Magnetostatic Forward Volume Wave Research Articles

Enhancement of a spin-wave self-focusing by a pulsed flat-top excitation field in a multi-domain state

We investigate a spin-wave (SW) self-focusing in a ferromagnetic FePd thin film with a perpendicular magnetic anisotropy by using micro-magnetic simulation. In a one-dimensional structure, a point-excitation of forward volume magnetostatic waves leads the SW propagation in the form of a wave packet. When SWs are excited over a wide area with a uniform amplitude distribution, the SW propagation occurs by taking not only a diverging component but also a focusing-like component. Interestingly, we can increase the focusing effect by reflecting the diverging waves at the magnetic phase boundary, such as domain walls. This SW focusing appears also in a two-dimensional system, and, furthermore, magnetic droplets can be easily formed at the focal points when the focused SW intensity exceeds an appropriate threshold. Based on these results, we can propose the flat-top excitation of the magnetostatic waves as an efficient way to generate the SW self-focusing and also to create magnetic droplets in a multi-domain state of perpendicularly magnetized systems.

Mode conversion characteristics of multimode magneto-optical Bragg diffraction cells

We study the dependence of magneto-optical (MO) coupling coefficients on the modal fields for the design of multi-mode MO Bragg cells. The mode conversion and diffraction efficiencies between the same order TM and TE modes can theoretically be up to about 98% by adjusting the excitation frequency of the fundamental-mode magneto-static forward volume wave (MSFVW) in the bismuth-substituted yttrium iron garnet film at the optimized thickness and length. The different order mode conversion is also available by means of the higher-mode MSFVWs. The resulting mode conversion-based switch function is discussed.

Fresnel diffraction of spin waves

The propagation of magnetostatic forward volume waves excited by a constricted coplanar waveguide is studied via inductive spectroscopy techniques. A series of devices consisting of pairs of sub-micrometer size antennae is used to perform a discrete mapping of the spin wave amplitude in the plane of a 30-nm thin YIG film. We found that the spin wave propagation remains well focused in a beam shape of width comparable to the constriction length and that the amplitude within the constriction displays oscillations, two features which are explained in terms of near-field Fresnel diffraction theory.

Spin wave absorber generated by artificial surface anisotropy for spin wave device network

Spin waves (SWs) have the potential to reduce the electric energy loss in signal processing networks. The SWs called magnetostatic forward volume waves (MSFVWs) are advantageous for networking due to their isotropic dispersion in the plane of a device. To control the MSFVW flow in a processing network based on yttrium iron garnet, we developed a SW absorber using artificial structures. The mechanical surface polishing method presented in this work can well control extrinsic damping without changing the SW dispersion of the host material. Furthermore, enhancement of the ferromagnetic resonance linewidth over 3 Oe was demonstrated.

Spin-wave logic devices based on isotropic forward volume magnetostatic waves

We propose the utilization of isotropic forward volume magnetostatic spin waves in modern wave-based logic devices and suggest a concrete design for a spin-wave majority gate operating with these waves. We demonstrate by numerical simulations that the proposed out-of-plane magnetized majority gate overcomes the limitations of anisotropic in-plane magnetized majority gates due to the high spin-wave transmission through the gate, which enables a reduced energy consumption of these devices. Moreover, the functionality of the out-of-plane majority gate is increased due to the lack of parasitic generation of short-wavelength exchange spin waves.

Confinement of magnetostatic forward volume waves in two-dimensional magnonic crystals with line defects

The mode patterns of magnetostatic forward volume waves (MSFVWs) propagating in two-dimensional magnonic crystals with line defects via periodic variation in thickness of square lattice in a yttrium iron garnet thin film are reported. The theoretical approach based on Walker's equation was employed to analyze the confinement of MSFVWs in the line defects. A good agreement between the theoretical predictions and the experimental results was obtained.

Self-oscillation of standing spin wave in ring resonator with proportional-integral-derivative control

We report on numerical analysis on self-oscillation of standing spin wave excited in a nanostructured active ring resonator, consists of a ferromagnetic nanowire with perpendicular anisotropy. The confined resonant modes are along the nanowire length. A positive feedback with proportional-integral-derivative gain control was adopted in the active ring. Stable excitation of the 1st order standing spin wave has been demonstrated with micromagnetic simulations, taking into account the thermal effect with a random field model. The stationary standing spin wave with a pre-determined set variable of precession amplitude was attained within 20 ns by optimizing the proportional-integral-derivative gain control parameters. The result indicates that a monochromatic oscillation frequency fosc is extracted from the initial thermal fluctuation state and selectively amplified with the positive feedback loop. The obtained fosc value of 5.22 GHz practically agrees with the theoretical prediction from dispersion relation of the magneto static forward volume wave. It was also confirmed that the fosc change due to the temperature rise can be compensated with an external perpendicular bias field Hb. The observed quick compensation time with an order of nano second suggests the fast operation speed in the practical device application.

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.

