Optimization of the response of magnetoresistive elements

A way to optimize the output signal of a general thin-film magnetoresistive element with a homogeneous magnetization field as used in applications with a saturating external magnetic field is presented. The element is assumed to be operated by four-point measurement. In order to be able to compare different elements, a figure of merit is defined. The general theory of the anisotropic magnetoresistance (AMR) effect is treated, and a few general rules for optimization are formulated. It is concluded that in order to obtain a maximum signal voltage amplitude, the current density in the elements should be constant, i.e., not affected by the AMR effect. It is shown, that the AMR effect on the current density in the element usually cannot be neglected. Some special configurations of magnetoresistive elements are treated in detail. The problem of four point contacts in an infinitely wide thin film is solved analytically, with the aid of a special transformation. It is found, that there is an optimum thickness of the thin film in an AMR device, which depends on the material and the deposition technique. For pseudo-Hall elements, an optimum length-to-width ratio is found ( approximately equals 1.35).