Backward Volume Magnetostatic Waves Research Articles

Спиновые волны в одномерных магнонных кристаллах с двумя пространственными периодами

The propagation of surface and backward volume magnetostatic waves in a one-dimensional magnonic crystal in the form of a yttrium iron garnet film with two periodic lattices of grooves with different periods etched on its surface was experimentally studied. It is shown that the form of the frequency dependence of the transmission coefficient of magnetostatic waves in such crystal is not a simple superposition of similar dependences for two magnonic crystals with the same lattice periods.

Giant sensitivity to magnetic field variation in the spin wave interferometer based on the system of exchange-coupled films of yttrium iron garnet

In this work, we present experimental data on the interference of backward volume magnetostatic wave (BVMSW) counter-propagating in the structure with two exchange-coupled yttrium iron garnet layers. The layers are engineered to have different saturation magnetization that gives a possibility to BVMSW resonantly interacting with exchange modes of the two-layer structure. The BVMSW is excited by two antennas placed on top of the structure, while the third one placed between them is used for the detection of inductive voltage V generated by waves superposition. It is shown that maximal changes of the output inductive signal δV with the variation of magnetic field δH occur if, first, the waves interfere destructively and, second, the frequency corresponds to the resonant interaction of BVMSW with the exchange waves. In this case, obtained data reveal large sensitivity S = δV/δH approaching S ≈ 267 dB/Oe in the vicinity ±0.1 Oe of the resonant field H. The observed high sensitivity is of great importance for the development of compact sensitive magnetometers operating at room temperature.

Cubic Anisotropy for a Reconfigurable Magnonic Crystal Based on Co2MnSi Heusler Alloy

We explore the possibility offered by magnetic materials with cubic anisotropy to realize reconfigurable magnonic crystals with a very simple geometry working at zero magnetic field. As a proof of concept, we use micromagnetic simulations to calculate the static and dynamic magnetic configurations of a squared antidot lattice made with ${\mathrm{Co}}_{2}\mathrm{Mn}\mathrm{Si}$ Heusler alloy having an anisotropy constant of about 17 \ifmmode\times\else\texttimes\fi{} ${10}^{3}\phantom{\rule{0.25em}{0ex}}{\mathrm{J}/\mathrm{m}}^{3}$. We show that the cubic anisotropy allows very different magnetic states to be obtained at remanence as a function of the direction of a saturation magnetic field, including quasiuniform remanent states that cannot be obtained in materials with the same magnetic parameters but without crystal anisotropy. This leads to the possibility to excite or extinct several quantized spin-wave modes whose frequencies can be tuned with the antidot dimensions. Reconfigurable magnetic states are demonstrated for antidot sizes in the range 300--350 nm for a ratio between the antidot size and spacing equal to 1/3. The transition between two different remanent states can be obtained with low-amplitude magnetic field (down to 3.5 mT) and with a switching time faster than 1 ns, which is of great interest for applications. Oppositely, for a particular orientation of the antidot lattice with respect to the cubic anisotropy axes, we also obtain a single stable remanent state independent of the saturation field direction. Finally, propagation properties and frequency band gaps in an antidot lattice with lateral antidot size of 100 nm are studied for frequency-filtering applications at remanence. Both magnetostatic surface waves and magnetostatic backward-volume wave configurations are explored for different positions of the microwave excitation with respect to the magnonic crystal.

