Origin and properties of the gap in the half-ferromagnetic Heusler alloys

We study the origin of the gap and the role of chemical composition in the half-ferromagnetic Heusler alloys using the full-potential screened Korringa-Kohn-Rostoker method. In the paramagnetic phase the C1b compounds, like NiMnSb, present a gap. Systems with 18 valence electrons, Zₜ, per unit cell, like CoTiSb, are semiconductors, but when Zₜ>18, antibonding states are also populated, thus the paramagnetic phase becomes unstable and the half-ferromagnetic one is stabilized. The minority occupied bands accommodate a total of nine electrons and the total magnetic moment per unit cell in μB is just the difference between Zₜ and 2×9. While the substitution of the transition metal atoms may preserve the half-ferromagnetic character, substituting the sp atom results in a practically rigid shift of the bands and the loss of half-metallicity. Finally we show that expanding or contracting the lattice parameter by 2% preserves the minority-spin gap.