Backward Volume Spin Waves Research Articles

A current-controlled magnonic reservoir for physical reservoir computing

Physical reservoir computers based on principles of magnonics promise energy efficient data processing and a reduction in the size and weight of the neuromorphic computing devices. The present work is a major step toward all-magnonic implementation of the recently proposed concept of a physical reservoir based on the spin wave active ring. The main component of the ring is a spin wave delay line employing a thin film of yttrium iron garnet (YIG) as the spin wave guiding medium. We propose controlling spin wave propagation in the YIG film electronically to enter input data into the reservoir. To this end, we exploit a physical effect of scattering of backward volume spin waves from a highly localized Oersted field of a dc current flowing through a metallic strip sitting on top of the YIG film. We find experimentally that a very small current (on the order of several milliamps) through the strip is able to control the amplitude of auto-oscillations in the ring. The use of the current control of spin wave propagation as a means to enter input data into the reservoir reduces the number of non-magnetic components of the reservoir to just one (a microwave amplifier). In addition, the proposed current-controlled magnonic reservoir demonstrates a record-high short-term memory capacity of 5.53, as our experiments show. Our findings open up an avenue for reduction of energy consumption by magnonic active-ring-based physical reservoirs, their micro-miniaturization, and all-magnonic implementation.

Experimental methods for the study of spin waves

Purpose of this paper is to give an overview of various experimental methods for investigation of spin waves characteristics. Methods. The paper presents a description of a number of experimental techniques, such as the probing method, the phase shift method, the method of measure of equiphase dependences, the method of intersecting wave beams, and the use of Fourier analysis of the complex transfer coefficient of spin waves to determine their spatial spectrum. The conditions for using the listed methods and the characteristics of spin waves that one can measure by means of these methods are discussed in detail. Results. The paper presents a number of fundamental results that have been obtained on the basis of described methods. For example, the probing method was successfully used to visualize the amplitude and phase distribution of spin waves in the ferrite film plane and, in particular, it was used to experimentally confirm the previously predicted appearance of super-directed propagation of surface and backward volume spin wave beams. The phase-shift measurement method made it possible to measure the dispersion dependence of spin waves in ferrite structures such as ferrite – metal and ferrite – dielectric – metal, where measurements cannot be made by the probing method. The method of measuring equiphase dependences of spin waves made it possible, in particular, to measure for the first time with great accuracy the value of an external magnetic field magnetizing an yttrium iron garnet film to saturation in various crystallographic directions. The method of intersecting wave beams has made it possible to clarify the mechanism of parametric instability of surface spin waves. Fourier analysis of the complex transfer coefficient of spin waves allowed to determine the spatial spectrum of these waves; in particular, dispersion dependences of higher modes of the backward volume spin wave were first measured using this method. Conclusion. The methods described in this paper may continue to be successfully used for investigations of spin waves characteristics in various magnon crystals, ferrite structures and meta-structures.

Spin-wave interconversion via thermoelectric point-contact control

The magnonic functionalities of magnonic devices, such as logic gates, majority gates, and multiplexers, critically depend on anisotropic spin-wave dispersions. Further, each magnonic function utilizes the advantages of distinct spin-wave modes. However, thus far, no method of directly combining magnonic functions to construct an integrated magnonic circuit has been proposed. Therefore, this paper presents a method for the interconversion of surface spin-waves and backward volume spin-waves using a thermoelectrically controlled magnetization gradient. The results of time- and frequency-domain spectroscopies, heat transfer analyses, and micromagnetic simulations demonstrate the effectiveness of the proposed method, through which spin-wave interconversion via thermoelectric control may be employed to develop integrated magnonic circuits.

Experimental visualization of dispersion characteristics of backward volume spin wave modes

Basing on the measurement of spatial spectra (spectra of wavenumbers), the dispersion characteristics of the first three modes of backward volume spin wave, propagating along the direction of a constant uniform magnetic field in a tangentially magnetized ferrite film, were visualized firstly. The study was carried out by microwave probing of spin waves with subsequent use of spatial Fourier analysis of the complex wave amplitude for a series of frequencies. It was found that experimental spatial spectrum of the backward volume spin wave modes has a fine structure and every m-th mode splits into n closely located satellite modes appearing due to the existence of layers with similar magnetic parameters in ferrite film. It was found that satellites of the first mode of this wave are excited most effectively, while satellites of the third mode - least effectively, and the effectiveness of satellites excitation decreases as the number n increases. It is found that the theoretical dispersion dependencies of the first three modes of the wave coincide well with the experimental dispersion dependencies of the satellite modes that are excited most effectively.

