Foldover Effect Research Articles

Inverse “Foldover” Resonance in an Yttrium Iron Garnet Film

Nonlinear magnetic resonance is studied in an in-plane magnetized yttrium iron garnet (YIG) film. For YIG films magnetized perpendicular to the plane, the effect referred to as the foldover resonance is well known. It arises because the precession frequency increases with the deviation of the magnetization. When the field is reduced, the frequency of the precession remains resonant because the demagnetizing field decreases with the deviation of the magnetization. The signal disappears when the radio frequency pump power is insufficient to maintain a nonequilibrium state of the system. In the in-plane magnetized yttrium iron garnet film, the precession frequency decreases with an increase in the pump amplitude. Accordingly, the foldover effect arises under an increase in the field. The fundamental difference is that the precession in the latter case should be unstable with respect to the decay into spin wave modes. The deviation angles of magnetization of about 10° are reached, and the rate of decay of the uniform precession into spin waves, which depends on the deviation angle of the magnetization, is measured. This study opens up another way of achieving the magnon density corresponding to the formation of its Bose–Einstein condensate.

Nonlinear features of the superconductor-ferromagnet-superconductor φ0 Josephson junction in the ferromagnetic resonance region.

We demonstrate the manifestations of nonlinear features in magnetic dynamics and I-V characteristics of a φ0 Josephson junction in the ferromagnetic resonance region. We show that at small values of the system parameters damping, spin-orbit interaction, and Josephson-to-magnetic energy ratio, the magnetic dynamics is reduced to the dynamics of a scalar Duffing oscillator driven by the Josephson oscillations. The role of the increasing superconducting current in the resonance region is clarified. Shifting of the ferromagnetic resonant frequency and the reversal of its damping dependence due to nonlinearity are demonstrated by the full Landau-Lifshitz-Gilbert-Josephson system of equations and in its different approximations. Finally, we demonstrate the negative differential resistance in the I-V characteristics and its correlation with the fold-over effect.

Power-Dependent Characteristics of Spin Current Transfer in Metal Bilayer Devices under High-Power Pulse Excitation.

The power-dependent transfer characteristics of spin currents generated at the interface of the permalloy/Pt bilayer device have been investigated over a wide power range from a few tens of milliwatt to 396 W. We built a high-power pulse excitation system for spin pumping, which achieves large electromotive force (EMF) values of 10 mV at 396 W excitation through the inverse spin Hall effect (ISHE) and demonstrates that the EMF generation after pulse excitation is very fast. Under strong pulse microwave excitation more than 80 W, the EMF spectrum exhibits an asymmetrical lineshape, which is well reproduced by simulations that take into account the fold-over effect due to the nonlinear ferromagnetic resonance excitation. The maximum output power at an external load through spin pumping and the ISHE is shown to increase in proportion to the square of the input microwave power (Pin) in the power range below 80 W. This power generation proportional to Pin2 is unique to spin current-mediated power flow. In the strong excitation regime with the fold-over type EMF spectra, the EMF values of the peak magnetic field position are found to increase less linearly due to spectral broadening. This feature can be used for power generation that increases nonlinearly with respect to the input excitation power, where the nonlinearity is adjusted by varying the magnetic field position.

Normal modes description of nonlinear ferromagnetic resonance for magnetic nanodots

The spatially-inhomogeneous magnetization dynamics in a cylindrical magnetic nanodot driven by ac spin-torque is analyzed. To this end, the Landau-Lifshitz-Gilbert-Slonczewski equation is reformulated as a system of coupled nonlinear ordinary differential equations which describe the time-evolution of normal modes amplitudes. This approach provides a class of models with reduced number of degrees of freedom and incremental accuracy between macrospin and full micromagnetics. By using this approach, the onset of foldover effect for fundamental and higher-order modes is demonstrated. The results are confirmed by full micromagnetic simulations.

Architecture and Optimization of a Low-Frequency Maglev Energy Harvester

Low-frequency harvesters are attractive due to their availability in the ambient environment. The paper presents the design, analysis and optimization of the magnetic levitation harvester. A new nonlinear model of the electromechanical coupling, depending on the magnet position versus coil is proposed. Additionally, the influence of magnetic suspension (stiffness), load resistance and magnet-coil configuration on the foldover effect is shown.

Nonlinearity in the Mechanical Response of Rubber as Investigated by High-Frequency DMA.

Nonlinear material response is analysed with the Fourier transform (FT) of the raw signal measured by a high-frequency dynamic mechanical analyzer (HF DMA). It is known from rheological behaviour of elastomers that reinforcing fillers additionally induce nonlinearity in an already inherently nonlinear system. This behaviour is often described in terms of a mechanical response of strain sweeps, essentially the transition from the linear viscoelastic (LVE) to the nonlinear viscoelastic (NVE) region. In the current investigation, the NVE region could be observed with respect to frequency under low-amplitude deformation. A foldover effect was observed, whereby the material exhibited a nonlinear dependency in relation to the increment of the filler amount above the percolation threshold. In addition, an apparent superharmonic resonance was observed within higher orders of vibrational modes which is further indication of nonlinearity. In this paper, the analytical approach is presented as a novel method to characterise the behaviour of the polymer–filler interaction by HF DMA.

