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In high-density perpendicular magnetic recording channels, nonlinear transition shift (NLTS) is one of the distortions that can degrade the system performance. Write precompensation is a standard method used to combat the negative effect of NLTS. In this paper, we propose a modified pattern-dependent noise predictive (PDNP) detection algorithm for use on channels with electronics noise, transition jitter noise, and NLTS. We show that this detector can offer significant improvement in bit-error-rate (BER) compared to conventional Viterbi and PDNP detectors. Moreover, the system performance can be further improved by combining the new detector with a simple write precompensation scheme. Index Terms--Jitter noise, NLTS, pattern-dependent noise prediction, perpendicular recording.

A dual-layer patterned element magnetic recording medium design is presented that is expected to satisfy areal densities at 10 Tb/[in.sup.2]. Each element consists of a small high anisotropy initial layer on top of which is deposited on an exchange-coupled soft layer of approximately equal thickness that extends in the recording direction almost to an adjacent element. This design has two distinct advantages. Reversal by precessional switching will occur for realistic record head field rise times (100-200 ps). Thermal stability for such small elements is maintained by hard section anisotropy fields that are an order of magnitude larger than the reversal field. Here, reversal mechanisms and system design are discussed in detail. Index Terms--Landau-Lifshitz equation, patterned media, perpendicular recording, precessional reversal.

Precessional reversal in composite patterned media elements has been studied for various applied field parameters. The decrease of the percentage of the elements covered by the applied field leads to a rapid increase of the reversal field and decrease of the critical rise time required for precessional reversal. For weak and strong applied fields, the reversal time respectively was found to decrease and increase with an increase of the applied field strength and decrease of the rise time. For certain (large) values of the applied field strength and pulse duration bands of non-reversal can be obtained. This behavior is associated with multiple precessional oscillations between two equilibrium states. Such oscillations can be eliminated by properly choosing the field pulse duration and element damping constant. Index Terms--Landau--Lifshitz equation, patterned media (PM), perpendicular magnetic recording, precessional magnetization reversal.

An expression for estimating error rate in a perpendicular magnetic recording system is developed. The probability of error is estimated for a dominant dibit error event. Noise includes stationary white Gaussian head/electronics noise and nonstationary colored medium transition noise. Error rate is determined for a variety of parameter changes. In particular, it is shown how two systems with the same total signal-to-noise ratio can have different error rates. Expansion of the model to include additional signal and noise effects as well as the evalation of different error events is discussed. Index Terms--Error rate, head/electronics noise, medium transition noise, perpendicular magnetic recording.

It is conceivable that early generations of patterned media will utilize read heads whose dimensions are several times larger than an 'island' of magnetization. For such a scenario, we propose a 'multiple islands per read head' model where the output from the read head is a function of the magnetization from several independently written tracks of islands. In particular, we focus on a '3 islands per read head' model where the output from the read head is a function of the magnetization from three independently written tracks of islands. The readback signal is determined from a finite track-width magnetoresistive (MR) head model using reciprocity calculations, and two noise sources--island position jitter and AWGN electronics noise--are considered. By sampling the noisy signal at intervals corresponding to the down-track island separation, we obtain a discrete-time readback channel model whose performance is obtained under maximum-likelihood sequence detection. Index Terms--Island position jitter, 'multiple islands per read head', patterned media.

To optimize a high-density magnetic recording system, one needs to know the tradeoffs between various components of the system including the read/write transducers, the magnetic medium, and the read channel. In this paper, we consider a channel model characterized by three parameters: the replay pulse width [T.sub.50], the transition jitter noise standard deviation [[sigma].sub.J], and the signal-to-electronic-noise ratio SN[R.sub.WG]. We utilize information-theoretic tools to determine the acceptable region for the channel parameters [T.sub.50] and [[sigma].sub.J] when optimal detection and linear coding techniques are used. This paper is an extension of a similar analysis for a system that utilized a minimum mean-squared error (MMSE) equalizer, a Viterbi detector, and a Reed-Solomon (RS) code. Our main conclusion is that there is a considerable potential gain to be achieved by using improved detection and coding schemes as compared with the present system. Index Terms--Information theory, jitter noise, parameter optimization, perpendicular magnetic recording.

