Anil Prabhakar

Proposal for a Standard Micromagnetic Problem: Spin Wave Dispersion in a Magnonic Waveguide

In this paper, we propose a standard micromagnetic problem, of a nanostripe of permalloy. We study the magnetization dynamics and describe methods of extracting features from simulations. Spin wave dispersion curves, relating frequency and wave vector, are obtained for wave propagation in different directions relative to the axis of the waveguide and the external applied field. Simulation results using both finite element (Nmag) and finite difference (OOMMF) methods are compared against analytic results, for different ranges of the wave vector.

Estimation of Stiction Force From Electrical and Optical Measurements on Cantilever Beams

In this paper, we estimate the stiction force from electrical (current-voltage) measurements on surface micromachined polysilicon cantilever beams. A bias voltage was applied between the beam and the substrate. At the pull-in voltage, the beam collapsed to the substrate and the current rose rapidly from zero. Similarly, at the pull-out voltage during bias sweep back, the current dropped rapidly to zero when the contact between the beam and the substrate was broken. An analytic model for the stiction force was developed in terms of the pull-in and pull-out voltages and was used to estimate a stiction force of about 70 nN from the measured electrical characteristics. This method of characterization is suitable for use in packaged devices. An analytic model was developed to estimate stiction force from optical surface-profile measurements of the curvature of long collapsed cantilever beams in a cantilever-beam array, in the absence of any electrostatic actuation. The force per unit length of about 14 nN/m thus obtained was used to compare the effects of surface roughness on stiction.

Wideband optical modulation via the magneto–optic interaction in a bismuth-lutetium-iron garnet film

Optical modulation with a bandwidth of about 3 GHz centered at 5.75 GHz was observed in a thin film of [BiLu]3Fe5O12 using the magneto-optical interaction. A microstrip transducer was placed in contact with the film and TM polarized optical guided modes were excited beneath and parallel to the transducer. The TM→TE mode conversion was measured as a function of the angle between an in-plane field, of up to 100 Oe, and the optical beam. The bandwidth of the modulation was limited by the microwave components used in the external circuit. The experiments qualitatively agree with a simple model that describes a modulation of the optical beam by a nonresonant precession of the magnetization about an equilibrium.

Evolution of Quantum States in an Electro-Optic Phase Modulator

We present a quantum mechanical model to evaluate the time evolution of quantum states of light in an electro-optic phase modulator (EOPM). The phase modulator is analogous to a multilevel atomic system with equally spaced energy levels, each of which corresponds to the sidebands of the phase modulated optical field. Using perturbation theory, we solve the equations governing the interaction of the optical field with a modulating field both with and without phase velocity mismatch. A unitary operator that evolves any given quantum state allows us to evaluate the response of EOPM for single photon, coherent and squeezed states. We apply these results to the analysis of frequency coded quantum key distribution scheme.

Nonlinear microwave-magnetic resonator operated as a bistable device

The excitation of large amplitude spin waves causes a shift in the resonance frequency of a ferrite resonator towards higher frequency values. Using this shift, a resonator can be designed to operate in a bistable mode where the history of the input power determines the output power. A theoretical calculation for a resonator with a linewidth of 1.5 MHz, measured at 10 GHz, predicts a discontinuous jump in output power by a factor of about 3.5 as the input power is increased to about 0.7 mW. The phenomenological model that describes the bistability also provides an explanation for the foldover of ferromagnetic resonance curves at high input power levels. An appropriate choice for the operating frequency ensures that the estimated input power required to observe the bistable behavior is below the predicted threshold power for spin-wave auto-oscillations at the main resonance.

Effects of high microwave power on collinear magnetostatic-optical wave interactions

In the collinear interaction between magnetostatic waves and optical guided modes, the use of high microwave power is experimentally observed to broaden the range of microwave frequencies over which a significant optical mode conversion occurs. A mechanism contributing to this broadening is described that is based on a nonlinear shift in the wavelength of the magnetostatic waves at high power along with magnetic damping. Comparisons between previous experiments and our theoretical predictions show that this mechanism can explain some, but not all, of the changes observed in the optical spectrum at high microwave power levels.

Analysis of random telegraph noise in spin valve heads with ultra-thin free layers

Random telegraph noise (RTN) in spin valve heads with ultra-thin free layers is analyzed in both time and frequency domain. RTN is characterized by random fluctuation between two meta-stable states and is attributed to thermally activated domain instability. Lifetime of each meta-stable state is changes with bias current, with both being equal when RTN amplitude peaks while asymmetry is near zero. The lifetime at equilibrium can be quantified by the flatness of RTN spectra and is correlated with the normalized peak area under RTN amplitude versus bias current curve. This area scales with the energy barrier associated with RTN. With the same RTN peak area, lifetime at equilibrium is shorter for heads with thinner free layers but otherwise the same structure. Impact on reader instability for ultra-high areal density recording is discussed.

Variations in auto‐oscillation frequency at the main resonance in rectangular yttrium–iron–garnet films

High power microwave experiments conducted on a rectangular yttrium‐iron‐garnet (YIG) film indicate a parabolic dependence of the square of the frequency of auto‐oscillations on microwave signal amplitudes, an observation that is qualitatively consistent with prior theoretical predictions. Forward volume magnetostatic waves were excited using a microstrip transducer kept in contact with a YIG film placed in a constant external magnetic field (Hdc=3.48 kG). Variations in the input microwave power (10 dBm<P<25 dBm) and frequency (5.1 GHz<f<5.7 GHz) were used to locate and study auto‐oscillations close to the Suhl instability at the main resonance. A novel method of viewing changes in the microwave passband using density plots enables us to study variations in the dipole gaps in the passband near the Suhl instability. A broadening of dipole gaps into fingerlike regions of weak transmission marks the onset of auto‐oscillations beyond the instability threshold. These regions are associated with a variety of sp...

Variations in the magneto-optic coupling coefficient in a bismuth-lutetium-iron-garnet film

Magnetostatic wave-optical interactions are studied in the transverse geometry using a [BiLu]/sub 3/Fe/sub 5/O/sub 12/ film. Non-monotonic variations in the magneto-optic coupling coefficient are observed as we increase the input microwave power at a fixed frequency. Similar variations are also seen in the transmitted microwave signal, though the features appear at higher power levels. The non-monotonic behavior is due to a shift in the microwave passband with increasing power. Density plots are used to correlate the two sets of data over a 350 MHz region. The discrepancy in power levels associated with a feature in the line plots is a consequence of the different curvatures of the two density plots.

Stiction force estimation from attachment length and electrostatic measurements on cantilever beams

An estimate of stiction force, rather than the more commonly reported surface energy, helps design reliable structures. Stiction is a major cause of failure in surface micromachined structures. We report on the modeling and estimation of the stiction force from simple I-V curves on cantilever beams which can be measured even on packaged devices. We have fabricated oxide anchored cantilever beams of polysilicon by surface micromachining. Current is measured for an applied bias between the beam and the substrate. Pull-in and pull-out voltages are determined as the points of maximum slope calculated by differentiating a cubic spline fit to the measured I-V data. The commercial package CoventorWare was used to develop an empirical model for estimating the pull-out voltage for the cases when there is no stiction and in the presence of stiction. A model is developed for finding the stiction force from the simulated and the experimental pull-out voltages. The method uses only measured values of pull-in and pull-out voltages and the beam length and does not require the value of Youngs modulus. We also discuss an independent visual method to estimate the process stiction force from the cantilever beam array that is normally used to estimate the surface adhesive energy. An analytical model is developed to calculate the stiction force from the attachment length of long stuck cantilever beams that are released in the same process.