Quantifying spin relaxation in mesoscopic Cu channels via a multitude of nonlocal spin valves

Abstract

We fabricate a large number $(g100)$ of nonlocal spin valves with mesoscopic Cu channels. A systematic method is used to extract Cu resistivity ${\ensuremath{\rho}}_{\mathrm{Cu}}$ and spin relaxation length ${\ensuremath{\lambda}}_{\mathrm{Cu}}$ from each given structure. A relationship between ${\ensuremath{\lambda}}_{\mathrm{Cu}}$ and ${\ensuremath{\rho}}_{\mathrm{Cu}}$ is established over a broad range of ${\ensuremath{\rho}}_{\mathrm{Cu}}$ (from 0.7 to $g10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{4pt}{0ex}}\mathrm{cm}$) with $g200$ 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 $(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for bulk scattering and a higher probability of $(1.6\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for surface scattering. Encouraging large values of ${\ensuremath{\lambda}}_{\mathrm{Cu}}$ ($\ensuremath{\sim}2.0\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ at 10 K and $\ensuremath{\sim}700\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ at 295 K) are achieved experimentally in structures with low ${\ensuremath{\rho}}_{\mathrm{Cu}}$ values ($\ensuremath{\le}1.0\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{4pt}{0ex}}\mathrm{cm}$ at 10 K and $\ensuremath{\le}4.0\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{4pt}{0ex}}\mathrm{cm}$ at 295 K).