In a perpendicular magnetic recording system, advanced read/write transducers, magnetic media, and signal processing techniques are combined to achieve the highest possible storage density, subject to severe constraints on reliability. This paper proposes a quasi-analytic methodology for exploring the complex design tradeoffs among these system components. We use a simple channel model, characterized by three parameters: isolated voltage pulse width, transition jitter noise variance, and additive electronic/replay head noise power. The system incorporates generalized partial-response equalization and maximum-likelihood detection, along with a Reed-Solomon error-correcting code characterized by its code rate. We calculate a family of 'design curves' from which we can determine, for a given set of channel parameters, the maximum user density that can be achieved with a specified codeword error rate, along with the corresponding code rate. The design curves can also be used to determine the acceptable range of channel parameters consistent with a target user density and codeword error rate. Index Terms--Additive noise, jitter noise, parameter optimization, perpendicular recording, Reed-Solomon code, Viterbi detector.

In this paper, we use micromagnetic simulation to study the switching field reduction and the switching field distribution in polycrystalline thin-film media. We first show that, for the coupled magnetic particles, the switching field of the high-anisotropy particle is reduced as a result of the exchange coupling with the low-anisotropy particle. The switching field reduction increases almost linearly with the anisotropy difference between the coupled particles. An optimal exchange exists that gives a maximum switching field reduction. This switching field reduction is more severe for a small applied field angle; therefore, the angular sensitivity of the switching field is reduced compared to the Stoner-Wohlfarth relation. Detailed micromagnetic simulations also show that in polycrystalline thin-film media, because of the variation and the reduction of the magnetic properties at the grain boundaries, the media coercivity can be reduced significantly. The primary reason for this switching field reduction is the exchange interaction between the grain boundary and the grain center region. Index Terms--Anisotropy distribution, grain size distribution, perpendicular magnetic recording, tilted perpendicular recording, switching field distribution, switching field reduction.

Noise caused by thermal magnetization fluctuations in giant magnetoresistive sensors, mainly in the free layer, limits the achievable signal-to-noise ratio and thus the density of magnetic recording systems. Here, we describe a quasi-analytical method to study this noise. First, by discretizing the free layer into sufficiently small rectangular cells, an equilibrium state of the free layer is obtained using a quasi-static energy minimization technique. A linear tensor relation between the magnetization spectra and the thermal fluctuations is found for the two approaches: 1) Landau-Lifshitz-Gilbert-Brown and 2) collective spin wave excitation. In the former, damping and thermal fields are added to each cell and then a Fourier transform is taken to obtain the spectra. For the eigenmode approach, the lossless dynamic equations are diagonalized, yielding the system's intrinsic eigenmodes. Then damping and thermal fluctuations are added to each eigenmode, independently. The sensor playback noise power spectrum density, a measurable quantity, is calculated by summing up the contributions from each eigenmode or cell magnetization. This computationally light treatment yields a clear physical picture of the phenomenon, relating damping, thermal fluctuation, and noise. We describe each step of the calculation procedure in detail and give examples. Index Terms--Diagonalization, dynamic damping parameter, eigenmode, GMR sensors, noise spectra, thermal fluctuation.

The recent proposal of tilted perpendicular recording for Tb/[in.sup.2] densities is extended here to examine the effects of intergranular exchange and anisotropy distributions on signal-to-noise ratio. This new recording system includes the single pole head, the medium and the soft underlayer as in perpendicular recording, but the medium anisotropy axes are titled at about 45[degrees], optimally in the crosstrack direction. Both analytical formulas and micromagnetic simulations are utilized and both tilted and conventional perpendicular media are considered. At 1.2 Tb/[in.sup.2] exchange optimization and suitable anisotropy distribution limits give percentage transition jitter of 10% and 30% for tilted and conventional perpendicular media, respectively. Index Terms--Micromagnetic simulation, perpendicular recording, signal-to-noise ratio, thermal stability, tilted perpendicular recording, track edge effect, transition jitter.

Previous studies have shown that tape medium noise is dominated by surface roughness. Here, we use error rate analysis to evaluate the effects of surface roughness as well as particle size distributions in a partial-response maximum-likelihood (PRML) channel. We use: 1) a modified self-consistent model, incorporating a log-normal particle size distribution and a random packing of the particles to simulate the recording process and 2) a predeveloped error rate model to evaluate the system performance with fixed head/medium combinations. Surface roughness is introduced as a varying random head/tape spacing during both the recording and the playback processes. The impact of mean particle length, roughness variance, and roughness correlation length on system performance is examined for a partial response (PR4) channel. A surface roughness variance changing from 5 to 10 nm yields, at 200 kfci with a particle length of 60 nm, a change of error rate from [10.sup .-10] to [10.sup.-5]. Because of the finite head read track width, roughness with shorter correlation lengths can be cross-track-averaged more readily and yields better system performance. We also found that larger particle size media have higher dc noise but lower roughness-induced transition noise. The shorter-particle-size media give better system performance, and the advantage increases with reducing roughness variance. Index Terms--Error rate, magnetic tape, partial-response maximum-likelihood (PRML), roughness correlation length, roughness noise, roughness variance.

