Theory of magnetostatic waves in moving ferrite films andapplications to rotation rate sensing

A first-order field theory for electromagnetic waves in moving ferrites and ferrite thin films is presented. The dominant effect of the motion is found to be the Doppler-shifted frequency observed in the moving frame. This gives rise to an anomalously large shift in wavenumber, due to the dispersive nature of the ferrite medium. Because of the large effect, it is suggested that a moving-medium experiment using magnetostatic waves could be used to distinguish between various competing forms for the dispersion term in the Fresnel-Fizeau coefficient. The results of the field theory are discussed with relation to relative and absolute rotation rate sensing. The author describes how magnetostatic waves could be used to measure relative rotation rates if confined to propagate around the perimeter of a rotating disk. Since the phase shift would be established in the time required to propagate around the disk, the response time could be significantly shorter than conventional tachometers. An experiment with counterpropagating magnetostatic waves is suggested to clarify the effect of a magnetic medium on the magnitude of the Sagnac effect     

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.     

The magnetostatic waves in ferrite film with losses

The influence of relaxation processes on dispersion equation solutions for surface and volume magnetostatic waves (MSW) propagating in a ferrite film is theoretically investigated. It is shown that dissipation is the main reason for the appearance of complementary MSW branches in frequency intervals which adjoin standard branches in spectra. The existence of threshold MSW wave numbers which upper bound the spectra of possible wave numbers is established. Asymptotic frequencies anf frequencies corresponding to the threshold values of wave numbers are calculated. The effects of dissipation on the ranges in which MSW exist are calculated. The frequency dispersion of the loss spectra is also calculated     

Efficient analysis of magnetostatic surface waves in printed andsuspended ferrite loaded strip lines

This paper analyzes the guidance of magnetostatic surface waves (MSSW) by a metallic strip printed on a ferrimagnetic slab or on a dielectric/ferrimagnetic structure (suspended configuration) in the frame of the magnetostatic approach. An integral spectral domain analysis (SDA) is used for this purpose. Shielding upper and/or lower ground planes are also considered. Some interesting new physical effects, such as backward and complex MSSWs in the suspended configuration are reported. Good agreement with previously published experimental and computed results confirms the validity of our approach     

The magnetic-wall effect on the characteristics of magnetostatic waves in an in-plane magnetized ferrite plate

The effect of the magnetic-wall boundary condition on the isofrequency and dispersion characteristics of magnetostatic waves propagating in an in-plane magnetized ferrite plate (film) is investigated. The situations are analyzed where this condition is satisfied on one of the ferrite’s surfaces and at a certain distance from it. It is found that, over the same frequency interval, such a structure supports several different types of waves simultaneously: bulk waves, surface waves, and waves whose amplitude is constant across the thickness of the ferrite film. The boundaries of the regions where bulk or surface waves propagate are determined. It is shown that a unidirectional wave propagates along the optical axis when the magnetic-wall boundary condition is satisfied on the ferrite’s surface. This means that energy is transported in the film in a single direction and cannot be transported in the opposite direction.     

Directional coupling of magnetostatic surface waves in layered magnetic thin films

The propagation characteristics of magnetostatic surface waves (m.s.s.w.) in a layered system of y.i.g. film, dielectric, y.i.g. film, are theoretically investigated. It is shown that the directional coupling of m.s.s.w. is possible between y.i.g. films. The directional coupling has frequency filtering characteristics due to dispersion of m.s.s.w.     

Standing spin waves in ferromagnetic thin films

A theory of spin wave resonance in ferromagnetic thin films is discussed in a manner that permits a computation of the real and imaginary parts of the circularly polarized RF fields as well as the power absorption spectrum. The case of the dc field intensity applied normal to the surface of the film is considered, and the saturation magnetization is taken as constant throughout the body of the film. Variations in dc fields near the surfaces are treated in the boundary conditions for the RF magnetization by considering the unsymmetrical nature of the exchange interaction at the surfaces. The boundary conditions are characterized by a constant for each surface that controls the degree of surface pinning in the RF magnetization. Damping is included in the formulation by means of a phenomenological constant in the spin wave equation and by simulaneous solution of this equation with Maxwell's equations for a conductor. The results of a computer program are presented showing the roles of the various parameters in determining the power absorption spectrum and RF fields. A comparison with experimental spectra is made, and an anomalous resonance at field intensities higher than that for the principal resonance is predicted.     

