Analytical formulas for the unshielded magnetoresistive head

The magnetostatic and frequency response characteristics of the unshielded magnetoresistive (UMR) head have been previously calculated by means of a numerical simulation which utilized the principle of reciprocity to reduce the computational task of solving the relevant micromagnetic equations. The results of the simulation were found to be in excellent agreement with measurements made on actual UMR heads [N. Smith and D. Wachenschwanz, IEEE Trans. Magn., MAG-23, p. 2494 (1987)]. In the present paper, we analyze an idealized UMR head, following in spirit the procedure outlined in the previous work; however, we formulate the problem by introducing simplifying approximations which retain the essential physics, deriving simple equations describing the bias magnetization distribution, and the frequency response. The equations obtained in this way are analytic and simple, yet in agreement with the micromagnetic simulation and experimental measurements. Furthermore, the analytic formulas provide a source of insight which may be of use in the design or optimization of UMR recording heads.