Persistent magnetic coherence in magnets

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 Y3Fe5O12 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.

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.

Room temperature and low-field resonant enhancement of spin Seebeck effect in partially compensated magnets

Resonant enhancement of spin Seebeck effect (SSE) due to phonons was recently discovered in Y[Formula: see text]Fe[Formula: see text]O[Formula: see text] (YIG). This effect is explained by hybridization between the magnon and phonon dispersions. However, this effect was observed at low temperatures and high magnetic fields, limiting the scope for applications. Here we report observation of phonon-resonant enhancement of SSE at room temperature and low magnetic field. We observe in Lu[Formula: see text]BiFe[Formula: see text]GaO[Formula: see text] an enhancement 700% greater than that in a YIG film and at very low magnetic fields around 10[Formula: see text] T, almost one order of magnitude lower than that of YIG. The result can be explained by the change in the magnon dispersion induced by magnetic compensation due to the presence of non-magnetic ion substitutions. Our study provides a way to tune the magnon response in a crystal by chemical doping, with potential applications for spintronic devices.

Phase-to-intensity conversion of magnonic spin currents and application to the design of a majority gate

Magnonic spin currents in the form of spin waves and their quanta, magnons, are a promising candidate for a new generation of wave-based logic devices beyond CMOS, where information is encoded in the phase of travelling spin-wave packets. The direct readout of this phase on a chip is of vital importance to couple magnonic circuits to conventional CMOS electronics. Here, we present the conversion of the spin-wave phase into a spin-wave intensity by local non-adiabatic parallel pumping in a microstructure. This conversion takes place within the spin-wave system itself and the resulting spin-wave intensity can be conveniently transformed into a DC voltage. We also demonstrate how the phase-to-intensity conversion can be used to extract the majority information from an all-magnonic majority gate. This conversion method promises a convenient readout of the magnon phase in future magnon-based devices.

Splitting of standing spin-wave modes in circular submicron ferromagnetic dot under axial symmetry violation

The spin wave dynamics in patterned magnetic nanostructures is under intensive study during the last two decades. On the one hand, this interest is generated by new physics that can be explored in such structures. On the other hand, with the development of nanolithography, patterned nanoelements and their arrays can be used in many practical applications (magnetic recording systems both as media and read-write heads, magnetic random access memory, and spin-torque oscillators just to name a few). In the present work the evolution of spin wave spectra of an array of non-interacting Permalloy submicron circular dots for the case of magnetic field deviation from the normal to the array plane have been studied by ferromagnetic resonance technique. It is shown that such symmetry violation leads to a splitting of spin-wave modes, and that the number of the split peaks depends on the mode number. A quantitative description of the observed spectra is given using a perturbation theory for small angles of field inclination from the symmetry direction. The obtained results give possibility to predict transformation of spin wave spectra depending on direction of the external magnetic field that can be important for spintronic and nanomagnetic applications.

Non-Gilbert-damping Mechanism in a Ferromagnetic Heusler Compound Probed by Nonlinear Spin Dynamics

The nonlinear decay of propagating spin waves in the low-Gilbert-damping Heusler film Co_{2}Mn_{0.6}Fe_{0.4}Si is reported. Here, two initial magnons with frequency f_{0} scatter into two secondary magnons with frequencies f_{1} and f_{2}. The most remarkable observation is that f_{1} stays fixed if f_{0} is changed. This indicates, that the f_{1} magnon mode has the lowest instability threshold, which, however, cannot be understood if only Gilbert damping is present. We show that the observed behavior is caused by interaction of the magnon modes f_{1} and f_{2} with the thermal magnon bath. This evidences a significant contribution of the intrinsic magnon-magnon scattering mechanisms to the magnetic damping in high-quality Heusler compounds.

Explosive electromagnetic radiation by the relaxation of a multimode magnon system

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.

Direct measurement of magnon temperature: new insight into magnon-phonon coupling in magnetic insulators

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.

Nonlinear emission of spin-wave caustics from an edge mode of a microstructured Co2Mn(0:6)Fe(0:4)Si waveguide

Magnetic Heusler materials with very low Gilbert damping are expected to show novel magnonic transport phenomena. We report nonlinear generation of higher harmonics leading to the emission of caustic spin-wave beams in a low-damping microstructured Co(2)Mn(0.6)Fe(0.4)Si Heusler waveguide. The source for the higher harmonic generation is a localized edge mode formed by the strongly inhomogeneous field distribution at the edges of the spin-wave waveguide. The radiation characteristics of the propagating caustic waves observed at twice and three times the excitation frequency are described by an analytical calculation based on the anisotropic dispersion of spin waves in a magnetic thin film.

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.

Optical detection of spin transport in nonmagnetic metals

We determine the dynamic magnetization induced in nonmagnetic metal wedges composed of silver, copper, and platinum by means of Brillouin light scattering microscopy. The magnetization is transferred from a ferromagnetic Ni80Fe20 layer to the metal wedge via the spin pumping effect. The spin pumping efficiency can be controlled by adding an insulating interlayer between the magnetic and nonmagnetic layer. By comparing the experimental results to a dynamical macroscopic spin-transport model we determine the transverse relaxation time of the pumped spin current which is much smaller than the longitudinal relaxation time.

Spin pumping by parametrically excited exchange magnons

We experimentally show that exchange magnons can be detected by using a combination of spin pumping and the inverse spin-Hall effect proving its wavelength integrating capability down to the submicrometer scale. The magnons were injected in a ferrite yttrium iron garnet film by parametric pumping and the inverse spin-Hall effect voltage was detected in an attached Pt layer. The role of the density, wavelength, and spatial localization of the magnons for the spin pumping efficiency is revealed.

