We investigate half-metallicity in [001] stacked (CrAs)$_n$/(GaAs)$_n$ heterostructures with $n leq 3$ by means of a combined many-body and electronic structure calculation. Interface states in the presence of strong electronic correlations are discussed for the case $n=1$. For $n=2,3$ our results indicate that the minority spin half-metallic gap is suppressed by local correlations at finite temperatures, and continuously shrinks upon increasing the heterostructure period. Although around room temperature the magnetization of the heterostructure deviates by only $2%$ from the ideal integer value, finite temperature polarization at $E_F$ is reduced by at least $25%$. Below the Fermi level the minority spin highest valence states are found to localize more on the GaAs layers while lowest conduction states have a many-body origin. Our results, therefore, suggest that in these heterostructures holes and electrons remain separated among different layers.
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