Spin-wave excitation and critical angles in a hybrid photon-magnon-coupled system

We studied “strongly enhanced” excitations of magnetostatic spin-waves in a hybrid magnon-photon-coupled system consisting of an inverted split-ring resonator and an yttrium iron garnet film. The backward-volume magnetostatic wave, magnetostatic surface wave, forward-volume magnetostatic wave modes, as well as multiple mixed modes were observed according to the direction of externally applied magnetic fields with respect to the spin-wave propagation direction. From experimental measurements, we found that there exist certain characteristic angles, which is to say, critical angles (θc, ϕc), whereby the group velocity of the excited spin-wave modes reaches zero, along with a single ferromagnetic resonance peak. Furthermore, we analytically derived the critical angles as sinθc=(Heff/H){2−(1+μ0Ms/Heff)sin2ϕc}−1/2, where Heff is the effective magnetic-field strength, H the externally applied field strength, and μ0Ms is the saturation magnetization. This analytical form is in quantitative agreement with estimations from experimentally observed spin-wave modes. This work not only provides a better understanding of multiple-mode spin-wave excitations in given field directions with the help of photon-magnon coupling, but also offers better coupling controllability based on the change of the external magnetic field direction.

Volume Magnetostatic Spin Waves in 3D Ferromagnetic Structures

Propagation of volume spin magnetostatic waves in meander-shaped ferromagnetic films with vertically and horizontally coupled segments is studied. Conditions under which forward and backward volume magnetostatic waves simultaneously exist in the films are determined. Micromagnetic simulation and expansion in terms of plane waves are used to calculate internal effective magnetic fields and dispersion characteristics of the waves in such structures. Spectra of coupled waves in meander-shaped vertically coupled ferromagnetic films are studied. Prospects for application of the above structures in the development of magnonic elements are analyzed.

Dispersion of the magnetostatic volume waves in a medium with damping

In magnetostatic approximation of electrodynamics the dispersion relation for magnetostatic back-ward volume waves (MSBVW) in a ferrite film, placed in a constant longitudinal and transverse alternating magnetic field is obtained. The magnetic field, damping and temperature influence on the spectrum and dispersion characteristics of the MSBVW is regarded.

Experimental investigation of the wave profile excited by a narrow transducer in a dielectric–ferrite–dielectric structure

The results from an experimental study of the diffraction profiles of magnetostatic backward volume waves (MSBVW) excited by a finite linear transducer placed on the surface of tangentially magnetized ferrite film in a dielectric–ferrite–dielectric structure are presented. Theoretical calculations and experimental data are compared.

Magnonic Band Structure and Filtering Properties of Square Antidot Lattices in Different Configurations: A Micromagnetic Study

We present the results of advanced micromagnetic simulations, performed using the open-source GPU-accelerated code MuMax <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , on spin waves excitation and propagation in two-dimensional magnonic crystals consisting of Permalloy (Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> square antidot lattices. The magnonic band structure of samples having a fixed periodicity a = 200 nm and different sides of the square holes, ranging from 30 to 90 nm, has been analyzed in both the magnetostatic surface wave and backward volume wave configurations, encompassing the first three artificial Brillouin zones. A careful analysis of both the dispersive character and the spatial profile of the most prominent eigenmodes permits interpretation of the main features of the transmission spectra of the simulated samples, which can be considered tunable magnonic filters. General conclusions are drawn about the choice of the optimal geometry for the design of signal processing devices based on square antidot lattices.

Cross Junction Spin Wave Logic Architecture

Backward volume magnetostatic spin wave interference in ferromagnetic cross is explored. Spin waves are excited at the two input arms of the cross, interference signal amplitude, and phase are detected in the other two, output arms of the cross. Spin wave scattering defines the out of phase interference in the output arms of the cross: the constructive (destructive) interference is observed at different input wave phase shifts in different output arms of the cross. Numeric simulations are in a good agreement with experiment. Based on the observed interference, we propose the cross junction spin wave logic device that operates as an OR or NOR logic gates. Spin wave phase represents the logic information. Destructive and constructive interference in the cross center determines the phase of the device output.

Magnonic crystals-based tunable microwave phase shifters

Tunable microwave phase shifters using magnetostatic backward volume waves in yttrium iron garnet/gadolinium gallium garnet thin film-based one-dimensional (1-D) and two-dimensional (2-D) magnonic crystals (MCs) are reported in this paper. Large differential phase shifts with small insertion loss variations were achieved in the passbands neighboring the bandgaps by tuning of the bias magnetic field. Large phase tuning rates up to 13.48 °/(Oe cm) and 25.9 °/(Oe cm) together with small insertion loss variations of 2.08 dB/cm and 0.97 dB/cm were demonstrated in the 1-D and 2-D MCs, respectively. An excellent agreement between the measured and the calculated results based on Walker's equation was obtained.

