analytic theory in combination with micromagnetic simulations give a quantitative description of the observed bistable dynamics.

Observation of coherence and partial decoherence of quantized spin waves in nanoscaled magnetic ring structures.

Experiments and simulations are reported, which demonstrate the influence of partial decoherence of spin-wave modes on the dynamics in small magnetic structures. Microfocus Brillouin light scattering spectroscopy was performed on 15 nm thick Ni81Fe19 rings with diameters from 1 to 3 microm. For the so-called "onion" magnetization state several effects were identified. First, in the pole regions of the rings spin-wave wells are created due to the inhomogeneous internal field leading to spin-wave confinement. Second, in the regions in between, modes are observed which show a well pronounced quantization in radial direction but a transition from partial to full coherency in azimuthal direction as a function of decreasing ring size. In particular for larger rings a continuous frequency variation with position is observed which is well reproduced by spin-wave calculations and micromagnetic simulations.

Observation of spontaneous coherence in Bose-Einstein condensate of magnons.

The room-temperature dynamics of a magnon gas driven by short microwave pumping pulses is studied. An overpopulation of the lowest energy level of the system following the pumping is observed. Using the sensitivity of the Brillouin light scattering technique to the coherence degree of the scattering magnons we demonstrate the spontaneous emergence of coherence of the magnons at the lowest level, if their density exceeds a critical value. This finding is clear proof of the quantum nature of the observed phenomenon and direct evidence of Bose-Einstein condensation of magnons at room temperature.

Line shape distortion in a nonlinear auto-oscillator near generation threshold: application to spin-torque nano-oscillators.

The power spectrum of an auto-oscillator with a large frequency nonlinearity in a noisy environment is calculated. The power spectrum becomes strongly non-Lorentzian, broadened, and asymmetric near the generation threshold. A Lorentzian spectrum is recovered far below and far above the threshold, which suggests that line shape distortions provide a signature of the threshold. We show that the developed theory adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.

Thermalization of a parametrically driven magnon gas leading to Bose-Einstein condensation.

The thermalization of parametrically pumped magnons caused by nonlinear multimagnon scattering processes and leading to the magnon Bose-Einstein condensation is investigated experimentally with high temporal resolution. The threshold pumping power necessary for the thermalization is determined. For pumping powers above this threshold the thermalization time has been found to decrease rapidly with power reaching the value down to 50 ns, which is much smaller than the magnon lifetime.

Parametrically stimulated recovery of a microwave signal stored in standing spin-wave modes of a magnetic film.

We demonstrate that a microwave signal carried by a packet of dipolar spin waves propagating in a tangentially magnetized magnetic film can be stored in the form of standing dipole-exchange spin-wave modes of the film and can be recovered by means of a double-frequency parametric pumping mechanism. This mechanism is based on the parametric amplification of the standing (thickness) modes of the film by external pumping. The time of recovery, duration, and power of the recovered pulse signal are controlled by the power of the pumping signal.