The influence of measuring current on the calculation of anisotropic magnetoresistance in magnetic nanostructures

Using a multiscale approach, we investigate the influence of measuring current on the calculated anisotropic magnetoresistance of nanostructures, derived from the magnetization configuration obtained with micromagnetic codes. We analyze the subtle implicit assumptions and potentially overlooked approximations inherent in standard procedures that largely disregard the inhomogeneous distribution of electric current within the sample and the magnetic field generated by the current itself. As a preliminary study, we review various methods for determining resistance from the calculated magnetization distribution. We then focus on the impact of non-uniform current distribution arising from variations in resistivity due to different local magnetization orientations. Finally, we assess the significance of the magnetic field produced by the measuring current. For these analyses, we develop self-consistent procedures that iteratively solve the micromagnetic problem using MuMax3 and the Laplace equation with COMSOL Multiphysics. In general, our results validate the standard approach of calculating anisotropic magnetoresistance directly from the angle of the magnetization provided by micromagnetic codes, especially for typical (small) values of the magnetoresistance coefficient. However, we demonstrate that materials with larger AMR coefficients may require more sophisticated calculation methods. An important aspect for comparison with experimental results is the analysis of electrical contacts, where the measuring current can significantly alter the magnetization distribution and, consequently, the magnetoresistance of the nanostructure, even for small AMR coefficients.