Yttrium Iron Garnet Sphere Research Articles

Photothermally modulated spatially resolved FMR detection of Walker modes in yttrium iron garnet spheres

The photothermally modulated (PM) ferromagnetic resonance (FMR) combines the high sensitivity of conventional FMR and spatial resolution. This technique has been applied to a single-crystalline yttrium iron garnet (YIG) sphere with a diameter of 2 mm. For the first time, the spatial variation of the high-frequency magnetization patterns known as Walker modes were visualized and it is thus shown that PM-FMR can even be applied to unfavourable geometries.

Large-signal stability and spectrum characterization of a medium power HBT using active load-pull techniques

Large-signal stability and spectrum characterizations of a half-watt HBT at 2 GHz for a class AB bias point are reported. Constant power, constant power-added efficiency, constant current gain contours, and second and third harmonic generation level contours over the whole Smith chart are presented. The characterization setup is an automated high power, multi-harmonic, active load-pull system that is based on six-port techniques and frequency discrimination using a controlled band pass YIG filter. >

Spin-wave chaotic transients

We report the observation of transient chaotic spin-wave auto-oscillations in X-band pulsed subsidiary-resonance experiments in a YIG sphere. Chaotic transients to a periodic attractor have been observed near a critical microwave power pc∼10 dB relative to the Suhl instability threshold. By an averaging of 100 randomly chosen initial conditions at each power, we estimate a critical exponent γ ∼ 0.57. In addition, we demonstrate that the results can be qualitatively understood within the framework of the standard two-mode model. Numerical simulations yield, for a particular set of parameters, chaotic transients obeying the predicted scaling law with a critical exponent γ ∼ 0.54.

Controlling spin-wave chaos

Microwave pumped spin-wave instabilities in YIG spheres were one of the first experimental systems used to demonstrate that chaos can be suppressed by small periodic modulations in an accessible system parameter. Here we show that the equations describing two interacting spin-wave modes account satisfactorily for the experimental results, as long as the field modulation is appropriately introduced in the model. The finite detuning parameters expressing the boundary conditions of the sample provide a natural way for introducing the field modulation. Thus the present results constitute additional evidence of the validity of the two-mode model with momentum-nonconserving driving Hamiltonian used to explain the sample size dependence of the self-oscillations.

Instability mechanism of collective spin wave oscillations in finite-size ferrite samples

A sample-size effect on spin wave auto-oscillations under parallel pumping is studied experimentally in tangentially magnetized rectangular samples of yttrium-iron garnet (YIG) films where one of the in-plane sizes is varied. A previously developed one-dimensional theoretical model of unstable collective oscillations in the system of parametrically excited spin waves is used to describe the mechanism of spin wave auto-oscillations observed in YIG films. Our results show that the one-dimensional model (that works well for YIG spheres) gives only qualitative description of the sample-size effect in YIG films and the incorporation of the second finite size (film thickness) in this model is needed to achieve quantitative agreement with experiment in the film geometry.

Fine structure and critical modes at the first-order Suhl instability in YIG spheres

The FMR fine structure of the first-order Suhl instability in YIG spheres, previously observed by Jantz and Schneider (1975), has been re-investigated both for the conditions of coincidence and subsidiary absorption (3 and 9 GHz) from room temperature down to 1.6K. The observed fine structure consists of several series of closely spaced resonances, indicating a critical wave vectork≠0 even for half the pumping frequency lower than the 45° spin-wave branch, which is in contrast to the prediction of Suhl's theory. The spacing of these resonances was analyzed in terms of spherical modes. We were able to determine the indices and the effective wave numbers (≈105 cm−1) of the critical modes. The very different dynamic behaviour observed at room temperature and at 1.6K can be attributed to a competition of different damping mechanisms—mainly surface pit scattering and three-magnon confluence processes — and their dependences on field, frequency, and temperature.

Multistability and chaos at parametrically excited spherical modes in an yttrium iron garnet sphere

The different behaviors observed in different regimes of field of recent high-power ferromagnetic resonance experiments on yttrium iron garnet spheres within the coincidence regime of the first-order Suhl instability, which showed a complex multistable behavior beneath auto-oscillations, are examined on the basis of a detailed model which utilizes the true eigenmodes of the sphere instead of plane spin waves.

