Theoretical Analysis of Gap Potential Functions and Corner Saturation in 2-D, Symmetric Magnetic Recording Heads With Tilted Gap Corners

Abstract

The 2-D, semi-infinite symmetrical head with gap corner angle $\alpha $ and in the absence of a soft underlayer was postulated in the early history of magnetic recording to develop the field theory necessary for modeling and understanding the record and readout processes. Practical and mathematical considerations limited the theory of this general head structure to corner angles $\alpha = 90^{\circ }$ (right-angled head) and $\alpha = 0^{\circ }$ (“thin” gap head). Thus, explicit and analytical solutions for the gap potential function and its Fourier transform (necessary for determining the fields beyond the head surface) as functions of corner angle for symmetrical heads remain unavailable. Moreover, saturation in the gap corners associated with the reduction of the gap corner angle is not well understood and characterized. In this paper, the scalar magnetic potential of a single 2-D corner is derived exactly, and the superposition of two corner potentials was then used to derive an approximate analytical expression for the gap potential function of 2-D symmetrical heads with arbitrary corner angle. The derived expressions for the potentials and fields were in excellent agreement with exact analytical solutions and with finite-element solutions for all $\alpha \leq 90^{\circ }$ . The derived expressions were also shown to predict accurately the surface potentials of other symmetrical head structures, including the tilted pole head, the parallel plate head, and the tilted plate head. An analytical approximation for the Fourier transform of the surface field for the 2-D symmetrical head was derived, showing the shift in the spectral gap nulls toward longer wavelengths with reducing gap corner angle. Systematic finite-element calculations of the static vector potential for the 2-D symmetrical head were carried out using a nonlinear B-H core material model for different driving fields and corner angles. Corner saturation was characterized by the driving fields that yield 10% root-mean-square deviation from the linear material response. The simulations correctly predicted the known saturation driving field $M_{s}$ /2 for right-angle heads ( $M_{\mathrm {s}}$ is the core saturation magnetization), and revealed a generalization for all $\alpha \leq 90^{\circ }$ in the form of the exponential dependence $aM_{s}\exp (b\alpha )$ , where the free parameters $a$ and $b$ were determined from fitting to the finite-element simulations for both field maxima and their gradients.