Analytic Three-Dimensional Model of a Double-Shielded Giant Magnetoresistive Perpendicular Head Using a Singular Function Expansion

By matching a singular function approximation to the Fourier solution at the air-bearing surface (ABS), we have derived a three-dimensional (3-D) analytic model of a shielded giant magnetoresistive (GMR) head, with side shields, for perpendicular replay. We present an explicit expression for the potential in the ABS and give values for the parameters in that expression for a range of practical head dimensions. Using only a few terms of this singular potential model, we show that the vertical field is accurate to within 1% of the sensor potential in the region of the medium for the majority of head dimensions suitable for magnetic recording.