Approximate Expressions for the Magnetic Potential and Fields of Two-Dimensional, Asymmetrical Magnetic Recording Heads

Abstract

Two-dimensional asymmetrical magnetic head are characterised by parallel inclination of the semi-infinite, inner gap walls, and where the gap length and head-to-underlayer separation are small compared to the other dimensions in the head. With head corner inclination, these structures contribute to reduction in the effective gap length of the head and therefore increase in the field magnitude and narrowing of the field distributions near the acute gap corner. Asymmetrical heads were therefore proposed for increasing the writing and readout resolutions in gapped magnetic head structures. There are currently no explicit or approximate analytical solutions for the potential and fields from two-dimensional asymmetrical magnetic heads. This paper is concerned with the detailed theoretical derivation of relatively simple closed-form approximations for the scalar magnetic potential and fields from twodimensional asymmetrical magnetic heads and their Fourier transforms, applicable to any arbitrary corner inclination angle. A general theory based on the translated Sine Fourier series is developed to model and study the reaction of a soft magnetic underlayer (SUL) on the surface potential of any magnetic head structure, and applied to the asymmetrical head. The approximate potential and field expressions derived in this paper demonstrated very good agreement with finite-element calculations of two-dimensional asymmetrical heads.