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The side-reading of a finite track-width shielded MR head is investigated both analytically and numerically. The head field (potential) utilized in a reciprocity calculation is obtained, and its Fourier transform is derived in semi-analytic forms. The off-track MR head response to a longitudinally magnetized micro-track and finite-width track is calculated from these results. Estimations on off-track spacing loss are undertaken for two types of shielded MR heads: finite track-width flush MR sensor and shields, and finite-width MR sensor with infinitely wide shields.

Thermally activated reversal of elongated particles having high aspect ratio through non-uniform structures produces weaker coercive forces than estimated by Neel-Brown's uniform magnetization reversal theory. The coercive forces are angular dependent and consistent with isolated single-domain particles. The energy barriers in the elongated particles are less than those caused by the uniform reversal process.

A three-dimensional micromagnetic model of the cross-track response of shielded magnetoresistive heads is presented in order to assess MR head performance in high track density recording applications. Both the down-track output pulse-width and the off-track output asymmetry decrease as the shield-to-shield separation decreases. For the same biasing level, the off-track asymmetry increases with the stripe height. Proper initialization is found to be crucial to the head response profile. If the horizontal magnetization components of the MR and the adjacent layer are not in an anti-parallel state, larger off-track asymmetry occurs. For improperly initialized heads, side-reading noise arises from local reversal of edge magnetizations in the un-pinned layer, which could be reduced by the presence of ideal shields.

Overwrite in thin film rigid disk recording has been studied experimentally using disks with a wide range of magnetic moment and coercivity. Standard f(sub 2)/f(sub 1) overwrite was investigated in detail at various recording currents and different flying heights. A theoretical model was developed using simple analytical approximations that relate demagnetization-field-induced position shift (hard transition shift) to the measured overwrite. The demagnetization fields due to the leading edge transitions were calculated analytically including a good approximation to the gapped head image. The results compare well with experimental measurements. A new overwrite measurement technique using the second harmonic component of a 0.5 f(sub 1) signal is also described in this work.

Micromagnetic modeling of small dimension magnetoresistive heads is reviewed. Recent simulation results are presented, pertaining to recording applications with high areal density nearing 1-10 Gigabits per square inch. The proper biasing and reproduce properties of the most interesting MR head configurations have been studied, in order to achieve design optimizations for ultra-high density MR heads. Initial comparisons between the performances of a shielded MR-SAL head and a dual MR head are obtained.

A micromagnetic model is utilized to study nonlinearities in high density recording. Head imaging is taken into account approximately to model near contact recording. The simulations are able to show detailed steps of a dibit transition formation and illustrate the effect of the image field. Nonlinear amplitude reduction as a result of zigzag transition percolation is calculated at different recording densities and flying heights. The numerical results agree very well with experiment. Effects of medium exchange coupling and medium orientation on the amplitude loss are also investigated.

General noise voltage relations based on magnetization correlations in thin film recording media have been developed. Transition position jitter or amplitude fluctuations are a consequence rather than an input to the model. The effect of non-stationarity due to recorded data patterns is included by a simplified first order model of the down track variation of the correlation function. Estimates of position jitter and amplitude fluctuations are given. An example of peak detection is utilized to illustrate the determination of error rates.

Analytical expressions for the vector magnetic fields and Fourier transforms associated with thin film heads are presented. These results are derived from accurate, approximate expressions for the surface field of an asymmetric thin film head determined from conformal mapping solutions. A 2-dimensional Green's function is integrated to yield exact analytic expressions for the fields, which are of no more complexity than the Karlqvist field approximations. In spite of their simplicity, these expressions accurately represent the fields at all corners, both at the gap and at the pole edges. These results are only approximate at spatial distances beyond the head edges and at wavelengths beyond about ten times the total head length. The Fourier transform of the surface field is also given in simple analytic form. As an example of the use of these expressions, it is shown how the effect of pole length to gap length ratio, p/g, on pulse superposition can be easily estimated.

The mechanisms of pulse asymmetry and nonlinearities in dibit recording have been analyzed by numerical simulation. Well oriented longitudinal tape media was modelled by 2-D discretization and subsequent iteration including distributions in particle orientations and intrinsic switching fields. Typical head-medium spacing was included as well as imaging of the demagnetization fields by the record head. Isolated transitions as well as dibits were recorded utilizing head fields typical of high density recording. Characteristic isolated pulse asymmetry is shown to be due predominantly to the demagnetization fields during the write process which substantially shift the phase of magnetization transitions with depth into the medium. In dibit recording with optimum or greater record currents, the second transition is shown to yield a larger playback voltage than that predicted by linear superposition. The vector magnetostatic fields cause an alignment of the centers of the second transition with depth into the medium.