Spin Wave Excitation and Propagation Properties in a Permalloy Film

Spin wave excitation and propagation properties in a permalloy were investigated using a vector network analyzer for the magnetostatic surface wave (MSSW) and magnetostatic backward volume wave (MSBVW) configurations. In the MSSW configuration, the excitation and transmission spectra show many peaks. They originate at the distance of antenna lines of the coplanar waveguide, and the waveguide design is important for selecting the excitation and transmission wave vectors of the spin wave. The attenuation length of the MSSW was estimated to be 7.1 µm, and the group velocity of the MSSW with a wave number of 0.26 µm-1 was estimated to be about 8.6 µm/ns for an external magnetic field of 20 mT. In the MSBVW configuration, however, the excitation spin wave spectrum shows a single peak, since many quantized peaks overlap. A transmission signal with a single peak was also detected, but this could be an artifact such as an induced current.

Two-Dimensional Magnonic Crystal With Periodic Thickness Variation in YIG Layer for Magnetostatic Volume Wave Propagation

The propagation characteristics of magnetostatic volume waves (MSVWs), namely, magnetostatic forward volume waves (MSFVWs) and magnetostatic backward volume waves (MSBVWs), in two-dimensional (2-D) magnonic crystals (MCs) with periodic thickness variation of square lattice in YIG layer are reported. The theoretical approach based on Walker's equation was employed to determine the bandgaps associated with the MSVWs. Experiments were conducted on a 2-D MC with periodic square lattices in YIG layer thickness to measure both the magnetic field-tuned and propagation direction-dependent bandgaps. A very good agreement between the measured and the calculated results was obtained.

Magnetic control of a meta-molecule

Metamaterials offer the prospect of new science and applications. They have been designed by shaping or changing the material of the individual meta-molecules to achieve properties not naturally attainable. Composite meta-molecules incorporating a magnetic component offer new opportunities. In this work we report on the interaction between a non-magnetic split ring resonator (SRR) and a thin film of yttrium iron garnet (YIG). Strong hybridized resonances are observed. While the SRR is characterized by a magnetic and electric resonance, in practice, it is found that the YIG couples strongly to this symmetric (electric) mode of the SRR. It is also demonstrated that the anti-crossing region provides fertile ground for the creation of elementary excitations such as backward volume magnetostatic waves.

Hot spin-wave resonators and scatterers

A method used to achieve efficient optical control of a spin wave system in yttrium iron garnet is described. Using a focused laser beam, spin wave resonators and reflectors are induced by controlled local thermal demagnetization of a thin film. We report on the formation of an optically induced potential well for magnetostatic surface spin waves (MSSWs) leading to the formation of a high-Q MSSW resonator, and a high potential barrier that efficiently reflects magnetostatic backward volume waves.

Application of the smith chart in the analysis of the relaxation properties of magnetostatic oscillations and spin waves in ferrite films

The relaxation properties of three main types of magnetostatic oscillations in a magnetostatic film resonator and nonlinear processes (parametric excitation of spin waves in the first and second bands in the presence of the tangential magnetization of the gallium-substituted yttrium-iron garnet film and foldover in the regime of normal magnetization) are studied in the frequency range 0.8–4.5 GHz. An original method is proposed for the determination of thresholds of the parametric excitation of spin waves using the deformations of Smith chart caused by variations in the measurement power level. The method is used in the highaccuracy analysis of the frequency dependences of threshold power in the presence of tangential magnetization in the regimes of resonances of both surface and backward volume magnetostatic waves. The frequencyfield dependences of the absorption spectra of three main types of magnetostatic oscillations in the linear regime are used to determine the saturation magnetization, anisotropy fields, and unloaded Q factors of resonator at each mode and to calculate the relaxation parameters of the corresponding magnetostatic oscillations. The experimentally measured threshold pump powers are used to calculate the relaxation line widths of the parametrically excited spin waves with the aid of the improved theory of parametric processes that takes into account both cubic and uniaxial anisotropy of the film.

