Exchange-correlation corrections for electronic properties of half-metallic Co$_2$FeSi and nonmagnetic semiconductor CoFeTiAl

We consider two cobalt-based full-Heusler compounds CoFeTiAl and Co$_2$FeSi, for which Coulomb correlation effects play an important role. Since the standard GGA scheme does not provide a precise description of the electronic properties near the Fermi level, we use a meta-GGA functional capable to improve the description of the electronic properties of CoFeTiAl and Co$_2$FeSi. In particular, we find a better agreement with the experiment for the magnetic moment and the energy-band gap. Moreover, our calculations show that pressure enhances the insulating properties of Co$_2$FeSi and CoTiFeAl.