Evaluation of the long range magnetostatic field is the most time-consuming part in a micromagnetic simulation. In a magnetic system with N particles, the traditional direct pairwise summation method yields O(N squared) asymptotic computation time. Here an adaptive fast algorithm fully implementing the multipole and local expansions of the field integral is shown to yield O(N) computation time. Fast Fourier transform techniques are generalized to entail finite size magnetic systems with nonperiodic boundary conditions, yielding O(N log2 N) computation time. Examples are given for calculating domain wall structures in Permalloy thin films. The efficiency of the fast Fourier transform makes it almost always the faster method for any large size system, while the multipole algorithm remains effective for more complex geometries and systems with highly irregular or nonuniform particle distributions.

Magnetic thin film domain wall motion under dynamic fields was analyzed using computer simulation models. The results showed that two-dimensional domain walls exhibited enhanced dynamical behavior under ac driving fields. At higher amplitude driving fields, wall structure transitions were observed. Transition threshold increased with the external frequency. Film thickness direction was dominant for low drives.

An analytical solution was used to solve the energy barrier problem in the thermal reversal of two interacting single domain particles. The results showed that the lowest energy barriers were saddle points of the energy surfaceand they corresponded to reversal modes during thermal agitation. Thermal switching was either asymmetric fanning or asymmetric coherent rotation, depending on the bond angle, when there was weak dipole coupling.

A micromagnetic cellular automaton model was used to analyze magnetization correlations and noise in polycrystalline thin-film recording media. The results showed that self-organized criticality with domain patterns characterized by the intergranular exchange and magnetostatic interactions was exhibited by the magnetization reversal process. The state of magnetization didnot entirely determine the domain width. Noise was observed to be related to this domain width.

Magnetization reversal mechanisms for single patterned media elements have been examined. Sizes and magnetic properties have been examined for parallelepipeds of fixed aspect ratio. For element sizes for 1 Tbit/[in.sup.2] recording magnetization reversal is nearly uniform for a uniform applied field. For fields covering a small percentage of the element volume nonuniform reversal occurs and the reversal field increases at a much smaller rate than inversely as the volume covered. Index Terms--Landau-Lifshitz equation, magnetic recording, micromagnetics, patterned media.

A micromagnetic Monte Carlo simulation is developed to study the thermal decay and erasure process for perpendicular recording media. The switching probability is calculated based on both the energy barrier analysis and the master equation. The results show that for current head media combination at 1 Tb/[in.sup.2], the erasure is severe for the neighboring tracks unless the bit-aspect ratio is increased. The magnetic write width for both side shielded (SS) and no side shield (NSS) head is about the same. The erase band for the SS write head is significantly smaller (20 nm less) than that for the NSS head, corresponding to 10 nm or 12% track pitch reduction. Index Terms--Erasure, perpendicular recording, thermal decay, tilted perpendicular recording, track edge effect.

The energy barrier to be overcome for thermal reversal, the reversal mode and the effective particle volume involved are determined by the saddle points of the energy surface. We investigate the influence of field misorientation, exchange-coupling and magnetostatic interaction for a 2:1 aspect ratio particle discretized into two subunits. Typically, increasing the field angle from 0[degrees] to 45[degrees] enhances the effective volume in both cases by more than 20%. Index Terms--Elongated ferromagnetic particles, field misorientation, thermal reversal.

A micromagnetic model for the writing process in perpendicular magnetic recording is developed to study the effect of the soft underlayer on the dynamic reversal of the recording layer. The upper part of the soft material is discretized micromagnetically, each spin following LLG dynamics; the remaining part has infinite permeability. The validity of the model is tested in the static case. Dynamically, high-frequency spin motion is observed in the soft layer. Nevertheless, the field inside the data layer follows the time dependence of the input waveform. Index Terms--LLG equation, perpendicular recording, soft underlayer.