Simultaneous observation of magnetostatic backward volume waves and surface waves in single crystal barium ferrite platelets with in-plane easy axis

Resonances corresponding to backward volume magnetostatic waves as well as magnetostatic surface waves have been observed in single crystal barium hexaferrite rectangular platelets with in-plane easy axis. Samples placed directly on waveguide wall or on a quartz substrate show a surface mode. A series of backward volume wave modes in the U-band are observed, with the sample placed on quartz showing a relatively few modes. Data on H-dependence of the mode frequency have been obtained for both kinds of magnetostatic waves and theoretical estimates of the mode frequencies are in reasonable agreement with the data. Quality-factor for the modes is in the range 400-750. The results are of interest for non-reciprocal ferrite devices in the U-band.

Propagation Characteristics of Magnetostatic Volume Waves in One-Dimensional Magnonic Crystals with Oblique Incidence

The propagation characteristics of magnetostatic volume waves (MSVWs), namely, magnetostatic forward volume waves (MSFVWs) and magnetostatic backward volume waves (MSBVWs), in one-dimensional (1-D) magnonic crystals (MCs) with oblique incidence are reported. The theoretical approach based on Walker's equation was used to analyze the bandgaps associated with the MSVWs. Experiments were conducted on a 1-D MC with periodic structure in YIG layer thickness to measure the bandgaps in the MSFVWs and the MSBVWs with the incident angles at 0, 14, and 25 degrees, and at 1650 and 1385 Oe bias magnetic fields, respectively. An excellent agreement between the measured and the calculated results was achieved.

Magnetostatic correlator of microwave signals with the internal wave front reversal

A new technique of the correlation processing of data based on the nonlinear interaction of signals of backward volume magnetostatic waves in yttrium-iron garnet thin films and a corresponding laboratory mock-up of the correlation receiver operating in the 6 cm wavelength range have been presented in this paper. It was proposed to use additional pumping pulse for obtaining a time-reversed signal pulse. The resultant correlation signal occurred during the nonlinear interaction of the delayed signal wave and the pumping-reversed wave. The specificity of the passage of broadband signals through the resonance system of waveguide of spin waves was taken into account. It has been found out that the resonance properties of the correlator affect the efficiency of the desired signal separation from the noise level. The resultant signal-to-noise ratio for the output signal was enhanced by more than 20 dB.

Influence of the amplitude and phase nonlinearity of a spin-wave delay line on the wideband chaotic microwave generation

Regimes of wideband chaotic microwave generation have been studied in a self-oscillating ring system with a nonlinear delay line, in which magnetostatic backward volume waves (MSBVWs) are excited. It is established that a change in length of the delay line influences on its amplitude and phase nonlineartity, thus making it possible to control the characteristics of the chaotic microwave signal generated in the ring. It is demonstrated for the first time that a wideband chaotic microwave signal with a continuous spectrum and a nearly Gaussian probability density distribution can be generated by exciting MSBVWs in a self-oscillating ring system with a nonlinear delay line based on single ferromagnetic film.

Anomalous Doppler effect observed during propagation of magnetostatic waves in ferromagnetic films and ferrite-dielectric-metal structures

The anomalous Doppler effect observed during propagation of magnetostatic backward volume waves in a free ferromagnetic film and magnetostatic surface waves in a ferrite-dielectric-metal structure is investigated. The effect is theoretically substantiated, and plots of Doppler frequency shift are constructed. The anomalous Doppler effect is qualitatively analyzed with the use of equifrequency curves.