S.W. Yuan

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. >

Statistical data analysis of magnetic recording noise mechanisms

Statistical data analysis using empirical eigenfunctions, known as the Karhunen-Loeve (K-L) expansion, is applied to characterize noise mechanisms in magnetic recording. Given any original data set and hence its correlation (covariance) matrix, an empirical orthogonal set of eigenfunctions can be obtained. The original data set can be expressed as an orthonormal expansion of these eigenfunctions. This feature of the K-L expansion can be used to study dominant noise profiles extracted from a large number of magnetization transition data. Two simple models of magnetization transitions are first utilized to investigate the validity of this expansion. Noises induced by transition center shifting (jitter), transition width fluctuation, amplitude modulation, and combined effects are respectively identified by the first several most important eigenfunctions in the expansion. Eigenfunction expansions of transition data obtained from experiments and numerical simulations are also obtained. >

Cross-track characteristics of shielded MR heads

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. >

Off-track spacing loss of shielded MR heads

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. >

Magnetoresistive heads for ultra high density recording

Micromagnetic modeling of small dimension magnetoresistive (MR) heads is reviewed. Recent simulation results are presented, pertaining to recording applications with high areal density nearing 1-10 Gb/in/sup 2/. The proper biasing and reproduction 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. >

Domain wall structures and dynamics in thin films

Computer simulation is used to study two-dimensional domain wall structures and dynamics in Permalloy thin films with easy axis parallel to the film plane. The effective wall mass and the viscosity coefficient are found to be one or two orders of magnitude greater than for one-dimensional bulk material. For external easy axis fields much larger than the anisotropy field, the wall motion exhibits turbulent behavior with vortex breakdown as a precursor, with an increasing hard axis field, the wall configuration changes from an asymmetric Bloch wall to a Neel wall. >

Inhomogeneities and coercivity of soft Permalloy thin films

Coercivity mechanisms in thin 1000-AA Permalloy films due to inhomogeneous distributions of in-plane uniaxial anisotropy are investigated numerically, utilizing a two-dimensional domain wall model. The distribution of anisotropy could be attributed to the polycrystalline grain structure of thin films, as well as magnetostrictive stress. Typical anisotropy orientation dispersion induced by polycrystalline grains does not appear to account for the wall coercive force observed in soft Permalloy films. Other mechanisms, such as stress-induced anisotropy, may be dominant. >

Biasing characteristics of unshielded, boundary exchange-coupled SAL/MR sensors

A magnetoresistive (MR) sensor with patterned exchange-biasing layer at its end regions exhibits quite and stable responses. A mathematical model simulating an unshielded, boundary exchange-biased SAL/MR structure is developed. The modeled results are in good agreement with the experimental data. However, biasing characteristics are quite different from modeled results assuming infinitely long stripes. For the boundary exchange-coupled SAL/MR design, the strip height has a significant impact on the biasing characteristics and the effect becomes even more pronounced as the track width is further reduced. >