Physical realization of complex dynamical pattern formation in magnetic active feedback rings

We report the clean experimental realization of cubic–quintic complex Ginzburg–Landau (CQCGL) physics in a single driven, damped system. Four numerically predicted categories of complex dynamical behavior and pattern formation are identified for bright and dark solitary waves propagating around an active magnetic thin film-based feedback ring: (1) periodic breathing; (2) complex recurrence; (3) spontaneous spatial shifting; and (4) intermittency. These nontransient, long lifetime behaviors are observed in self-generated spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide. The waveguide is operated in a ring geometry in which the net losses are directly compensated for via linear amplification on each round trip (of the order of 100 ns). These behaviors exhibit periods ranging from tens to thousands of round trip times (of the order of μs) and are stable for 1000s of periods (of the order of ms). We present ten observations of these dynamical behaviors which span the experimentally accessible ranges of attractive cubic nonlinearity, dispersion, and external field strength that support the self-generation of backward volume spin waves in a four-wave-mixing dominant regime. Three-wave splitting is not explicitly forbidden and is treated as an additional source of nonlinear losses. All observed behaviors are robust over wide parameter regimes, making them promising for technological applications. We present ten experimental observations which span all categories of dynamical behavior previously theoretically predicted to be observable. This represents a complete experimental verification of the CQCGL equation as a model for the study of fundamental, complex nonlinear dynamics for driven, damped waves evolving in nonlinear, dispersive systems. The reported dynamical pattern formation of self-generated dark solitary waves in attractive nonlinearity without external sources or potentials, however, is entirely novel and is presented for both the periodic breather and complex recurrence behaviors.

Spin current and spin waves at a platinum/yttrium iron garnet interface: impact of microwave power and temperature

The spectra of ferromagnetic resonance and spin current of the heterostructure consisting of an epitaxial film of yttrium iron garnet Y3Fe5O12 (YIG) grown on a gallium gadolinium garnet (Gd3Ga5O12) substrate and with 10 nm thick platinum (Pt) film on top were studied at frequencies f = 2–18 GHz under applied power in the range of 20 μW–50 mW as well as temperatures T = 77–300 K. The standing spin-wave resonances (SWRs) with both magnetostatic backward volume spin waves and magnetostatic surface spin waves (MSSWs) were detected. The SWR evolution was investigated with change of microwave power. Due to generation of spin current perpendicular to the Pt/YIG interface and the inverse spin Hall effect the charge current on the Pt film was registered and analyzed. The SWR resulted in deviations of spin current spectral lines from a Lorentz line form, indicating that at high microwave power the main contribution is made by MSSW. As the temperature decreases, the amplitude of the spin current decreases, although the width of the spectral line remains the same while the magnetization increases at lower temperatures. A decrease in spin Hall angle with cooling may explain this behavior of the spin current at low temperatures.

Implementing a Magnonic Reservoir Computer Model Based on Time-Delay Multiplexing

Recently we demonstrated experimentally that microwave oscillators based on the time delay feedback provided by traveling spin waves could operate as reservoir computers. In the present paper, we extend this concept by adding the feature of time multiplexing made available by the large propagation times/distances of traveling spin waves. The system utilizes the nonlinear behavior of propagating magnetostatic surface spin waves in a yttrium-iron garnet thin film and the time delay inherent in the active ring configuration to process time dependent data streams. Higher reservoir dimensionality is obtained through the time-multiplexing method, emulating "virtual" neurons as temporally separated spin-wave pulses circulating in the active ring below the auto-oscillation threshold. To demonstrate the efficacy of the concept, the active ring reservoir computer is evaluated on the short-term memory and parity check benchmark tasks, and the physical system parameters are tuned to optimize performance. By incorporating a reference line to mix the input signal directly onto the active ring output, both the amplitude and phase nonlinearity of the spin waves can be exploited, resulting in significant improvement on the nonlinear parity check task. We also find that the fading memory capacity of the system can be easily tuned by controlling the active ring gain. Finally, we show that the addition of a second spin-wave delay line configured to transmit backward volume spin waves can partly compensate dispersive pulse broadening and enhance the fading memory capacity of the active ring.

