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 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.

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.

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.

Storage-recovery phenomenon in magnonic crystal.

The phenomenon of coherent wave trapping and restoration is demonstrated experimentally in a magnonic crystal. Unlike the conventional scheme used in photonics, the trapping occurs not due to the deceleration of the incident wave when it enters the periodic structure but due to excitation of the quasinormal modes of the artificial crystal. This excitation occurs at the group velocity minima of the decelerated wave in narrow frequency regions near the edges of the band gaps of the crystal. The restoration of the traveling wave is implemented by means of phase-sensitive parametric amplification of the stored mode.

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.

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.

Spin wave excitations of a magnetic pillar with dipolar coupling between the layers.

It is demonstrated analytically that the spectrum of small-amplitude spatially uniform magnetization excitations in an in-plane magnetized magnetic pillar with two ferromagnetic layers coupled by dipole-dipole interaction can be approximately described by the traditional Kittel formula with reduced saturation magnetization and effective anisotropy field. The spectrum consists of a quasi-symmetric and a quasi-antisymmetric mode, and the apparent reduction of saturation magnetization for the quasi-symmetric mode (≤50%) is much larger than that for the quasi-antisymmetric mode (≤10%). The effect of dynamic dipolar coupling between the nano-pillar layers could be partly responsible for the apparent reduction of static magnetization seen in many spin-torque experiments performed on magnetic nano-pillars.

Resonant nonlinear damping of quantized spin waves in ferromagnetic nanowires: a spin torque ferromagnetic resonance study.

We use spin torque ferromagnetic resonance to measure the spectral properties of dipole-exchange spin waves in Permalloy nanowires. Our measurements reveal that geometric confinement has a profound effect on the damping of spin waves in the nanowire geometry. The damping parameter of the lowest-energy quantized spin-wave mode depends on applied magnetic field in a resonant way and exhibits a maximum at a field that increases with decreasing nanowire width. This enhancement of damping originates from a nonlinear resonant three-magnon confluence process allowed at a particular bias field value determined by quantization of the spin-wave spectrum in the nanowire geometry.

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.

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.

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.

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.

Reversal of momentum relaxation.

A new phenomenon of momentum relaxation reversal has been discovered experimentally and explained theoretically for dipolar spin waves in magnetic garnet films. It is shown that the process of momentum relaxation, caused by the scattering of a signal wave on defects, can be reversed, and the signal can be restituted after it left the scattering region. The reversal of momentum relaxation is achieved by frequency-selective parametric amplification of a narrow band of scattered waves having low group velocities and frequencies close to the frequency of the original signal wave. The phenomenon can be used for the development of a new type of active microwave delay lines.