Transition noise is dominant in high-density magnetic recording using thin-film media. In this paper transition noise is measured for a variety of perpendicular media. Both frequency- and time-domain measurements are utilized. In the frequency domain, the normalized spectra are virtually frequency-independent within the measurement bandwidth corresponding to a dominance of transition jitter. The time-domain measurements yield the transition parameter a and cross-track correlation length s with a knowledge of the read-track width and an assumption of the transition shape. For all media measured, the percentages of the jitter mode are over 70%. Index Terms--Cross-track correlation length, perpendicular recording, transition noise, transition parameter.

An analytical model is developed for calculating the cross-track correlation length in a perpendicular recording system, including both the medium inter-granular exchange and the magnetostatic interactions. For a typical range of parameters in current perpendicular recording systems, the cross-track correlation length varies from about 0.7-0.9 of the average grain diameter: (D) at zero exchange, to about 2-3 (D) at a strong exchange field of 0.1 [H.sub.K]. The relation with jitter noise is also investigated. Index Terms--Cross-track correlation length, inter-granular exchange, magnetostatics, transition noise.

The single-domain ferromagnetic particle with uniaxial anisotropy coupled to a single-domain superparamagnetic particle to enhance thermal stability of recording media is analyzed. The thermally agitated magnetization reversal can be reduced to the random magnetization dynamics of the first particle with an effectively larger anisotropy field and the magnetic external field is altered in a manner that depends on the sign of the coupling and can be either enhanced or suppressed.

High-frequency measurements and theoretical analysis of data on giant magnetoresistance thermal magnetization fluctuation noise are presented. An experimental setup for the measurement of this noise at high frequencies is proposed. The measured noise increases with bias current and demonstrates two distinct resonance peaks within 6 GHz. Damping parameters are extracted from resonance linewidth data. Small variations are seen within a given manufacturing batch of eight heads. Data fitting to the measured-noise power spectrum and comparison between eigenmode and Landau-Lifshitz-Gilbert theories. Index Terms--Dynamic damping parameter, giant magnetoresistance heads, magnetization noise spectra, thermal fluctuations.

Thermal decay of interacting magnetic grains in perpendicular thin films is studied by a new approach where damping and thermal fluctuations are added to each independent normal mode of the system around equilibrium. Optimal path and asymptotic analysis are used to obtain the collective reversal barrier and the mean exit time. The results show a reduction of thermal decay with decreasing magnetostatic interaction and/or increasing exchange coupling. The reversal barrier of an individual grain using a mean field interaction is compared with allowing neighbors to collectively rotate. It is found that collective effects yield a reversal barrier lower than a mean field analysis. This difference increases with increasing inter-granular interaction. Index Terms--Coupled grains, perpendicular thin-film media, thermal decay.

The playback signal characteristics in perpendicular recording is analyzed using three-dimensional geometry. Analytical expressions are deduced for both the width of the pulse and the asymptotic value taken by the signal when the sensor is far away from the transition. Index Terms--Fourier transform, perpendicular recording, reciprocity.

An analytic recording model for the transition parameter and the nonlinear transition shift (NLTS) with the rise-time effect has been developed. In this model, the Schwartz-Christoffel transformation is used to calculate the combined image field from the single-pole writer and the soft underlayer. It is shown that both medium velocity and finite head-field rise-time increase the transition parameter. The NLTS for a dibit pattern increases with linear density, but decreases with medium velocity. A large transition parameter arises because a finite rise time reduces the record field-gradient as the bit time is reduced. For a dibit, the demagnetizing field from the first bit increases the transition interval of the dibit, while the write-time difference of the second bit and the reference bit decreases the interval. Index Terms--Nonlinear transition shift, perpendicular recording, rise-time effect, transition parameter.

The transition parameter and cross-track correlation length are obtained by mode analysis of measured noise. The amplitude mode is the second most dominant noise made in the total nonstationary transition noise and it emerges due to the decline in the sensing area of the giant magnetoresistance (GMR) head with an increase in density recording.

The effect of intergranular interactions on thermal energy barrier distribution in perpendicular media is examined. The width of the energy barrier distribution declines due to intergranular exchange whereas the barrier width increases substantially as a result of magnetostatic interactions.

An analytic model for reversal field versus pulse time in a fine magnetic grain is developed for the case when the external magnetic field H(sub 0) is parallel to the axis of uniaxial anisotropy. The expressions include both thermal fluctuations and magnetization dynamics.

Micromagnetic simulations of planar isotopic magnetic thin film recording media are performed to study initial magnetization reversal processes in response to pulses with linear and exponential ramps. In addition, the effects of exchange coupling and gyromagnetic damping are examined.