Complete band gaps for magnetostatic forward volume waves in a two-dimensional magnonic crystal

We report on the formation of a complete band gap for spin waves in a two-dimensional magnonic crystal consisting of a periodic hole lattice. We go beyond the partial band gaps observed so far in that we apply a magnetic field perpendicular to the permalloy thin film. We explore the relevant geometrical parameters using micromagnetic simulations. In nanopatterned devices we obtain complete band gaps of up to 1.4 GHz. The magnetostatic forward volume waves addressed here overcome in particular spin-wave localization effects. These effects have led to complicated and highly anisotropic miniband formation or Bragg reflection in in-plane fields for a long time. We demonstrate how direct band-gap tailoring via geometrical lattice symmetries becomes possible in nanostructured magnetic antidot lattices.

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.

A cut-off millimeter wave resonator technique for mapping magnetic parameters in hexagonal ferrites

A high-frequency technique (50 GHz) for determining the magnetic parameters from localized excitations in magnetic materials has been proposed and used for the case of barium hexaferrites. The technique involves the formation of a cut-off resonator in a metal iris–ferrite–metal structure in which magnetostatic forward volume waves are excited only in the region under the iris. Magnetic and high-frequency parameters obtained for barium hexaferrite are in agreement with previously reported values. The possibility of extending the technique for mapping magnetic parameters for films on large substrates is discussed.

Magnetic and Dielectric Excitations in the W-Band in Aluminum Substituted Barium and Strontium Hexaferrites

Single crystal strontium and barium hexaferrites in which Al is substituted for Fe have uniaxial anisotropy fields on the order of 20-30 kOe and have magnetic excitations at 75-110 GHz. Here, we discuss results of investigations on magnetostatic forward volume waves and dielectric resonances in such ferrites. Data on the mode frequencies were utilized to characterize the ferrites in terms of saturation magnetization, anisotropy field, gyromagnetic ratio, dielectric permittivity, and dielectric and magnetic losses. A refined theory of magnetostatic forward volume waves with explicit characteristic equation for the dominant mode is presented. The estimates on the mode characteristics are in very good agreement with the data.

Characteristics of microwave magneto-optic modulation based on magnetostatic waves

According to the magneto-optic (MO) perturbation theory, the coupled-mode equations for guided optical waves (GOWs) with microwave magneto-static waves (MSWs) in MO film waveguides are presented, which cannot only be used to analyze the MO modulation induced by MSW pulses, but also explain the optical pulse compression caused by chirped MSWs. The rectangular pulse modulation of continuous guided optical waves by magnetostatic forward volume waves (MSFVWs) excited under normal bias magnetic field is theoretically studied in detail. It is shown that: (1) the diffracted light pulse approximates to an isosceles trapezoid, which is in agreement with the experimental results, and the duration time and the flat-top response time are equal to the sum and difference between the width and transit time of the rectangular MSFVW pulse, respectively; (2) utilizing a small duty factor of MSFVW pulse helps to improve the modulating data rate, which is in inverse proportion to the transit time, and the relative peak intensity of the diffracted light pulse is less than the corresponding Bragg diffraction efficiency when the MSW duty factor is less than 0.5.

Magnetostatic-Wave-Based Magneto-Optic Pulse Compression by Control of Phase Mismatching

Microwave magnetostatic waves (MSWs) as moving gratings in magneto-optic (MO) film can lead to the Bragg diffraction of guided optical waves (GOWs). The MO coupling characteristics are responsible for the amplitude and phase frequency spectra of diffracted pulses and even result in the compression of chirped optical pulses in time domain. We theoretically investigate the noncollinear diffraction of linearly chirped Gaussian optical pulses by continuous magnetostatic forward volume waves in detail. For a given chirped optical pulse, with the increase of phase-mismatching slopes, the compression efficiency (CE) is gradually improved up to the maximum followed by the transition of diffracted pulses from single peak to multi peaks. The larger the chirp parameter is, the smaller the required phase-mismatching slope to achieve the maximal CE is. However, the rise of the chirp parameter or phase-mismatching slope reduces the relative peak intensity of the diffracted pulse. Lastly, it is pointed out that the phase-mismatching slope can be greatly increased by using the high-order modes of MSWs and GOWs.

DIFFRACTION EFFICIENCY ENHANCEMENT OF GUIDED OPTICAL WAVES BY MAGNETOSTATIC FORWARD VOLUME WAVES IN THE YTTRIUM-IRON-GARNET WAVEGUIDE COATED WITH PERFECT MENTAL LAYERS

The diffraction efficiency (DE) of guided optical waves (GOWs) and the magneto-optic (MO) −3 dB bandwidth are key parameters in MO Bragg cells. To improve the diffraction performance, the MO Stokes interaction between magnetostatic forward volume waves (MSFVWs) and GOWs are studied by use of the coupledmode theory in metal clad yttrium-iron-garnet (YIG) waveguides. Our analysis shows that, by adjusting the spacing of the metal layer from the ferrite surface, (1) the DE can be further increased by 7.32 dB compared with that of the inclined magnetization, but the MO bandwidth will be dropped down to the low level in the optimizing waveguide configuration; (2) when the DE and the MO bandwidth should be considered synthetically, a DE improvement of 3.9 dB with a bandwidth about 560 MHz is achieved corresponding to the large gainbandwidth product. Thus, the YIG waveguide coated with perfect metal layers can be used to improve the performance of MO Bragg cells.