Spin Waves Interference under Excitation by Focusing Transducers: Logic and Signal Processing

Micro-focused Brillouin–Mandelstam light scattering technique and micromagnetic simulations were used to study surface (SSW) and backward volume (BVSW) spin waves (SW) interference under excitation by curvilinear focusing transducers placed oppositely to each other on a top of a tangentially magnetized yttrium iron garnet (YIG) film. It is shown that due to anisotropic propagation, the 2D interference patterns for both SSW and BVSW focused beams are nonreciprocal. Due to chromatic aberration and caustics formation of the focusing transducers, the interference pattern of the focused SW beams depends on the excitation frequency and is sensitive to local nonuniformities in the YIG film. The obtained results demonstrate the possibility to use curvilinear SW focusing transducers for information technologies based on magnonic optics.

Backward volume vs Damon–Eshbach: A traveling spin wave spectroscopy comparison

We compare the characteristics of electrically transduced Damon–Eshbach spin-wave (DESW) and backward volume spin-wave (BVSW) configurations within the same, 30 nm thick, ferromagnetic, CoFeB waveguide. Sub-micrometer U-shaped antennas are used to deliver the necessary in-plane and out-of-plane RF fields. We measure the spin-wave transmission with respect to in-plane field orientation, frequency, and propagation distance. Unlike DESW, BVSWs are reciprocally transduced and collected for either direction of propagation, but their ability to transport energy is lower than DESWs for two reasons. This arises first because BVSWs are inductively transduced less efficiently than DESWs. Also, in the range of wavevectors (∼5 rad μm−1) typically excited by our antennas, the group velocity of BVSWs stays lower than that of DESW, which leads to reduced propagation ability that impact transmission signals in an exponential manner. In contrast, the group velocity of DESWs is maximum at low fields and decreases continuously with the applied field. The essential features of the measured SW characteristics are well reciprocated by a simple, 1D analytical model, which can be used to assess the potential of each configuration.

Tracking the Suhl instability versus angle and frequency for the backward volume mode in an yttrium iron garnet film

Using parametric excitation, we have studied the minimum frequency associated with the backward volume (BV) spin wave branch in a thin film of the ferrimagnetic material yttrium iron garnet (YIG) for the magnetic field lying in plane and parallel to the wave vector as well as for out-of-plane field angles. We find that there is a drastic change in the efficiency of parametric excitation between two different pumping frequency regimes.

Nonreciprocity of backward volume spin wave beams excited by the curved focusing transducer

The focusing effect for spin waves excited by a curved micrometer-sized coplanar waveguide transducer on top of a 5-μm-thick epitaxial yttrium iron garnet film is studied by means of the micro-focused Mandelstam-Brillouin light scattering technique and micromagnetic simulations. The curvilinear transducer is designed to focus the backward volume spin waves on the in-plane bias magnetic field applied along the symmetry axis of the transducer. We show that two-dimensional maps of spin wave intensity exhibit nonreciprocal properties without mirror symmetry with respect to the magnetic field direction and the focusing effect. The observed effects are the consequence of nonreciprocity of the backward volume spin waves travelling at an angle toward the bias field direction.

Time-domain propagating spin-wave spectroscopy for forward spin waves in a ferromagnetic metal

We performed time-domain propagating spin-wave spectroscopy for forward spin waves in a ferromagnetic metallic waveguide in the presence of electric current. The forward spin waves exhibit a large propagation delay and a 35% amplitude change with a smaller current injection of 6 × 1010 A/m2, showing a 2 times larger modulation than backward volume spin waves. By measuring electric-current effects in 4 distinct experimental configurations, we found that a current-induced Doppler shift coincided with an Oersted field frequency shift under our experimental conditions. By separating the two phenomena, we evaluated each contribution on the propagating forward spin-wave packet.

Superdirected beam of the backward volume spin wave

Visualized patterns of the backward volume spin wave (BVSW) excited by arbitrarily oriented linear transducer in tangentially magnetized ferrite film are investigated experimentally in the plane of ferrite film for the case where the transducer length D is much larger than the wavelength λ0. Superdirected BVSW beam having zero angular width and minimal smearing of the beam energy along the film surface is observed experimentally. Thus, it is proved that such phenomenon as “superdirected propagation of the wave” exists in the nature.

