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 is rather controlled by spin-flip scattering at the interface. This condition can be formulated as \alpha<(l/L)/T, where \alpha is the relative deviation of the magnetization from saturation, l and L the mean-free path and the spin-diffusion length in the non-magnetic channel, and T 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.