Williams-Comstock model with finite-length transition functions

The theory of the third-order-polynomial (TOP) and fifth-order-polynomial (FOP) magnetization transitions is presented. These transitions have a finite length, rather than an asymptotic approach to ±Mr., which is the case with some widely-used transition functions. The Williams-Comstock model is used to obtain the transition parameters, which are equal to half the transition lengths, resulting in quadratic equations and simple expressions. In this analysis, the write-field gradient is maximized with respect to the deep-gap field, as well as with respect to the distance of the transition from gap center, which results in a higher gradient than is obtained with the original Williams-Comstock approach, at the expense of a higher write current. Analytic expressions are obtained for the read pulses of inductive and shielded magnetoresistive heads, and equations for nonlinear transition shift are derived for the arctangent and the TOP transitions. The results are compared with those obtained using arctangent and tanh transitions and with experiment. In addition, certain aspects of the write-process Q function and the optimum deep-gap field are discussed.