A new magnetic recording system is evaluated that includes the single-pole head, a new medium design, and the soft underlayer of perpendicular recording. The proposed medium consists of perpendicular grains with anisotropy directions tilted optimally about 45[degrees] with respect to the perpendicular direction. Here, focus is on the tilt angle at 45[degrees] in the crosstrack direction, including a small but typical dispersion. The write pole consists of a tapered-neck single-pole head with a very small throat height that yields maximized write fields without increased edge track degradation. The advantages of tilted perpendicular recording are discussed using theoretical and numerical micromagnetic analyses. This design achieves a much higher signal-to-noise ratio (SNR) than conventional recording, because it is less sensitive to medium orientation distributions and, for the same thermal decay, can utilize media with much smaller grain sizes. The switching speed is much more rapid due to increased recording torque. Estimated recording limits for tilted perpendicular recording with a medium-jitter SNR of 17 dB are beyond densities of 1 Tb/[in.sup.2] and data rates of 1 Gb/s. Index Terms--Data rate, micromagnetic simulation, perpendicular recording, recording method, signal-to-noise ratio, thermal stability, tilted perpendicular recording, track edge effect, transition parameter.

We have developed a three-dimensional micromagnetic perpendicular recording model to analyze high-density perpendicular write fields. Here, we compare a tapered-neck pole with a very small throat height to various write pole designs for a single-pole head. In studying the effects of throat height and write pole-return pole spacing, we found that, for a large throat height, both the write field and field gradient decrease as the throat height increases. The write field shape changes significantly at the leading edge for a write pole-return pole spacing less than 300 nm. The effects of soft-underlayer (SUL) permeability, saturation, and thickness basically follow the analytical formula. The net recording field is almost constant for SUL permeability above about 50. Index Terms--Micromagnetic simulation, perpendicular recording, write field analysis, write pole design.

We have measured and analyzed signal-dependent noise spectra of metal particle (MP) tapes. For all the tapes examined, the signal-dependent noise is higher than the dc saturation noise. The total signal-dependent noise power first increases with density and then saturates. The measurement indicates that without write equalization, the broad-band signal-dependent noise power increases with recording density, indicative of transition noise. With write equalization, the broad-band signal-dependent noise is approximately independent of density and has a level equal to the high density limit without write equalization. We used a specially designed pattern to eliminate tape speed variations and find the precise recording positions. We used a Karhunen-Loeve expansion with the time-domain data to determine the noise modes and their recording density dependency. The analysis shows that amplitude and jitter modes dominate for all the MP tapes examined. Different noise mode contributions are observed for different coating thicknesses. The amplitude mode dominates for relatively thick coatings, while the jitter mode dominates for thin coatings, as in thin-film disk media. Index Terms--Noise mode, signal-dependent noise, tape medium noise, transition noise.

We investigated the potential of extending conventional magnetic recording technology to a one terabit per square inch (Tb/[in.sup.2]) density using a simple model, focusing on the off-track capability of a hypothetical perpendicular recording system. Our simulation considered the medium's granular structure, head side reading, and side writing. However, as a first approximation, interactions between grains were neglected. We investigated the characteristics of both an isolated transition and a pseudorandom sequence. The signal-to-noise ratio is very low (around 10 dB) at such a density. Direct bit-by-bit simulation on 80 000 bits of a 1023-bit pseudorandom sequence yielded the bit-error rate (BER). By changing the squeeze position of the side track, a series of 'bathtub' curves was calculated and thus, 747 curves at various BER thresholds were investigated. We also studied different detection schemes and the block failure rate after error-correction code. Index Terms--Bit-error rate, block failure rate, off-track capability, perpendicular recording, squeeze, terabit recording.