Magnetic-field-induced intermittency in spin-wave experiments

Chaotic behavior in spin-wave systems is usually observed with the variation of the driving parameter, namely, the incident microwave power. A variety of interesting phenomena can occur if one keeps the power fixed beyond the auto-oscillation threshold and varies another available parameter. We demonstrate this with X-band subsidiary-resonance experiments in an yttrium iron garnet (YIG) sphere with varying dc magnetic field. Besides period-doubling bifurcations, intermittent temporal bursting resulting from the collision of neighbouring period-I and chaotic attractors has been observed. These phenomena are qualitatively investigated in the light of the theory of crisis in dissipative systems due to Grebogi, Ott, Romeiras, and Yorke. In addition, for fixed magnetic field and varying microwave power, we observe that transient periods prior to auto-oscillation have a power-law dependence on the driving parameter, similarly to crisis-induced phenomena at higher power levels.

Collective spin-wave oscillations in finite-size ferromagnetic samples.

A theory of collective oscillations in a system of spin waves parametrically excited by homogeneous parallel pumping in a finite-size ferromagnetic sample is developed. This theory is an extension of the well-known S theory of spin-wave collective oscillations in an infinite ferromagnetic medium for the case when the boundary conditions in a magnetic sample of finite size D are taken into account. The unstable collective oscillations in the system of parametric spin waves manifest themselves as low-frequency autooscillations of magnetization and demonstrate a variety of bifurcations and transition to chaos. We show that by introducing boundary conditions and taking into account the finite size of the sample it is possible to explain the following experimentally observed properties of spin-wave autooscillations that were not explained by the existing models of this phenomenon: (i) the difference between the threshold of parametric excitation of spin waves ${\mathit{h}}_{\mathrm{th}}$ and the threshold of autooscillations ${\mathit{h}}_{\mathrm{osc}}$; (ii) the finite value of the autooscillation frequency ${\mathit{f}}_{\mathrm{osc}}$ at the threshold of autooscillations; (iii) the dependences of the threshold ${\mathit{h}}_{\mathrm{osc}}$ and the frequency ${\mathit{f}}_{\mathrm{osc}}$ of the spin-wave autooscillations on the size of the ferromagnetic sample. The results of the theory are in good qualitative agreement with the results of experiments in which the influence of sample size on the spin-wave autooscillations was studied in yttrium iron garnet spheres.

The resolution function of single-crystal diffractometers at a synchrotron-radiation source: the influence of absorption and extinction on the FWHM

For the input of the correct intensity-data-collection parameters – the scan width and the number of steps – the expected full widths at half-maximum of the Bragg intensity profiles (FWHM) for the whole θ range under consideration must be known. These FWHMs depend on the divergence of the incident synchrotron beam, on the monochromator and on the mosaic structure of the sample used. They are also affected by absorption and extinction. A simple but very effective resolution function for a triple-crystal diffractometer, applicable also to single- and double-crystal diffractometers, is given, taking all the dependences mentioned above into account. The calculated FWHMs are compared with the measured ones of three different single-crystal samples, namely the FWHMs of a YIG sphere and an Si sphere, obtained at various wavelengths in the range 0.3 to 2.2 A with the new Huber four-circle diffractometer set up at HASYLAB and the FWHMs of a CaF2 sphere, given in the literature and measured with the old five-circle Stoe diffractometer at HASYLAB (DESY, Hamburg, Germany). It is shown that, with use of the proposed resolution function, the beam characteristics – divergence and wavelength spread – as well as the characteristics of the samples – mosaic spread and mosaic block size – can be determined from comparison with experimental FWHMs, measured at different wavelengths.

Subsaturation ferromagnetic resonance in yttrium iron garnet spheres

Experimental data is presented for ferromagnetic resonance in an yttrium iron garnet sphere slightly below the threshold field for saturation. It is found that significantly different behavior occurs depending on whether the dc field is aligned with the [111], [100], or [110] axes of the crystal. Explanations are proposed to account for the observed behavior, which in the [100] and [110] cases involve the formation of macroscopic magnetization patterns. These two cases also exhibit frequency reversal below threshold, in which the frequency is observed to increase as the field is decreased.

