Effect of the spin-orbit interaction on the band gap of half metals

The spin-orbit interaction can cause a nonvanishing density of states (DOS) within the minority-spin band gap of half metals around the Fermi level. We examine the magnitude of the effect in Heusler alloys, zinc-blende half metals, and diluted magnetic semiconductors, using first-principles calculations. We find that the ratio of spin-down to spin-up DOS at the Fermi level can range from below 1% (e.g., 0.5% for NiMnSb) over several percents [4.2% for (Ga,Mn)As] to 13% for MnBi. This gives a spin polarization P at $E_F$ ranging from above $99\%$ for NiMnSb to $P\approx 92\%$ for (Ga,Mn)As and to $P\approx 77\%$ for MnBi.