We describe micromagnetic simulations that examine the effect of intergranular exchange on thermal stability of dibit transitions in two-dimensional (2-D) isotropic longitudinal media. We found that, by maintaining the constant [M.sub.r]t, the writing coercivity and the average grain planar area, with increasing [h.sub.e] [K.sub.u] is reduced. Increasing the intergranular exchange enhances thermal decay and yields a smaller signal-to-noise ratio (SNR) at [10.sup.9] s. However, if both [K.sub.u] and [M.sub.r]t are fixed, increases slightly if the writing coercivity is held constant but decreases slightly at a fixed intrinsic loop closure field. For both cases, a smaller SNR is always found at a higher exchange initially and after ten years. Thus, for 2-D isotropic longitudinal media, the intergranular exchange must be reduced to achieve a higher SNR at [10.sup.9] s. Index Terms--2-D isotropic longitudinal media, intergranular exchange, micromagnetic simulation, thermal stability.

We describe micromagnetic simulations to examine the effect of intergranular exchange on thermal stability of dibit transitions in slightly oriented longitudinal media. We found that, by increasing the intergranular exchange and the anisotropy orientation ratio, [K.sub.u] is reduced to maintain the fixed [M.sub.r]t, the writing coercivity, and the average grain planar area. Within the drive working temperatures (T [less than or equal to] 350 K), to increase signal-to-noise ratio (SNR) at [10.sup.9] s, both the exchange and the anisotropy orientation ratio must be reduced. However, if both [K.sub.u] and [M.sub.r]t are fixed, for a constant circumferential loop closure field, a larger SNR is always exhibited at a higher OR([M.sub.r]) initially and at [10.sup.9] s. For both cases, if the intergranular exchange cannot be neglected, SNR always slightly increases with increasing OR([M.sub.r]). Index Terms--Intergranular exchange, micromagnetic simulation, oriented longitudinal media, thermal stability.

The paper theoretically examines playback characteristics of a giant magnetoresistive (GMR) head for perpendicular recorded magnetization transitions with a soft underlayer. The magnetic scalar potential, calculated numerically by the finite-element method, is fitted to a simple formula involving geometry-dependent parameters. The reciprocity principle leads to the shape of the single pulse signal. For high permeability of the underlayer the pulse has an error function-type dependence on distance. Within this approximation, the paper derives simple formulas for the pulsewidth [T.sub.50], [D.sub.50], and transition-noise-limited signal-to-noise ratio. Index Terms--Magnetic scalar potential, perpendicular recording, resolution, single pulsewidth, SNR.

We describe simulations using a medium model with random grain structure, to study the servo position error signal (PES) in a perpendicular recording system. Under various detection schemes, values of the PES null position jitter and the PES sensitivity variation at the null point are calculated. To evaluate the effect of medium noise on the PES detection, the values are compared to those of media with different average grain in-plane areas and grain size distributions. For both the PES null position jitter and the PES sensitivity variation at the null point, decreasing the average grain in-plane area or the grain size distribution yields smaller fluctuation. The servo PES has a strong dependence on the average--medium grain in-plane area. When PES of longitudinal recording systems is compared with that of perpendicular systems, perpendicular recording yields much better results because of a sharp write-field gradient at the track edge. Index Terms--Grain size, grain size distribution, perpendicular recording, position error signal (PES), PES sensitivity, servo PES detection scheme.

An experimental technique has been developed to accurately measure the time dependence of playback voltage due to the decay of recorded magnetization patterns. A 'calibration' procedure is utilized to minimize the effect of magnetoresistive head sensitivity variations. This technique is applied to a systematic study of the dependence of the signal decay on recording bit density and magnetic layer thickness in longitudinal thin film media. A Neel-Arrhenius type model is introduced to calculate the degradation of a square wave magnetization pattern subject to thermal agitation. Because the equivalent external field which reduces the energy barrier is the time and spatially varying magnetostatic field produced by magnetic transitions, an iterative procedure is utilized to obtain the time dependent magnetization. The model takes into account distributions of grain volume and anisotropy axis. The calculation results are compared with the experimental data and good agreement is obtained. Index Terms - Magnetic disk recording, stability.

Simple analytical expressions for the longitudinal surface fields from four types of shielded magnetoresistive (MR) heads, i.e., single element MR heads (both centered and off-center), dual-stripe heads, and 'differential' MR heads are derived using superposition and Schwarz-Christoffel transformation. These expressions are utilized to study playback pulse shape and spectra. For the centered shielded MR head as well as the dual stripe shielded MR head, simple accurate formulas for [PW.sub.50] and [D.sub.50] are derived. For the dual stripe MR head, the model predicts the position of the first spectral gap null accurately, as well as the voltage spectral shape.

