The term Semimetal designates materials whose energy tops of the valence band exceeds the energy of the bottom of conduction band. In this case, there is a range of energies where electrons and holes coexist in equilibrium.
The term Half-metal denotes a material in which spin splitting of states is observed at the Fermi level, such that only electrons with one spin direction are present at the Fermi level. This is the ideal. However, I met works when the same term designated materials in which electrons with opposite spin are also present at the Fermi level, only their concentration is much lower.
From these definitions, it is evident that none of the mentioned materials has a gap at the Fermi level.
The term Semimetal designates materials whose energy tops of the valence band exceeds the energy of the bottom of conduction band. In this case, there is a range of energies where electrons and holes coexist in equilibrium.
The term Half-metal denotes a material in which spin splitting of states is observed at the Fermi level, such that only electrons with one spin direction are present at the Fermi level. This is the ideal. However, I met works when the same term designated materials in which electrons with opposite spin are also present at the Fermi level, only their concentration is much lower.
From these definitions, it is evident that none of the mentioned materials has a gap at the Fermi level.
Alexander has already explained in a good way. I just want to add about half metals. Actually, spin splitting is present in all ferromagnetic metals that means spin up and down DoS are different at Fermi level that define the spin polarisation of a ferromagnet. If the polarisation is 100%, only one spin band crossing the Fermi level and other direction has a gap. Such ferromagnets are known as Half metallic ferromagnets such as CrO2, LSMO, LCMO etc