Probing the Relationship between Anisotropic Magnetoresistance and Magnetization of ferromagnetic films

The anisotropic magnetoresistance (AMR) in thin permalloy strips was calculated at each steps during magnetization by the finite element method. The magnetization at equilibrium under different external fields was obtained by micromagnetic simulations, while the resistance with different magnetization was obtained by solving the Poisson equations iteratively until self-consistence. We find that the relation between magnetization and AMR deviates from the Stoner-Wohlfarth prediction when the magnetization is reduced from saturation. The reason is that the demagnetization is not necessarily from coherent rotation of the magnetic moment. We conclude that it is necessary to use numeric simulations to optimize the responses of AMR sensors.