We study the electronic and magnetic properties of the interfaces between the half-metallic Heusler alloy NiMnSb and the binary semiconductors InP and GaAs using two different state-of-the-art full-potential textit{ab-initio} electronic structure methods. Although in the case of most NiMnSb/InP(001) contacts the half-metallicity is lost, it is possible to keep a high degree of spin-polarization when the interface is made up by Ni and P layers. In the case of the GaAs semiconductor the larger hybridization between the Ni-$d$ and As-$p$ orbitals with respect to the hybridization between the Ni-$d$ and P-$p$ orbitals destroys this polarization. The (111) interfaces present strong interface states but also in this case there are few interfaces presenting a high spin-polarization at the Fermi level which can reach values up to 74%.
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