We studied the anisotropic magnetoresistance (AMR) properties of multilayered Co/Pd thin film electrodes as function of magnetic field and electrode width. The multilayered structure induces perpendicular magnetization anisotropy (PMA), found to considerably modify the AMR.

The magnetoresistance for fields out-of-plane (ρ_op) is considerably different than for in-plane fields transverse to current direction (ρ_ip), although in both cases current is perpendicular to the magnetic field. Moreover, opposed to other very thin films where ρ_op is smaller than ρ_ip, our films show an opposite effects, the origin of which is not clear.

We are able to understand the rich AMR properties of the electrodes by an expanded Stoner-Wolfarth model, where we introduce an additional energy scale related to the PMA.  By minimizing the free energy of the system, through a numerical refinement process, we extract anisotropic constants of the electrodes. This is done by reconstructing the magnetoresistance behavior of the electrodes, using only the linear terms in the dependence of resistivity on the magnetization orientation. Our anisotropic constants coincide remarkably with the literature (measured by other methods).

Thus, our refinement process is an excellent method to easily and accurately extract anisotropic constants also in nano-scale magnetic systems, which cannot be accessed otherwise.