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Infinite series involving associated Legendre functions of general degree and order are used to describe the scalar potential in the vicinity of a cubic corner. The method of analysis closely follows methods used to describe the magnetic field in the gap of a ring head for magnetic recording and the degree of the Legendre functions can be approximated when the determinant of the derived matrix vanishes. We solve with both Dirichlet and Neumann boundary conditions, but study symmetric and antisymmetric solutions separately. Other geometries considered are the two-dimensional straight edge and the quarter-plane. We also discuss the degeneracy of higher order eigenvalues. [ABSTRACT FROM AUTHOR]

We have extended an earlier two-dimensional (2-D) analysis to provide a relatively simple approach to calculating the transmission of magnetic fields in three-dimensional (3-D) multilayered structures. The approach accommodates complex structures composed of an arbitrary number of layers, each of which may have an arbitrary magnetization direction and anisotropic permeability. The procedure relies on an initial transformation into the 2-D spatial frequency domain and then the use of transmission matrices to relate the fields in the different layers. The approach is general in that it provides a method for finding the field configuration for any set of 3-D magnetic sources embedded in a layered magnetic structure with a linear B-H relationship. In this paper, we concentrate on the analytical formulation and we illustrate the method by using it to determine both the external and internal fields of some relatively simple finite 3-D geometric shapes. We also derive new 3-D expressions for the flux density at the surface of a multilayered magnetic recording medium. In a companion paper, the procedure is applied to examine readback responses for a variety of 3-D magnetic recording configurations. [ABSTRACT FROM AUTHOR]

By matching a singular function approximation to the Fourier solution at the air-bearing surface (ABS), we have derived a three-dimensional (3-D) analytic model of a shielded giant magnetoresistive (GMR) head, with side shields, for perpendicular replay. We present an explicit expression for the potential in the ABS and give values for the parameters in that expression for a range of practical head dimensions. Using only a few terms of this singular potential model, we show that the vertical field is accurate to within 1% of the sensor potential in the region of the medium for the majority of head dimensions suitable for magnetic recording. [ABSTRACT FROM AUTHOR]

We investigated the effects of transition curvature on T50 and Vp-p for a shielded giant magnetoresistive (GMR) element reading a single, isolated transition recorded on a perpendicular medium in the presence of a soft magnetic underlayer. We considered displacement and rotation of the read head relative to the recorded track and a range of read head geometries. The curvature of the transition adversely affects T50, which also increases with azimuth angle. Both T50 and Vp-p decrease as either the GMR element or the element-side shield spacing is reduced. [ABSTRACT FROM AUTHOR]

Using the Fourier method, we have derived a three-dimensional, fully analytic model of a shielded magnetoresistive or giant magnetoresistive head for perpendicular replay. The head may include side shields. The field and the spectral response function are expressed in closed form. Here, we use the model to show the effect of varying the sensor-shield spacings and the air-bearing-surface-underlayer separation on the field and response of the sensor at high areal density. [ABSTRACT FROM AUTHOR]

In a move to extend the storage capabilities of magnetic storage systems beyond 1 Tb/in², the use of patterned media has often been cited. Here, recorded domains are constrained by the geometry of the magnetic island and not the geometry of the recording head. Conventional two-dimensional readout modeling techniques, using the reciprocity integral, rely on the assumption that the across-track medium magnetization is uniform under the giant magnetoresistive replay head. However, in the case of a geometrically constrained medium this is not the case. This paper investigates the effect that the island geometry has on the characteristics of the replay signal in perpendicular patterned magnetic media storage through the extension of the reciprocity integral to three dimensions. The paper describes replay pulses that offer different characteristics from those obtained by conventional two-dimensional techniques. The origins of these differences arc explained by the variation in medium magnetization across the track. [ABSTRACT FROM AUTHOR]

We have used a series of singular expansion functions to represent the potential across the gap of a shielded pole head in the presence of a highly permeable underlayer. This method of analysis reduces the size of the system of equations to be solved for the series coefficients to the number of coefficients that will be used. Just two series terms suffice to evaluate the magnetic potential to within 1 % of the pole potential at any point on the air-bearing sur- face for a large range of head dimensions. Here, we express the surface field spectrum analytically. Including just two series terms provides an excellent estimate. [ABSTRACT FROM AUTHOR]

This paper describes a relatively simple approach to calculating the frequency response for a two-dimensional (2-D) magnetic recording system with a medium that can include an arbitrary number of layers. Each layer may have an arbitrary magnetization direction, anisotropic permeability, and exchange coupling. The approach relies on an initial transformation into the spatial frequency domain and then the use of transmission matrices to relate the fields in the different layers. The approach is general in that it provides a method for finding the field configuration for any set of 2-D magnetic sources embedded in a layered magnetic medium with a linear B-H relationship. Here, we focus on calculating the readback response for a variety of longitudinal and perpendicular recording configurations. Since the permeability may have any wavelength dependence, we can easily include the effect of exchange coupling in the underlayer. [ABSTRACT FROM AUTHOR]

Presents a study that introduced a method of obtaining approximate field components for a two-dimensional perpendicular magnetic recording head in the presence of a soft magnetic underlayer. Assessment of the use and application of the method; Calculation of formulas for the potential at the air-bearing surface across a pole-shield gap or beyond a pole edge; Demonstration of the accuracy of the field component estimates for an unshielded single pole and for a symmetrically shielded single pole.