Lyapunov Exponent Spectrum for Two-Mode Model in Spin-Wave Chaos

The results of numerical experiments on the two-mode model for yttrium iron garnet sphere in the parallel-pumping configuration are reported and the complete Lyapunov exponent spectrum is presented. A rather complicated structure of the Lyapunov exponent spectrum can be recognized by the appearance of the associated peak in the Kolmogorov-Sinai entropy and the Lyapunov dimension diagrams. The results confirm an important connexion between the effective number of spin-wave modes involved and the Lyapunov dimension of the attractors.

Self-oscillations in spin-wave instabilities.

An experimental and theoretical study of bifurcations leading to self-oscillations in spin-wave instabilities pumped by microwave fields is presented. The experiments were done with spheres of yttrium iron garnet of various diameters pumped by X-band microwave radiation in the parallel pumping and subsidiary resonance configurations. The results reveal a variety of bifurcations and chaos depending on the experimental parameters. Generally the frequency and threshold of the self-oscillations show a definite dependence on sample size not predicted by the existing models. On the theoretical side we show that the usual equations describing two interacting spin-wave modes predict various types of bifurcations, depending on the set of parameters. In particular we investigate Hopf bifurcations and homoclinic phenomena. We also show that the introduction of boundary conditions and momentum symmetry breaking in the spin-wave pumping in finite samples accounts for important quantitative features of the experimental observations not explained by the existing models.

Temperature-induced multistability in spin-wave turbulence

Parametrically excited spin-waves in magnetic spheres of yttrium iron garnet give rise to complex multistable behaviour occuring for special experimental conditions at room temperature, but vanishing at helium temperature. We conclude that, in addition to the well-known nonlinear dipolar couplings, a novel “temperature-induced” nonlinearity occurs, which is only effective at higher temperature.

Different types of intermittency observed in transverse-pumped spin-wave instabilities

The dynamic behaviour of magnetization in YIG spheres was studied by FMR within the coincidence regime of the first-order Suhl instability. For certain ranges of the control parameters (magnetic field, microwave frequency and amplitude, etc.) the time-resolved absorption signal shows auto-oscillations changing over to chaos by intermettency. We clearly observed each of the types I–III and rather often crises.

Parametric excitation of spherical modes in ferromagnetic spheres by perpendicular and parallel pumping

The fine structures of the threshold of subsidiary absorption and parallel pumping, observed on highly polished YIG spheres in 1975 by W. Jantz et al., are discussed with a model which uses instead of plane spin-waves the true modes regarding the shape of the sphere. These spherical modes are magnetostatic modes taking additionally the exchange interaction into account. At the closely spaced resonances of the fine structure of parallel pumping single spherical modes with angular-momentum quantum numberm=0 are excited, whereas at the resonances of subsidiary absorption pairs of spherical modes with big angular-momentum quantum numbers (|m|≈1000) satisfying the selection rulem+m′=1 are excited. The analysis of the fine structure of subsidiary absorption shows that in regimes where the plane wave approximation predicts the excitation of spin-waves with formalk→0, modes withk≈1.5·105 cm−1 have the lowest threshold. This discrepancy is discussed with the effect of surface pit scattering, which increases the threshold of modes withk < 2π/λpit, where λpit is a typical size of the surface pits. Consequently modes withk≈22π/λpit instead ofk→0 have the lowest threshold.

The temperature dependence of the ferromagnetic and paramagnetic resonance spectra in thin yttrium-iron-garnet films

The ferromagnetic resonance (FMR) spectra of an yttrium-iron-garnet (YIG) film were studied from room temperature to 120 K above TC (TC = 553 K). The spectra were measured for a magnetic field parallel to the film as well as perpendicular to it. In the ferromagnetic phase the FMR lines represent the magnetostatic modes whose field positions and spacing are determined by the magnetization of the sample. When anisotropy terms are added to the theoretical expressions for magnetostatic waves of Damon and van de Vaart [J. Appl. Phys. 36, 3453 (1965)] for the perpendicular orientation and of Damon and Eshbach [J. Phys. Chem. Solids 19, 308 (1961)] for the parallel one, a good agreement is obtained between the experimental results and theory. Magnetization values extracted from the FMR spectra are also in good agreement with the published magnetization data for YIG, obtained by a vibrating sample magnetometer. At temperatures higher than 413 K the normalized cubic anisotropy K1/M is found to be practically temperature independent, in contrast with previous studies on YIG spheres which conclude that K1/M → 0 when approaching TC. In the paramagnetic phase we observe an anisotropy in the resonance fields due to the sample shape and the induced magnetization. The linewidths ΔH have also been measured and the product [ΔH − ΔH(TC)] × T is found to be practically linearly dependent on T − TC in a wide range of temperatures. ΔH(TC) is the linewidth at TC. This result is in good agreement with recent experimental studies of paramagnetic YIG linewidths and in fair agreement with Huber’s zero-field theory of paramagnetic linewidths near TC of non-Heisenberg ferromagnets, where the ‘‘critical speeding-up’’ effect is absent [J. Phys. Chem. Solids 36, 723 (1975)].