The process of magnetization reversal in a fine ferromagnetic grain with a strong uniaxial anisotropy is simulated for the case of an instantaneously applied reversal magnetic field. This nonlinear diffusion is forbidden for either a strong reversal field and/or a small grain size.

The dynamic magnetization process in thin film platelets is studied by numerical micromagnetics. Initial work including a magnetostrictive energy dissipation mechanism results in complete magnetization reversal.

A three-dimensional micromagnetic model with cubic discretization was used to study the magnetization reversal in elongated particles for a variety of aspect ratios, shapes and particle sizes. Findings showed that cubic discretization need to be as fine as the exchange length to simulate a rectangular particle. Roughness arising from cubic discretization is well if the discretization size is on the order of the exchange length for curved shapes.

A study was conducted to analyze the mechanism of nonlinear damping during large angle magnetization reversal. A single grain was subdivided and solved using the gyromagnetic term. The magnetic moment was then reassembled in a novel equilibrium direction. Experimental results indicated irregular oscillations at a well defined mean mean value. Findings also showed that the average magnetization decreases.

A study was conducted to analyze the scaling of hysteresis and transition parameter with grain size in longitudinal thin film media. Closely packed hexagonal grains were used in the simulation. It was assumed that each grain was uniformly magnetized. Single transitions were then written using the Karlqvist head field assuming perfect imaging. Experimental results indicated that the smallest obtainable transition parameter was half the grain size.

A study was conducted to determine the feasibility of reversing single bit per particle media at a 1 GHz data rate with a density of 100 Gb/in squared in magnetic recordings. The media particles were cubic with 40 nm side length, 80 n center to center spacing and perpendicular uniaxial anisotropy. The reversal of individual elongated particles was also examined with fields from a moving probe. The minimum bit cell time needed to achieve reversal was much longer than the 1 ns corresponding to a 1 GHz data rate.

A simplified general expression is given for SNR for digital magnetic recording for transition noise dominant systems. High density media is assumed in which the transition parameter scales with the in-plane grain diameter. At a fixed normalized code density, the SNR varies as the square of the bit spacing times the read track width divided by the grain diameter cubed. This scaling law is shown to be quite general and useful for error rate analysis. Density optimization argues for track width narrowing rather than bit length reduction, limited by edge track considerations. Utilization of Arrhenius thermal signal decay yields limiting density estimates, neglecting electronics noise, in the range 50-100 Gbit/[in.sup.2] increasing with an increase in medium thickness/grain diameter ratio. Index Terms - areal density limits, partial response error rates, signal to noise ratio, thin film recording media.

An analytical formula is developed for calculating the magnetostatic field from a longitudinal magnetic transition with a hyperbolic tangent transition shape. This formula is utilized to study the dependence of nonlinear transition shift of a dibit pattern on recording parameters, such as flying height and recording bit density. It is found that at very low densities the nonlinear transition shift varies with bit length B as N(B) [similar to] 1/[B.sup.3]. The power factor decreases with increasing density and it decreases faster for higher flying height. For practical recording densities, the power [approximately] 2. The relation N(B) is then used to determine the optimal write precompensation level theoretically. Index Terms - Magnetostatic fields, Nonlinear transition shift, write precompensation.

Thermally assisted reversal in noninteracting single domain particles is studied through the use of a micromagnetic model with a stochastic fluctuation field. The magnetization decay of these particles at high and low anisotropy fields is studied and compared to Arrhenius-Neel decay. Estimates of the attempt frequency are made by fitting to exponential decay. The attempt frequency is also examined while varying the applied field, the anisotropy field, and the temperature. Special attention is given to combinations of these variables which give a constant height of the energy barrier to reversal. It is shown that the attempt frequency can vary dramatically even for a constant height of the energy barrier. The basic scaling laws of the system are discussed, and the scaled attempt frequencies are plotted to test their universality. Index Terms-Arrhenius-Neel decay, attempt frequency, Langevin equation, scaling laws, thermal decay.