Radiation of caustic beams from a collapsing bullet

We show both theoretically and experimentally that a collapsing (2+1)-dimensional wave packet in a medium with cubic nonlinearity and a two-dimensional dispersion of an order higher than parabolic irradiates untrapped dispersive waves. The studies are performed for a spin-wave bullet propagating in an in-plane magnetized ferrimagnetic film. An induced uniaxial anisotropy in such a medium leads to the formation of narrow spin-wave caustic beams whose angles to the bullet's propagation direction are modified by the motion of the source.

Wide-range wavevector selectivity of magnon gases in Brillouin light scattering spectroscopy

Brillouin light scattering spectroscopy is a powerful technique for the study of fast magnetization dynamics with both frequency and wavevector resolutions. Here, we report on a distinct improvement of this spectroscopic technique toward two-dimensional wide-range wavevector selectivity in a backward scattering geometry. Spin-wave wavevectors oriented perpendicularly to the bias magnetic field are investigated by tilting the sample within the magnet gap. Wavevectors which are oriented parallel to the applied magnetic field are analyzed by turning the entire setup, including the magnet system. The setup features a wide selectivity of wavevectors up to 2.04x10(5) rad/cm for both orientations, and allows selecting and measuring wavevectors of dipole- and exchange-dominated spin waves of any orientation to the magnetization simultaneously.

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.

An electro-optic modulator-assisted wavevector-resolving Brillouin light scattering setup

Brillouin light scattering spectroscopy is a powerful technique which incorporates several extensions such as space-, time-, phase-, and wavevector-resolution. Here, we report on the improvement of the wavevector-resolving setup by including an electro-optic modulator. This provides a reference to calibrate the position of the diaphragm hole which is used for wavevector selection. The accuracy of this calibration is only limited by the accuracy of the wavevector measurement itself. To demonstrate the validity of the approach the wavevectors of dipole-dominated spin waves excited by a microstrip antenna were measured.

Phase sensitive Brillouin scattering measurements with a novel magneto-optic modulator

A recently reported phase sensitive Brillouin light scattering technique is improved by use of a magnetic modulator. This modulator is based on Brillouin light scattering in a thin ferrite film. Using this magnetic modulator in time and space Brillouin light scattering measurements, we have increased phase contrast and excluded influence of optical inhomogeneities in the sample. We also demonstrate that the quality of the resulting interference patterns can be improved by data postprocessing using the simultaneously recorded information about the reference light.

Formation of guided spin-wave bullets in ferrimagnetic film stripes

The formation of quasi-2D nonlinear spin-wave eigenmodes in longitudinally magnetized stripes of a ferrimagnetic film, the so-called guided spin-wave bullets, was experimentally observed by using time- and space-resolved Brillouin light scattering spectroscopy and confirmed by numerical simulation. They represent stable spin-wave packets propagating along a waveguide structure, for which both transversal instability and interaction with the side edges of the waveguide are important. The experiments and the numerical simulation of the evolution of the spin-wave excitations show that the shape of the formed packets and their behavior are strongly influenced by the confinement conditions. The discovery of these modes demonstrates the existence of quasistable nonlinear solutions in the transition regime between one-dimensional and two-dimensional wave packet propagation.

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.

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.

Parametric generation of forward and phase-conjugated spin-wave bullets in magnetic films

We show experimentally as well as by numerical simulation that interaction of a linear two-dimensional spin-wave packet with quasiuniform pulsed pumping leads to the formation of strongly self-focused nonlinear spin-wave bullets propagating in both forward and reversed directions. The focusing of the reversed, phase-conjugated wave bullet is stronger than that of the forward one, because not only the nonlinear four-wave self-focusing effect but also linear focusing due to two-dimensional phase conjugation contributes to the focusing of the reversed bullet.

Tunneling of dipolar spin waves through a region of inhomogeneous magnetic field

We show experimentally and by numerical simulations that spin waves propagating in a magnetic film can pass through a region of a magnetic field inhomogeneity or they can be reflected by the region depending on the sign of the inhomogeneity. If the reflecting region is narrow enough, spin-wave tunneling takes place. We investigate the tunneling mechanism and demonstrate that it has a magnetic dipole origin.

Self-generation of two-dimensional spin-wave bullets

The experimental observation of self-generation of two-dimensional, self-focusing nonlinear spin wave packets-spin wave bullets-in an active ring is reported. The ring is composed of a ferrite film with two antennae for excitation and detection of the wave packets, and a microwave amplifier connecting the antennae and closing the ring. Experimental observation has been made by using the time and space resolved Brillouin light scattering technique. The parameters of spin wave bullets self-generated from noise in an active ring are similar to those of bullets coherently excited by external microwave pulses. The observed self-generation process provides unambiguous evidence that wave bullets are intrinsic excitations of a two-dimensional nonlinear medium with dissipation that is focusing in both directions.

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.

Wave front reversal of a dipolar spin wave pulse in a nonstationary three-wave parametric interaction

The effects of wave front reversal and inversion of the time profile are observed experimentally for a dipolar spin wave pulse (carrier frequency omega(1)) interacting in a yttrium-iron garnet film with a weakly localized nonstationary parametric pumping (carrier frequency omega(p) congruent with 2omega(1)) in a three-wave process with conservation law omega(p) = omega(1)+omega(2), where omega(2) is the carrier frequency of the reversed pulse. Theoretical analysis based on the solution of the system of equations for envelopes of interacting wave packets by means of a Green's function formalism gives a quantitative description of the observed phenomena.