Direct measurement of foldover in cavity magnon-polariton systems

An approach to directly measure the nonlinear foldover effect for cavity magnon polaritons is demonstrated by placing a nonlinear medium (yttrium iron garnet) into a Fabry-Perot-like microwave cavity. The resulting bistability features can exhibit clockwise, counterclockwise, and butterflylike hysteresis loops and are solely dependent on the relative weight of the magnonlike and photonlike components. In addition to accurately describing our experimental observations, our model also allows us to calculate the crucial system conditions required to produce photonlike foldover effects. Though the photon subsystem has no nonlinear components of its own, these photonlike foldover effects are produced through light-matter interactions with a nonlinear magnetic subsystem. Our model's description of these nonlinear light-matter interactions and their effects is not limited to ferromagnetic systems and should be generally applicable to other coherent coupled systems.

Nonlinear response and bistability of driven ion acoustic waves

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Foldover of nonlinear eigenmodes in magnetic thin film based feedback rings

The foldover effect of nonlinear eigenmodes in feedback ring systems was observed. Experiments made use of a system that consisted of a magnetic thin film strip, which supported the propagation of spin waves, and a microwave amplifier, which amplified the signal from the output of the magnetic strip and then fed it back to the input of the magnetic strip. The signal amplitude vs frequency response in this ring system showed resonant peaks which resulted from ring eigenmodes. With an increase in the resonance amplitude, those resonant peaks evolved from symmetric peaks to asymmetric ones and then folded over to higher frequencies. The experimental observations were reproduced by theoretical calculations that took into account the nonlinearity-produced frequency shift of the traveling spin waves.

Nonlinear spin-torque microwave resonance near the loss of spin state stability

Abstract The paper analyzes microwave resonant response of the spin-torque diode. The considered spin-torque diode is a magnetic tunnel junction with a nano-pillar structure. The magnetization of the free layer has a tilt caused by an action of the inclined magnetic field in the plane of the structure. Taking into account the effect of spin torque transfer we define stability regions of stationary states of magnetization in the free layer as a function of the azimuth angle of the magnetic field and bias DC current. Microwave volt-watt sensitivity of the spin diode for the obtained stationary states is calculated. It is shown that non-linear frequency shift of the resonance line width limits maximum sensitivity of the spin diode near the critical bias current corresponding to the point of the transition to the self-oscillating mode. Besides that, overlapping of frequency branches occurs in the resonant response as the critical point approach, which is different from the foldover effect in the nonlinear ferromagnetic resonance induced by an alternating magnetic field.

Nonlinear dynamics of a magnetically driven Duffing-type spring–magnet oscillator in the static magnetic field of a coil

We study the nonlinear oscillations of a forced and weakly dissipative spring–magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet–coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels.

Radar-Coding and Geocoding Lookup Tables for the Fusion of GIS and SAR Data in Mountain Areas

Synthetic aperture radar (SAR) image orthorectification induces an important alteration of information due to the side-looking geometry of SAR acquisition. In high-relief areas, the difficulty is increased by the foldover effect: The images acquired with low incidence angles cannot be registered by a bijective transformation like polynomial transformations, as usually proposed by conventional software. In this letter, a simple and efficient method, fitted to geocoded data and SAR images, is introduced to propose a generic coregistration tool that takes SAR geometry into account without requiring the exact sensor model, specific parameters, and precise navigation data. This method is based on a simulated SAR image and on the computation of lookup tables (LUTs) that represent the coordinate transform from one geometry to the other. Results are presented on a high-relief area in the Alps, where satellite and airborne SAR images are used for glacier evolution monitoring. A comparison to other sensor-independent approaches has been performed, showing that the proposed approach performs better in mountain areas. The resulting LUTs allow merging SAR data with the georeferenced data, either in ground geometry by orthorectifying the SAR information or in radar geometry by the inverse transformation, namely, radar-coding data from a geographic information system, to improve the analysis of SAR images and the result interpretation.

Foldover ferromagnetic resonance and damping in permalloy microstrips

We have investigated the foldover ferromagnetic resonance in ferromagnetic permalloy (Py) microstrips by microwave photovoltage and photoresistance techniques. We have found that the linewidth of the nonlinear ferromagnetic resonance is strongly dependent on the precession angle of magnetization. Therefore, we have revised the Anderson-Suhl instability, which enables us to quantitatively describe the foldover effect in Py microstrips. The calculation from this proposed model shows excellent agreement with experimental data.

