Quantifying Spin Relaxation In Mesoscopic Cu Channels Via A Multitude Of Nonlocal Spin Valves

We fabricate a large number (>100) of nonlocal spin valves with mesoscopic Cu channels. A systematic method is used to extract Cu resistivity. Cu and spin relaxation length lambda(Cu) from each given structure. A relationship between lambda(Cu) and rho(Cu) is established over a broad range of rho(Cu) (from 0.7 to >10 mu Omega cm) with >200 data points obtained at 10 and 295 K. Quantitative analysis of the relationship indicates that the spin relaxation can be described by the Elliott-Yafet model with a low spin-flip probability of (1.9 +/- 0.2) x 10(-4) for bulk scattering and a higher probability of (1.6 +/- 0.2) x 10(-3) for surface scattering. Encouraging large values of lambda(Cu) (similar to 2.0 mu m at 10 K and similar to 700 nm at 295 K) are achieved experimentally in structures with low rho(Cu) values (similar to 1.0 mu Omega cm at 10 K and <= 4.0 mu Omega cm at 295 K).