Coupling between guided-wave optical modes—a dynamical system model

We provide a derivation of bidirectional coupled-mode equations from Maxwell's equations. The theoretical description of the collinear magneto-optical interaction of magnetostatic forward volume waves with guided optical modes is generalized. Its behavior is expressed using solutions to the coupled-mode equations. In some cases, applying the conservation of energy yields exact solutions that can be formed in terms of elementary transcendental functions. The auxiliary function method is used to find a series solution based on the solution of the homogeneous boundary value problem. Using the derived solutions, simulations show that the parallel antiparallel magneto-optical interaction bandwidth and structure can be tuned through selection of power applied to two transducers. They also show that equivalent mode power conversion can take place in half the propagation distance for parallel anitparallel magneto-optical interaction compared to pure traveling wave magneto-optical interaction.

Multiple Diffractions of Guided Optical Waves with Multifrequency Magnetostatic Forward Waves in Magnetooptic Film Waveguides

The multifrequency diffraction effects of guided optical waves with multiple magnetostatic forward volume waves (MSFVWs) excited in magnetooptic (MO) film waveguides under a normal bias magnetic field are theoretically studied for the first time. Multifrequency MO coupled-mode equations and the analytic solution for small-signal approximation are presented. It is shown that, in the small-signal case, the second or higher order diffraction can be neglected in multifrequency MO coupling and the principal diffraction efficiency (PDE) is proportional to the MSFVW power. Thus, the method of determining the small-signal or linear dynamic range is very important for the design of MO spectrum analyzers. The process of multiple diffractions caused by two MSFVW signals in a third-order MO coupling approximation is analyzed in detail. The small-signal limit can be determined according to the MSFVW power dependences of the PDEs, instead of those of the depletions. The multi-frequency diffraction theory can be applied to the quantitative evaluation of linear and nonlinear effects occurring in MO multi-frequency applications.

Magneto-Optic Coupling Theory for Guided Optical Waves andMagnetostatic Waves Using an Arbitrarily Tilted Bias Magnetic Field

We report the magneto-optic (MO) coupling interaction of guided opticalwaves (GOWs) with magnetostatic waves (MSWs) in MO film waveguidesusing arbitrarily tilted bias magnetic fields. The universal MOcoupled-mode equations are obtained and can be applied to the collinearor noncollinear interactions of the GOWs with magnetostatic forwardvolume wave (MSFVW), magnetostatic backward volume wave (MSBVW) andmagnetostatic surface wave (MSSW). As a typical example, thenoncollinear diffraction interaction of the GOW with the MSFVW excitedby single-element microstrip line transducer in the yttrium-iron-garnet(YIG) film is analysed in detail. For the case of normal magnetization,the calculated plot is consistent with the experimental results in thefirst passband. By comparison, the diffraction efficiency (DE) canfurther be improved by optimizing the magnetization direction. Themaximum DE gain can reach 5.7 dB under the appropriately inclined biasmagnetic field at φ = 180 degrees and θ = 9 degrees.

Electrodynamic theory of multiport structures using magnetostatic waves in ferrite films and its applications

The paper presents an electrodynamic analysis of tunable multiport ferrite-dielectric structures with parallel transmission lines of an arbitrary type, coupled through propagating magnetostatic modes of magnetized multilayered ferrite films. The structures are supposed to be excited at one port by an incident electromagnetic wave, and amplitudes and phases of electromagnetic waves at other ports are obtained by an analytical procedure. The model holds for an arbitrary direction of a magnetizing field and describes the interaction of magnetostatic modes in ferrite films of a finite width. The solution is obtained in a self-consistent approach, i.e., a reaction of magnetostatic waves (MSWs) on transducers, which excite them, is taken into account. Derived closed-form expressions for response functions of multiports provide the base for the modeling of a wide class of MSW devices: multichannel adjustable filters and delay lines, directional couplers, frequency-selective power dividers, tunable oscillators and active filters, and multiport resonators. The theory is also valid for the analysis of multi-element, interdigital, and meander MSW transducers. Applications of a general theory are demonstrated for numerical calculations of frequency responses of surface and forward volume MSW filters, delay lines with new types of strip-line transducers (two-port and T-type), and for the analysis of a phenomenon of mutual coupling of transducers in conventional devices.

Excitation and Reception of Electromagnetic, Magnetostatic and Spin Waves in Ferrite Films

The paper presents a new universal formulation of electromagnetic fields in microwave ferrite-dielectric waveguiding structures from the given magnetic field distribution of an external source. The solution is derived from the linearized Landau-Lifshits equation using an orthogonality condition for eigenwaves of a magnetization. The magnetization excited in ferrite is obtained in an electrodynamic, magnetostatic or dipole-exchange approximation, depending on the approximation used for eigenwaves. Results are applied for the formulation and the analytical solution of self-consistent electrodynamic problems of an excitation and a reception of waves in ferrite films by transmission lines of an arbitrary type. Numerical calculations are performed for filters and delay lines on the base of symmetric strip-lines using surface and forward volume magnetostatic waves in ferrite films.