Analysis of Magnetoresistance in Arrays of Connected Nano-Rings

We study the anisotropic magnetoresistance (AMR) of a 2-D periodic square array of connected permalloy rings with periodicity of 1 mum combining experimental and computational techniques. The computational model consists of two parts: 1) the computation of the magnetization and 2) the computation of the current density. For 1), we use standard micromagnetic methods. For 2), we start from a potential difference applied across the sample, compute the resulting electric potential, and subsequently the corresponding current density based on a uniform conductivity. We take into account the backreaction of the magnetoresistive effects onto the current density by self-consistently computing the current density and conductivity until they converge. We compare the experimentally measured AMR curve (as a function of the applied field) with the numerically computed results and find good agreement. The numerical data provides insight into the characteristics of the AMR data. Finally, we demonstrate the importance of taking into account the spatial variation of the current density when computing the AMR