Analysis of the distribution of magnetostatic surface waves by scanning the surface of a ferrite slab

A technique for the experimental visualization of the distribution of the amplitudes and phases of the magnetostatic waves propagating in ferrite-film structures is developed. It is shown that applying the Fourier transform to the data obtained with the use of this technique, it is possible to investigate the mode composition of the magnetostatic waves and find dispersion dependences for each mode. On the basis of the proposed technique, distributions of magnetostatic surface waves in bilateral samples of ferrite films are investigated. It is found that, at a wavelength comparable with the substrate thickness, the ferrite film at the opposite side of the substrate significantly changes the wave distribution in the sample and causes spatial beating along the propagation axis.     

Propagation of magnetostatic surface waves in a ferrite plate magnetized by a spatially periodic transverse field

Propagation of magnetostatic surface waves (MSSWs) in a ferrite plate magnetized by a spatially periodic transverse field has been considered. The parameters of MSSW propagation have been calculated by the Hamilton-Auld method. It is shown that only noncollinear MSSWs, whose wave-beam trajectories as well as wave numbers and angles, which determine the directions of the vectors of the phase and group velocities, are described by functions that are periodic in the direction of the wave propagation, can exist in this field. The period of these functions is determined by the period of the spatially periodic field. The frequency range of existence of the collinear waves is narrower than that of the waves in a uniformly magnetized plate. The characteristics of wave propagation in a nonuniform spatially periodic field are compared to the characteristics of wave propagation in nonuniform fields of known types.     

RF relaxation oscillations in polycrystalline TiO2 thin films

Negative resistance oscillations were studied in polycrystalline TiO₂ thin films in the TiTiO₂Cr device structure. Stable oscillations were readily produced in the 1–3 MHz frequency range and showed lifetimes of more than 8 × 10¹¹ cycles. A simple equivalent circuit model for current controlled negative resistance (CCNR) devices was used to interpret the bias voltage and temperature dependence of amplitude and frequency of negative resistance oscillations. Bias voltage dependence was found not to involve changes in the device parameters. Temperature variations produced changes in the device threshold and minimum (holding) voltages and the “on” and “off” state resistances. The “on” state and “off” state resistances showed thermal activation energies of 0.006 and 0.052 eV respectively. I-V characteristics for these devices are shown to be in agreement with the theory of filamentary double injection space charge limited currents.     

Control of magnetostatic waves in thin films by means of spatially nonuniform bias fields

Although magnetostatic wave devices normally employ spatially uniform magnetic bias, control of important features of the modes is afforded through judicious use of dc field gradients. Such control can be the basis for new forms of microwave signal processors.Gradients in either the field magnitude, direction, or both can be employed to affect wave dispersion or mode spectra. This is done to control prespecified characteristics such as frequency, rf energy distribution, impedance, and the velocity of energy propagation.Very general mathematical analyses of both the forward volume wave and surface wave geometries are developed for cases where the effective magnetic bias has, depending upon the mode, transverse spatial variation along either the ferrite film width or thickness caused by the applied field, saturation magnetization, magnetic anisotropy — or some combination.Computer simulation has been used to obtain eigenfrequencies and eigenmodes when the bias is uniform or nonuniform. The latter cases reveal that a great deal of control over the mode energy distributions can be exercised by the proper choice of gradients. For example, a forward volume wave can be forced to have strong field-displacement characteristics that are either nearly reciprocal or very strongly nonreciprocal.This research was supported, in part, by the Joint Services Electronic Program (JSEP) under Contract DAAG29-83-K-0003 administered by the Research Laboratory of Electronics (RLE); the National Science Foundation under Grant 8008628-DAR; and STAS 0356 administered by the Battelle Research Triangle Park Office.     

Effect of a magnetic wall and a conducting plane on the characteristics of magnetostatic waves in an in-plane-magnetized ferrite plate

The dispersion relations for an in-plane-magnetized ferrite plate with an arbitrary combination of magnetic-wall or perfectly conducting plane boundary conditions imposed at a distance from the plate’s surfaces are compared. A rule is formulated so that a dispersion relation for one of the structures can be used to derive the equation for any other structure. The isofrequency and dispersion characteristics of magnetostatic waves in a metal/ferrite/magnetic-wall structure are investigated. It is found that, in this case, the waves are characterized not only by a unidirectional propagation over the entire range of their existence (～5 GHz) but also by the presence of a nearly straight section of the dispersion curve (～2 GHz). In this structure, volume waves, surface waves, and waves with an amplitude that is constant over the plate thickness are seen to exist within the same frequency interval.     

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.     