Presents a study that examined the dynamic switching time in two classes of magnetic recording media by considering two different particle orientation distribution functions. Background on the two classes of magnetic recording media used; Calculation of the switching constant using the Landau-Lifshitz-Gilbert equation of motion; Relationship between the reciprocal of switching time and the difference between the applied and anisotropy fields.

Presents an analytical solution for the magnetic field of a thin-film head of arbitrary dimensions in the presence of a soft magnetic underlayer. Information on the magnetic potential at each pole; Fourier coefficients and field components for thin-film recording heads; Accuracy of approximations that require no Fourier coefficients.

Describes the write fields and replay characteristics of gapped heads with magnetically recessed leading poles for high-frequency digital video. Information on Eddy currents; Geometry of the model used for the gapped heads; Predicted effect of leading pole recession and frequency on the horizontal field of a gapped Sendust head; Evaluation of the effects of wear in the video heads.

Derives expressions for the magnetization distributions that result in one-sided fluxes in infinitely long cylinders whose cross sections are confocal ellipses. Illustration of the cross section of a hollow elliptical cylinder; Relationship of the magnetization distributions to the expressions for a circular cylinder; Examples of flux distributions due to specific magnetizations.

Investigates the effect of throat height reduction in gapped heads constructed from realistic, saturable materials using a finite element method. Two-dimensional finite-element model of a gapped magnetic head; Effect of pole tip saturation in a gapped head; Effect of throat height on the maximum horizontal field of a planar gapped head.

Presents a study which focused on integrals that arise in two-dimensional models of shielded magnetoresistive heads. Coefficient integrals; Potential integrals; Field integrals.

Focuses on a study which used a finite element models to explore the effect that secondary gaps in near-saturated metal-in-gap (MIG) video heads. Methodology used; Discussion on the horizontal and vertical fields of single-sided MIG.

Presents information on a study which offered two analytic solutions for idealized mathematical models of double-element shielded magnetoresistive magnetic recording heads. Use of the Fourier analysis or conformal mapping ideas to study the magnetic field of a recording head; Magnetic field calculations; Comparison with approximate results; Conclusion.

Presents information on a study which investigated the number of Fourier terms needed to evaluate the field components of a magnetic recording head. Development of the approximations; Discussion; Conclusions.

Presents information on a study which focused on a method used for approximation of fields and spectral response functions of perpendicular recording heads. Approximation of the potential; Approximation of head characteristics; Extension of the method for heads of finite length; Conclusions.

Presents information on a study which reexamined the magnetic field of a ring head using a conformal mapping, and by Fan, using Fourier techniques. Review of methods; Exact harmonic coefficients; Conclusions.

Examines the effects of shield recession on the head-field components and on the replay characteristics of a shielded magnetoresistive (MR) sensor. Schematic diagram of a idealized MR sensor with recessed shields; How to obtain the magnetic potential or the head-field components; Conclusion.

Discusses that a new theoretical analysis of an asymmetrically shielded magnetoresistive sensor in the presence of a high-permeability underlayer is obtained by conformal mapping. Theoretical analysis of the study; Results of the study; Calculations of the magnetic field; Functions of spectral response; Conclusions.

The size, shape, and distribution of islands in a patterned medium depends on the patterning process adopted. The off-track performance in this case is mainly dominated by inter-track interference due to the neighboring islands. In this paper, the effect that the island distribution has on the off-track performance is investigated with respect to read channel bit-error-rate performance. [ABSTRACT FROM AUTHOR]

Presents a study which examined the effects of gap length, head-underlayer separation and return pole potential on the magnitude and direction of the field of a gapped magnetic head for perpendicular recording. Optimization of the head geometry for various media parameters; Description of the model; Results.

Presents a study which examined the effects of off-axis fields on the recording properties of perpendicular magnetic recording media. Investigation of the validity of modeling perpendicular recording with the use of a one-dimensional model; Discussion of hysteresis simulations; Details of recording simulations.

Proposes a technique in the application of a keepered media system. Concept of the keepered-media-reproduction with Dual Magnetoresistive (DMR) heads; Information on keeper layer components; Feasibility of keepered-medium reproduction with DMR heads.

Presents a study on the application of Dual Magnetoresistive reproductive mode to improve the design and operation of high-performance multi-track Read-While-Write (RWW) heads. Mathematical model; Analysis of results; Experimental measurements.

Presents a study that developed a method of calculating the Fourier coefficients for a single unshielded magnetic pole head. Equations used for the calculation of Fourier coefficients; Comparison on the results of the calculation of Fourier coefficients using different equations.