Optical excitation of spin waves in epitaxial iron garnet films: MSSW vs BVMSW.

In most of the previous studies of the spin wave optical generation in magnetic dielectrics, the backward volume spin waves were excited. Here we modified the parameters of the circularly polarized optical pump beams emitted by femtosecond laser to reveal surface spin waves in bismuth iron garnet thin film. Beams that are larger than 10 μm in diameter generate both surface and volume spin waves with only one spectral peak near the ferromagnetic resonance. On the contrary, narrower beams excite predominantly surface spin waves of higher frequency, providing an additional peak in the spin wave spectrum. Thus different interference patterns of the magnetization dynamics are achievable. This may significantly broaden the capabilities of spin wave based devices.

Magnonic beam splitter: The building block of parallel magnonic circuitry

We demonstrate a magnonic beam splitter that works by inter-converting magnetostatic surface and backward-volume spin waves propagating in orthogonal sections of a T-shaped yttrium iron garnet structure. The inter-conversion is enabled by the overlap of the surface and volume spin wave bands. This overlap results from the demagnetising field induced along the transversely magnetised section(-s) of the structure and the quantization of the transverse wave number of the propagating spin waves (which are therefore better described as waveguide modes). In agreement with numerical micromagnetic simulations, our Brillouin light scattering imaging experiments reveal that, depending on the frequency, the incident fundamental waveguide magnonic modes may also be converted into higher order waveguide modes. The magnonic beam splitter demonstrated here is an important step towards the development of parallel logic circuitry of magnonics.

Propagating spectroscopy of backward volume spin waves in a metallic FeNi film

We report a propagating spin wave spectroscopy for a magnetostatic backward volume spin wave in a metallic Fe19Ni81 film. We show that the mutual-inductance between two independent antennas detects a small but clear propagation signal of backward volume spin waves. All experimental data are consistent with the time-domain propagating spin-wave spectroscopy. The control of propagating backward spin wave enables to realize the miniaturize spin-wave circuit.

Localized parametric generation of spin waves in a longitudinally magnetized Ni81Fe19 waveguide

We demonstrate that in a longitudinally magnetized Ni81Fe19 waveguide spin waves can be generated via parallel parametric generation by a microstrip antenna. By employing microfocus Brillouin light scattering spectroscopy, we show that this method provides an efficient excitation source for backward volume spin waves. We analyze the spatial distribution of the generated spin waves, proving that odd and even waveguide modes can be excited. Furthermore, we study the spin-wave propagation along the Ni81Fe19 waveguide, revealing that the generation process takes place underneath the antenna due to its threshold nature.

Direct Brillouin light scattering observation of dark spin-wave envelope solitons in magnetic films

The formation and evolution of dark spin-wave envelope solitons have been studied in a yttrium iron garnet (YIG) film. The Brillouin light scattering (BLS) technique has been used to map the propagation and evolution of the excited dark solitons. Experiments have been carried out using (1) a YIG-film delay-line structure supporting propagation of backward volume spin waves, (2) time- and space-resolved forward-scattering BLS, (3) a fixed magnetic field of 1000 Oe applied along the propagation direction, and (4) a soliton excitation technique based on the nonlinear interaction of two large amplitude cw input signals with fixed frequency enabling an induced modulation instability. Theoretical interpretation of the experiments based on numerical solution of the Ginzburg-Landau equation taking into account the conditions of nonlinear spin-wave dissipation is given. It is found that the dark soliton formation process involves competition between effects of nonlinearity and dispersion, and that nonlinear damping effects play an important role.

Generation of propagating backward volume spin waves by phase-sensitive mode conversion in two-dimensional microstructures

We present the generation of propagating backward volume (BV) spin waves in a T shaped Ni81Fe19 microstructure. These waves are created from counterpropagating Damon Eshbach spin waves, which are excited using microstrip antennas. By employing Brillouin light scattering microscopy, we show how the phase relation between the counterpropagating waves determines the mode generated in the center of the structure, and prove its propagation inside the longitudinally magnetized part of the T shaped microstructure. This gives access to the effective generation of backward volume spin waves with full control over the generated transverse mode.

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.