H.N. Bertram

SNR and density limit estimates: a comparison of longitudinal and perpendicular recording

Simplified Neel-Arrhenius analysis is utilized to determine limiting densities versus SNR for longitudinal and keepered-perpendicular media. Dominant transition noise is assumed and the effects of grain size distribution and storage above room temperature are included. Perpendicular recording potentially exhibits a higher density than longitudinal; for example, at SNR=20 dB, the limiting densities are approximately 500 and 100 Gbit/in/sup 2/, respectively.

Magnetic recording configuration for densities beyond 1 Tb/in/sup 2/ and data rates beyond 1 Gb/s

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/spl deg/ with respect to the perpendicular direction. Here, focus is on the tilt angle at 45/spl deg/ 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.

Fast adaptive algorithms for micromagnetics

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/sup 2/) asymptotic computation time. 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 log/sub 2/ 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. >

Signal to noise ratio scaling and density limit estimates in longitudinal magnetic recording

A simplified general expression is given for SNR for digital magnetic recording for transition noise dominant systems. High density media are 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.

Arrhenius–Néel thermal decay in polycrystalline thin film media

A simple expression for the remanent coercivity versus field time duration has been developed for polycrystalline thin film media with two-dimensional random anisotropy axis orientation. Explicit averaging of the thermally induced reversal for random grains is shown to be well approximated by the thermal decay of one particle with anisotropy axis at an angle of ≈21° to the applied field. The expression has no adjustable parameters and two slightly different forms apply to noninteracting and weakly interacting grains. Applicability is shown to be for times greater than approximately 100 ns. Good agreement is shown with measurements on two series of thin films with varying coating thickness.

Recording and transition noise simulations in thin film media

Micromagnetic simulations of the recording of a single transition in thin-film metallic media are presented. The film is modeled as a planar array of hexagonal single-domain particles with long-range magnetostatic as well as possible nearest-neighbor exchange interactions. Magnetization configurations are determined by following the Landau-Lifshitz equations of motion with finite damping. The media parameters used here approximate Co films. The recording geometry resembles a close flying head with a small gap. Transition fluctuations, a source of transition noise, are also suited for both non-exchange-coupled and exchange-coupled media. It is shown that intergranular exchange coupling can significantly enhance transition noise and that films with well defined nonmagnetic grain boundaries exhibit better signal-to-noise ratios. >

Transition jitter estimates in tilted and conventional perpendicular recording media at 1 Tb/in/sup 2/

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/spl deg/, 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.

Fundamentals of the magnetic recording process

The basic phenomena associated with the recording and reproduction of signals on magnetic recording media are described. Fields due to magnetized media and heads are reviewed along with their Fourier transforms. The playback-isolated voltage pulse and square-wave voltage spectrum are discussed in detail for various magnetization orientations. Descriptive models of the recording process are given for both longitudinal and vertical recording.

Transition noise analysis of thin film magnetic recording media

A simple but accurate expression for general non-stationary noise correlation in the presence of a recorded transition is analyzed in terms of both noise voltage and spectral measurements. The parameters of this analysis are solely the cross track correlation width s, the transition shape and parameter a, the head-medium 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 position and amplitude jitter of a fixed transition shape. The relative weights depend on 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. >

A simple statistical model of partial erasure in thin film disk recording systems

A simple statistical model of the partial erasure effect in metallic thin-film recording is given. Experimental data are shown and used to determine a fundamental parameter of the micromagnetic structure of the medium. This single parameter determines the extent of erasure at any transition separation. Since it has no (first-order) dependence on the rate of zigzags, it is anticipated that it will be relatively independent of the transition noise amplitude of the medium. >