Thin film media under consideration for high density recording in the range of 5 Gbit/[in.sup.2] and beyond will utilize extremely small grains in order to achieve acceptable signal-to-noise ratio limits. Numerical simulations of the reversal process including thermal fluctuations are utilized to determine medium coercivity versus field duration. Typically media with grain diameter 10 nm will have a 23% decrease in coercivity over a 1-100 nsec range. Index Terms - coercivity, dynamics, micromagnetics, thermal fluctuations

A 3D micromagnetic model is used to examine nucleation field dependence on exchange length, particle size and external field angle for long ferromagnetic particles. Reasonable agreement is shown between the model's predictions and recent experiments on Ni particles. Illustrations of the reversal mode are included which show reversal beginning at the ends and proceeding towards the center of the particle. The amount of discretization necessary for accurate modelling is investigated. For a tape particle with a radius equal to the exchange length, a discretization along the length of the particle is found to be adequate.

The dynamics of thermally activated reversal in elongated ferromagnetic particles is studied. A micromagnetic model is used which accounts for thermal fluctuations through the addition of a stochastic fluctuation field. Results are given approximating a particle of 5:1 aspect ratio, with exchange length equal to particle radius, which is typical of current particulate media. Fast relaxation of the magnetization is observed. Thermal effective volumes inferred from our results can be significantly less than particle volumes.

In this work, experimental techniques involving spectral and temporal analysis were used to determine the weights of each noise 'mode'. A criterion for accurate spectral analysis to determine the cross track correlation length and transition parameter is presented.

The gyromagnetic switching process in longitudinal thin film recording media is studied by using numerical micromagnetics. The dynamic recording process of medium magnetization transition is examined in detail. The head field rise time required for the formation of a magnetization transition is studied at different deep gap field magnitudes for media with damping constants ranging from 0.01 to 1.0. The gyromagnetic switching limit on medium recording data rata is investigated for cases with various damping constants and record head field rise times.

A combined head-medium micromagnetic model is used to analyze servo systems for 10 Gbit/[in.sup.2] recording. Servo patterns are recorded using a micromagnetic medium model to accurately describe the edge-track and noise phenomena. A micromagnetic spin-valve model is then used to replay the recorded information and obtain the position error signal (PES) as a function of off-track position. The results show that the PES linearity is a strong function of the write gap width and deep gap field.

The crystalline anisotropy constant in both thin film and particulate recording media has been determined utilizing high field torque measurements and transimission electron microscopy (TEM). Extrapolation of torque measurements at 45 [degrees] to the film plane yields a 'infinite field torque' that depends solely on the anisotropy constant, the distribution of easy axes, and the saturation magnetization. The distribution of easy axes was determined by TEM measurements. Using this technique the crystalline anisotropy constant of a CoCrTa thin film disk ([M.sub.s] = 690emu/cc) was found to be 2.2x[10.sup.6] erg/cc. A floppy disk with Co-[Gamma][Fe.sub.2][O.sub.3] particles ([M.sub.s] = 120emu/cc) yielded crystalline anisotropy constant of approximately 6.0x [10.sup.5erg/cc.]

Advances in 3D simulations of magnetoresistive heads and media are combined to permit detailed analysis of track-edge recording effects in hard disk applications. Vector Preisach models for thin film media were combined together with 3D micro-magnetic models of dual stripe heads into a single simulation system. This has permitted prediction of servo gain non-linearities in dual stripe heads used in embedded servo disk drives. The models are used to determine the impact of linewidth and alignment tolerances on servo gain nonlinearity.

In this work, the effects of substrate texture on thin film disk noise have been studied via recording spectral analysis. Both the total texture noise power and spectral shape were found to be dependent upon not only the texture, but also the recording density. An analytical expression for the texture noise spectrum was derived by relating texture noise to the disk surface topography. It was found that the texture noise can be characterized by the texture roughness [[Sigma].sub.P] and the down-track correlation length l. The values of l and [[Sigma].sub.P] were determined by fitting the theoretical expression with the measured spectrum. AFM measurements were also performed to examine the surface structure of the textured disk. The results agree with that of the recording spectral analysis.

Square wave recording in polycrystalline longitudinal thin films is studied by using micromagnetic simulation. Track edge recording is examined for various media with different microstructual properties. Signals and medium nonlinearities are studied by including the track edge recording. From the simulated magnetization patterns, it is found that media with higher intergranular exchange coupling has larger track edge area. The introduction of random anisotropy field magnitude reduces the track edge area. Media with higher intergranular exchange coupling will also have transition percolation occur at a lower recording density. At high recording densities partial erasure starts at the track edges, which yields a reduced effective track width. Magnetic poles at the track edges cause broadening of the playback signals, resulting in a larger [PW.sub.50] with increased playback track width.