Effects of structural nonplanarity on the magnetoresistance of Permalloy circular rings

We have measured magnetoresistance in single, 1 mu m external diameter, Permalloy (Ni80Fe20) circular rings with inner diameters of 150, 300, and 600 nm and film thickness of 25 nm. The ring structures were deposited on 25-nm-thick, 250-nm-wide Au nanocontacts previously fabricated on a SiO2/Si substrate by e-beam lithography. Using a four contact geometry, we studied the dependence of the magnetoresistance on the direction of the applied field. The experimental data were compared with simulations based on the conventional anisotropic magnetoresistance effect and on numerical simulations of the current distribution within the samples combined with micromagnetic simulations of the field dependent magnetization profile. Two different approaches were used for the simulations: one assumes flat magnetic structures with the Au contacts deposited on top of them; in the second approach the simulations were carried out using nonplanar magnetic structures deposited on the Au contacts. The magnetoresistance curves calculated using the second approach differ considerably from those obtained assuming flat magnetic structures and reproduce the experimental curves. The results presented demonstrate that the nonplanarity of the magnetic structures affects profoundly the magnetoresistive behavior of the ring structures.