Spin injection from a half-metal at finite temperatures

Spin injection from a half-metallic electrode in the presence of thermal spin disorder is analyzed using a combination of random matrix theory, spin-diffusion theory, and explicit simulations for the tight-binding s-d model. It is shown that efficient spin injection from a half-metal is possible as long as the effective resistance of the normal metal does not exceed a characteristic value, which does not depend on the resistance of the half-metallic electrode but, rather, is controlled by spin-flip scattering at the interface. This condition can be formulated as α l/ l sf T −1 c , where α is the relative deviation of the magnetization from saturation, l and l sf are the mean-free path and the spin-diffusion length in the nonmagnetic channel, and Tc is the transparency of the tunnel barrier at the interface (if present). The general conclusions are confirmed by tight-binding s-d model calculations. A rough estimate suggests that efficient spin injection from true half-metallic ferromagnets into silicon or copper may be possible at room temperature across a transparent interface.