Spin-torque driven ferromagnetic resonance in a nonlinear regime

Spin-valve based nanojunctions incorporating Co∣Ni multilayers with perpendicular anisotropy were used to study spin-torque driven ferromagnetic resonance (ST-FMR) in a nonlinear regime. Perpendicular field swept resonance lines were measured under a large amplitude microwave current excitation, which produces a large angle precession of the Co∣Ni layer magnetization. With increasing rf power the resonance lines broaden and become asymmetric, with their peak shifting to lower applied field. A nonhysteretic step jump in ST-FMR voltage signal was also observed at high powers. The results are analyzed in terms of the foldover effect of a forced nonlinear oscillator and compared to macrospin simulations. The ST-FMR nonhysteretic step response may have applications in frequency and amplitude tunable nanoscale field sensors.

Direct measurement of nonlinear ferromagnetic damping via the intrinsic foldover effect

An approach to measure precisely nonlinear ferromagnetic damping is demonstrated by using spin dynamos in combination with sensitive electrical probing techniques. The directly measured intrinsic foldover effect unravels a 50-year-old mystery of ferromagnetic metals. Pivotal importance of nonlinear ferromagnetic damping is uncovered via its distinct dependence on the frequency, amplitude, and initial conditions. The experimental results are in excellent agreement with a nonlinear oscillator model, which revises the pioneer work of Anderson and Suhl for nonlinear magnetization dynamics.

Cramer-Rao bounds for target parameters in space-based radar applications

The Cramer-Rao (CR) bounds for target Doppler and power are presented when detecting targets using a space-based radar (SBR) platform. The target in noise-only case is considered first and the results are compared with those obtained for a centro-symmetric uniform linear pulse array. When clutter is also present, the effect of the Earth's rotation and range foldover becomes significant; and they must be taken into consideration. The CR bounds are computed for target Doppler and power, and compared with their variance estimates obtained from simulation results corresponding to various airborne and SBR situations. From the simulation results, the Earth's rotation together with range foldover significantly increase the CR bounds for both target Doppler and power. This is in agreement with other results that show the Earth's rotation and range foldover together degrade the clutter suppression performance of adaptive processing algorithms. It is shown that when both the Earth's rotation effect and range foldover effect are present in the data, target detection is difficult, and it is necessary to introduce waveform diversity into the transmit design to minimize the effect of clutter and other interference. In this context, using waveform diversity on transmit, it is possible to compensate the degradation in terms of the CR bounds and achieve performance close to the ideal case.

Bistable Resonance In Gravity‐driven Film Flows

AbstractWe study the flow of a viscous liquid down an inclined plane with a sinusoidal bottom profile. Applying the integral boundarylayer method leads to a nonlinear ordinary differential equation for the film thickness. Linear resonance between the free surface and the bottom contour is observed via a regular perturbation approach. Considering nonlinear contributions, the resonance curve shows a foldover effect which is typical for nonlinear oscillators. In order to understand the origin of this bistable behaviour we derive a simple model equation and show an analogy to the Duffing oscillator. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ferromagnetic resonance of ferrite ferrofluids at high microwave power levels

The effects of high microwave power level upon the ferromagnetic resonance line of ferrofluids at room temperature are investigated. The distortions of the resonance line with increasing power levels give evidence of an apparent foldover effect attributed to spin-wave instabilities. The critical microwave power to onset the instabilities decreases exponentially with the concentration of magnetic particles in the ferrofluid sample.

Spatial instability of the nonlinear ferromagnetic resonance in uniaxial films

The spatial instability of the nonlinear magnetization precession in uniaxial films with low magnetization is analyzed analytically and numerically solving Landau–Lifshitz equations. The foldover effect is essential in this geometry. The formation of spatial soliton-like magnetization precessions is predicted for nonuniform driving inductions exceeding the threshold value. Time–space instability boundaries of the obtained soliton-like structures are calculated. The numerical simulations show that these structures are stabilized at the boundaries of the foldover region. This behavior is in qualitative agreement with a recent experiment where a spatial pattern formation by a nonuniformly driven ferromagnetic resonance in a garnet film has been observed.

Determination of the ferrimagnetic precession cone of in-plane magnetized garnet films using optical modulation technique

Magnetic garnet films of composition (A, Bi)3(Fe, B)5 O12 are grown by liquid phase epitaxy on [111] oriented substrates of Gd3 Ga5 O12, where A=yttrium or lutetium and B=aluminum or gallium. The ferrimagnetic resonance (FMR) of in-plane magnetized films is studied by analyzing the modulation of light, which passes the film parallel to the film normal. Modulation efficiencies up to 1.8% at 2.9 GHz are observed at a wavelength of 0.633 μm. From the measured modulation intensities the precession angles of the FMR are derived. The dependence of the precession cone on the excitation frequency or on the external induction shows a foldover effect which, however, is smaller than for the FMR of perpendicularly magnetized films. Maximum precession angles up to 14° are achieved and the experiments indicate that saturation occurs. Light modulation is also observed at the first harmonic frequency, but the intensity is about 300 times weaker than at the fundamental frequency.