The Fourier method is used to provide new analytic solutions for idealized
mathematical models of double-element shielded magnetoresistive (MR) recording
heads. The general two-dimensional model allows analysis of various recording head
configurations; a single pole head, a ring head, a dual stripe head and a differential
head. The analysis accommodates both longitudinal recording (with no soft magnetic
underlayer present) and perpendicular recording (in the presence of a soft underlayer).
Typical field, spectral response function and output voltage pulse plots for double-element
MR heads are given and compared to published, approximate solutions. The
integrals arising in the determination of the Fourier series coefficients, magnetic potential
and magnetic field components are expressed either as rapidly convergent infinite
series or in terms of special functions to provide a more efficient means of evaluation
than numerical integration. It is shown that, in many situations, it is only necessary
to take the first Fourier coefficient in the calculation of output voltage pulse shapes
in order to achieve sufficiently accurate results. Bi-variate regression techniques are
used to provide a convenient method to approximate the first Fourier series coefficient
for a broad range of typical head dimensions.
The thesis goes on to examine high speed switching behaviour in two classes
of recording media by considering two different particle orientation distributions; 2D
random media - intended to simulate a modern thin film rigid disk, and 3D oriented
media- simulating a single domain particulate tape media. The gyromagnetic
switching constant of a medium is calculated directly from the Landau - Lifshitz -
Gilbert (L-L-G) equation of motion, which is solved numerically. The switching constants
produced are discussed and compared with published experimental values for
different media
