Magnetoresistance calculation in current-perpendicular-to-plane giant magnetoresistance spin valves with current-confined paths

We compared the magnetoresistance (MR) ratios of current-confined-path (CCP) current-perpendicular-to-plane (CPP) giant MR spin valves (SVs) calculated using the two-current-model. The simplified two-current model, which places the parasitic resistance external to the two-current network, has been inaccurate in determining the overall resistance of a SV in parallel magnetization configuration. The characteristics of the error in MR depend on the parasitic resistance value, the spin asymmetry coefficient, and the spacer layer resistivity. In comparison to the complete two-current model, we found that although the simplified model could generally predict the trend of various MR behaviors, it also overestimates MR for different CCP densities. A more comprehensive calculation on the CCP SVs was then performed using the spin-drift-diffusion equations based on the Valet-Fert model. It was found that the MR behavior upon considering spin relaxation in the ferromagnetic layers has a closer match with results predicted by the simplified model due to the strong reduction in spin accumulation in the parasitic layers. Spin relaxation in the spacer layer, however, shows a competing effect that tends to reduce the MR ratios. Our results in this paper are useful for accurate evaluation of MR performance in a CPP SV sensor with current-confined paths. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3054445]