A general review of studies on microstructure, magnetic properties and recording performance of bicrystal media grown on single crystal substrates, a NiP/Al substrate and a glass substrate is given. With similar magnetic properties, a direct experimental comparison of recording performance of CoCrPtTa/Cr/NiP films between the media with Cr (200) and Cr (110) textures on glass ceramic substrate is provided. Typically, 5-6 dB SNR improvement is observed for medium with Cr (200) texture from recording densities of 40kfci to 140kfci. Medium with Cr (200) texture has [approximately]100% bicrystal cluster microstructure and has smaller and more uniform Cr grains. A noise mechanism is discussed that relates the bicrystal microstructure to an effective random anisotropy field magnitude. Micromagnetic simulations show the latter will reduce medium noise when there is relatively large intergranular exchange coupling between the grains. However, when the intergranular exchange coupling is small, the introduction of random anisotropy field magnitude will increase the medium noise. The other noise mechainsm could be due to larger Cr grain size. A bigger magnetic cluster could be formed because more Co alloy grains on a larger Cr grain are coupled together through stronger inner intergranular exchange force, which leads to higher media noise.

Scanning Magneto-Resistance Microscopy (SMRM) is a technique which we have developed whereby commercial magneto-resistive (MR) heads are used to both image and record magnetic media. A high resolution, linearized positioning stage is used to raster-scan the recording media (either a hard disk platter or tape coupon) with respect to the MR read/inductive write head. The scanning is performed with the slider in physical contact with the media. Thermal asperities are not present since the contact is continuous rather than intermittent, and the scan speed is slow. This report describes the SMRM hardware, and SMRM measurements of isolated transitions from two different types of MR heads are analyzed and compared to corresponding spin stand data.

Overwrite in particulate tape media is studied utilizing a micromagnetic simulation model. Seven different media, including traditional thick tape and thin metal-particle tape, are simulated to study the effect of tape thickness and demagnetizing ratio on overwrite. Recording head parameters, such as the record gap, the record current, and head-medium spacing, are analyzed for overwrite in the thick tape media. An analytical formula is developed to describe the overwrite ratio as a function of the frequency ratio before and after overwrite.

Hysteresis and baseline shift in shielded permanent magnet stabilized MR/SAL playback heads are studied via a 3D micromagnetic simulation. The hysteretic behavior is examined by calculation of playback voltages and uniform field transfer curves. The overlap region between the MR/SAL layers and the permanent magnet is seen to have a strong effect on the stability of the device. The amount of hysteresis is studied versus the width of the overlap region and the off-track position of the head.

The playback properties and spectra of a shielded magnetoresistive head are examined utilizing a Fourier series method. Semi-analytic solutions are given for the magnetic scalar potential and spectra in terms of coefficients which have been numerically determined for common geometries. Voltage pulses are generated by convolving the potential with the derivative of a tanh longitudinal magnetization transition. Expressions for the P[W.sub.50] versus flying height are obtained by fitting the widths of the theoretically determined playback pulses. It is found that the playback properties of a shielded magnetoresistive head depend strongly on the geometry.

High density disk drive systems utilize fine grain polycrystalline thin films as a storage medium. These films exhibit noise that is pattern dependent and has appreciable magnitude near the center of each recorded transition. A model for error rates in a PRML channel is presented to explore how variations in medium noise parameters effect system performance. The channel is assumed to be characterized by both pattern dependent nonstationary medium noise and white Gaussian electronic and/or head noise. Results are presented in terms of both error rate and sensitivity of error rate to changes in medium parameters.

A simple but accurate expression for general non-stationary noise correlation i the presence of a recorded transition is analyzed in terms of both noise voltag and spectral measurements. The parameters of this analysis are solely the cross track correlation width s, the transition shape and parameter a, the head-mediu spacing d, and the replay gap length g. It is shown that although the noise varies continuously through the transition, a reasonable decomposition that accounts for a large percentage of the total noise is into conventional positio and amplitude jitter of a fixed transition shape. The relative weights depend o the head-medium parameters; for current head-medium configurations and for longitudinal recording, position jitter dominates. A simple closed form expression for the noise power spectrum is given. Published experimental measurements of signal and noise spectra made with pseudo-random write data compare extremely well with this theoretical analysis, and lead to very good estimates for a and s. The analysis is general and applies for low-density recording with both inductive and magnetoresistive heads as well as all magnetization orientations.

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.

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.