Magnetoresistance and Domain Structure in Thin Nickel Films

Abstract

Magnetoresistance measurements have been used to determine the magnetic domain structure of nickel films. The magnetoresistance results are discussed in terms of a new representation in which the resistivity components parallel and transverse to the current, measured simultaneously as the applied magnetic field varies in magnitude or direction, are regarded as Cartesian coordinates. This representation is independent of the direction of the current relative to any preferred orientations in the film. Marked differences are found between the measured magnetoresistance and the behavior expected of a single-domain film. The nature of the differences indicates that these films must at least contain an angular distribution of uniaxial magnetic regions in the film plane. A particular model having these properties is developed. Here local anisotropy axes are uniformly distributed in direction and are superimposed on a common uniaxial anisotropy. The local and common anisotropy energies are assumed of different strength; their ratio $K$ is regarded as a parameter. The magnetic behavior of the model is easily studied for a complete range of $K$ values, because the model can be transformed into an equivalent distribution of singly uniaxial domains with a nonuniform distribution of axial directions about the common axis of the film and a corresponding range of equivalent anisotropy strengths. The magnetoresistance for this model is computed numerically and found to be in over-all agreement with the measurements. It is shown that a distribution of $K$ values can account for the remaining quantitative differences between experiment and the model.