The spin-dependence of the interface resistance between ferromagnetic Fe and InAs is calculated from first-principles for specular and disordered (001) interfaces. Because of the symmetry mismatch in the minority-spin channel, the specular interface acts as an efficient spin filter with a transmitted current polarisation between 98 an 89%. The resistance of a specular interface in the diffusive regime is comparable to the resistance of a few microns of bulk InAs. Symmetry-breaking arising from interface disorder reduces the spin asymmetry substantially and we conclude that efficient spin injection from Fe into InAs can only be realized using high quality epitaxial interfaces.
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