Electromagnetic waves: microwave components and devices

Part 1 Electromagnetic waves: Maxwell's equations electromagnetic waves in non-conducting media energy flow in an electromagnetic wave electromagnetic waves in conducting materials propagation of waves in plasmas polarization of waves propagation in gyromagnetic media boundary conditions. Part 2 Waves guided by perfectly conducting boundaries: TEM transmission lines reflection of waves by a conducting plane transverse electric waves transverse magnetic waves propagation in a rectangular waveguide power flow in rectangular waveguide higher-order modes in a rectangular waveguide other waveguides. Part 3 Waves with dielectric boundaries: reflection of waves by a dielectric boundary total internal reflection the Brewster angle dielectric waveguides mono-mode and multi-mode optical fibres radomes, windows and optical blooming quasi TEM waveguides non-TEM waveguides. Part 4 Waves with imperfectly conducting boundaries: waves incident normally on a conducting surface transmission through a thin conducting sheet electromagnetic screening waves incident obliquely on a conducting surface losses in transmission lines and waveguides microwave attenuators microwave loads. Part 5 Antennas: magnetic vector potential retarded potentials small electric dipole the reciprocity theorem small magnetic dipole half-wave dipole dipole arrays radiation from apertures slot antennas phased array antennas. Part 6 Coupling between wave-guiding systems: discontinuities broadband matching techniques coupling without change of mode coupling with change of mode coupling by apertures effect of holes in screens on screening effectiveness waveguide directional couplers distributed coupling. Part 7 Electromagnetic resonators and filters: transmission-line resonators cavity resonators effect of resonance on screened enclosures dielectric resonators Fabry-Perot resonators filter theory transmission-line filters waveguide filters optical filters. Part 8 Ferrite devices: microwave properties of ferrites resonance isolators phase shifters and circulators junction circulators Faraday rotation devices edge mode devices YIG filters. Part 9 Solid state microwave devices: semiconductor materials diodes transistors detectors and mixers switches oscillators amplifiers monolithic microwave integrated circuits LEDs and laser diodes. Part 10 Vacuum devices: space-charge waves Klystron amplifiers slow-wave structures travelling wave tubes crossed-field tubes fast-wave devices electron accelerators. Part 11 Microwave measurements: measurement of frequency measurement of power measurement of gain and loss measurement of return loss (part contents).

Tunable microwave and millimeter-wave band-pass filters

The authors present an overview of tunable microwave and millimeter-wave bandpass filters realized in different technologies. Some general design principles are described. Recent progress in the performance of various tunable filters is reported. The authors survey magnetically tunable filters (ferrimagnetic resonance filters, magnetostatic-wave filters, evanescent waveguide filters, E-plane printed circuit filters), electronically tunable filters, and mechanically tunable filters. The typical performance parameters are summarized. This comparison shown that none of these devices can simultaneously satisfy all requirements for perfect tunable filters. For microwave systems where multioctave tuning is essential, a YIG filter is an obvious choice. In systems where the requirement of high power handling capability combined with low insertion loss, predominates, mechanically tunable filters and magnetically tunable E-plane filters are recommended. If the tuning speed is a crucial requirement, varactor-tuned filters or E-plane filters with ferrite toroids are devices of choice. For millimeter-wave design, the most promising structures are ferrimagnetic resonance filters utilizing hexagonal ferrite resonators or, up to 60 GHz, magnetically tunable E-plane printed circuit filters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Novel wideband 2–18 GHz clock extraction circuit for optical transmission systems

A novel circuit technique that provides wideband clock extraction for digital regenerative repeaters is described. The scheme employs a closed loop electronically tuned YIG filter than can be locked to the fundamental or harmonics of the extracted clock.