Theory of Symmetry and Asymmetry in Two-Dimensional Magnetic Recording Heads
Edress Mohamed, Ammar Isam
Date: 17 May 2016
University of Exeter
PhD in Mathematics
As part of the natural evolution and continued optimisation of their designs, current and future magnetic recording heads, used and proposed in technologies such as perpendicular recording, shingled magnetic recording and two-dimensional magnetic recording, often exhibit asymmetry in their structure. They consist of two semi-infinite ...
As part of the natural evolution and continued optimisation of their designs, current and future magnetic recording heads, used and proposed in technologies such as perpendicular recording, shingled magnetic recording and two-dimensional magnetic recording, often exhibit asymmetry in their structure. They consist of two semi-infinite poles separated by a gap (where the recording field is produced), with an inner gap faces inclined at an angle. Modelling of the fields from asymmetrical structures is complex, and no explicit solutions are currently available (only implicit conformal mapping solutions are available for rational inclination angles). Moreover, there is limited understanding on the correlation between the gap corner angle and the magnitude, distribution and wavelength response of these head structures. This research was therefore set out to investigate approximate analytical and semi-analytical methods for modelling the magnetic potentials and fields of two-dimensional symmetrical and asymmetrical magnetic recording heads, and deliver a quantitative understanding of the behaviour of the potentials and fields as functions of gap corner angles. The accuracy of the derived expressions (written in terms of the normalised root-mean-square deviation) was assessed by comparison to exact available solutions for limited cases, and to finite-element calculations on Comsol Multiphysics. Two analytical methods were derived to approximately model the fields from two-dimensional heads with tilted gap corners in the presence and absence of a soft magnetic underlayer (SUL): in the first method, the potential near a single, two-dimensional corner held at a constant potential is derived exactly through solution of Laplace's equation for the scalar potential in polar coordinates. Then through appropriate choice of enclosing boundary conditions, the potentials and fields of two corners at equal and opposite potentials and displaced from each other by a distance equal to the gap length were superposed to map the potential and field for asymmetrical and symmetrical heads. For asymmetrical heads, the superposition approximation provided good agreement to finite-element calculations for the limited range of exterior corner angles 0 from 0 (right-angled corner) to 45, due to the mismatch of surface charge densities on both poles for this geometry. For symmetrical head structures, the superposition approximation was found to yield remarkable agreement to exact solutions for all gap corner orientations from 0 (right-angled head) to 90 ("thin" gap head). In the second method derived in this research for modelling asymmetrical heads involved using a rational function approximation with free parameters to model the surface potential of asymmetrical heads. The free parameters and their functional dependence on corner angle were determined through fitting to finite-element calculations, enabling the derivation of analytical expressions for the magnetic fields that are in good agreement with exact solutions for all corner angels (0 to 90). To complement the two approximate methods for modelling the fields from asymmetrical and symmetrical heads, a new general approach based on the sine integral transform was derived to model the reaction of soft underlayers on the surface potential or field of any two-dimensional head structure, for sufficiently close head-to-underlayer separations. This method produces an infinite series of correction terms whose coefficients are functions of the head-to-underlayer separation and gap corner angle, that are added to the surface potential or field in the absence of an underlayer. This new approach demonstrated good agreement with finite-element calculations for sufficiently close head-to-underlayer separations, and with the classical Green's functions solutions for increasing separations. Using the derived analytical method and explicit expressions in this work, an understanding of the nature of the magnetic fields and their spectra as functions of the gap corner angles is gained. This understanding and analytical theory will benefit the modelling, design and optimisation of high performance magnetic recording heads.
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