Parametric properties of the electron spin relaxation in InAs quantum dots

The electron spin relaxation rates Γ under different conditions in InAs quantum dots (QDs) with local elastic twists have been calculated by using the perturbation method. It is shown from the calculational results that the rate Γ is dominated by the magnitude of the absolute value of anisotropic electron g factor, and markedly influenced by the difference between the values of g_α, which indicates there is a proper size for InAs QDs to minimize the rate. The relaxation rate is noticeably affected by the orientations of the magnetic field n(θ,?), and the ratio of the rates can be obtained by changing orientations of the field in QDs, where the maximum in our calculation is Γ_max/Γ_min≈6.4.     

Simultaneous propagation of magnetostatic and spin-elastic waves in nonellipsoidal ferrimagnets

Spin-wave propagation parallel to the static biasing field is considered in the presence of magnetostatic boundary effects for a saturated nonellipsoidal ferrimagnet. It is shown that two principal branches exist in the delay-field characteristics, over the same biasing range, with delay decreasing monotonically with applied field. The predominantly magnetostatic branch is related to the experiments of Kedzie, the coupling mechanisms of wire antennas to spin waves, and observations on magnetostatic-mode parametric amplifiers.     

Comprehensive analysis of strip- and slot-line guided forward,backward, and complex magnetostatic waves

This paper presents a comprehensive and accurate analysis of the guidance of volume and surface magnetostatic waves by strips or slots in the presence of a ferrite slab magnetized to saturation by an external uniform magnetic field. The strip/slot can be directly printed on the ferrite surface or separated from it by means of a dielectric layer of arbitrary thickness. The problem is posed in terms of a suitable integral equation accounting for the magnetostatic limit. This equation is solved by using a spectral-domain formulation. The proposed method allows for the consideration of arbitrary magnetization angles and the presence of upper and/or lower ground planes. Strip-guided forward, backward, and complex surface magnetostatic waves have been obtained and analyzed in terms of the appropriate waveguide parameters. Slot-guided backward volume magnetostatic waves have been also computed and studied. Theoretical results have been checked against theoretical (magnetostatic and full wave) and experimental data available in the literature with reasonable agreement     

Dispersion of spin waves and magnetoelastic waves in YIG

Microwave pulse-echo experiments have been performed using YIG samples, and data are presented illustrating a variety of elastic, magnetoelasfic, and spin wave propagation phenomena. Both disks and rods of YIG were used, with excitation at X-band frequencies. The spin wave mode of propagation shows very strongly dispersive behavior when the spin wavelength is comparable to one of the sample dimensions. The group velocity is obtained from the magnetostatic mode spectrum of the appropriate configuration and is combined with the spatial variation of the internal magnetic field to compute the delay time. Exchange effects are important in the case of the disk and are included in the analysis. The agreement between theoretical and experimental delay times is quite satisfactory for all configuration.     

Effect of cobalt substitution on the optical properties of bismuth ferrite thin films

Effect of cobalt substitution on the band gap and absorption coefficient of the BiFeO₃ thin films formed on quartz substrate by low cost spin coating method have been investigated. BiFe_1−xCo_xO₃ (x=0, 0.03, 0.06 and 0.10) thin films are polycrystalline and it retains the rhombohedral distorted perovskite structure up to 10 mole % of Co substitution. Smooth and compact surface morphology with uniform size particles are observed in SEM micrographs. Narrowing and broadening of band gap is observed as a function of Co content. Two strong emission peaks at ~2.51 eV and ~2.38 eV are recorded for all films with noticeable change in intensity. Results obtained from the optical absorption and photoluminescence spectroscopy experiments have shown that there exists an inverse correlation between the variation in the band gap and the concentration of oxygen vacancies. Band gap decreased by ~100 meV and absorption coefficient increased by 28% at the wavelength of 375 nm in 6 mole % Co substituted thin film and these observations are necessary requirements to improve the efficiency of photovoltaic devices.     

Bragg resonances of magnetostatic surface waves in a ferrite-magnonic-crystal-dielectric-metal structure

Formation of Bragg resonances of surface spin waves (SSWs) propagating in a magnonic-crystaldielectric-metal (MC-D-M) structure is studied. It is shown that, in an MC-D-M structure with a finite dielectric interlayer of thickness t, Bragg resonances of the SSWs with the wavenumbers k < 1/t can be destroyed whereas the resonances of the SSWs with k > 1/t persist and lead to formation of rejection bands in the wave spectrum.     

Propagation of magnetostatic surface waves in multiple magnetic layer structures

The dispersion of magnetostatic surface waves (m.s.s.w.s) propagating in structures consisting of up to four magnetic layers has been calculated. The m.s.s.w. dispersion and velocity can be controlled by selecting layer thickness and magnetisation. Experiments performed with layered y.i.g. structures were in agreement with the analysis.