Abstract
We calculated the electronic structures of several Co$_2$-based full Heusler compounds with $4d$ transition elements \textit{T} and Si, Co$_2$\textit{T}Si (\textit{T} = Y, Zr and Nb), by using the all electron full potential band method and found that the Co$_2$ZrSi is half-metallic ferromagnet. The calculated atomic resolved density of states (DOSs) for Co$_2$ZrSi showed that it had a considerably large minority spin gap ($0.94\;\text{eV}$) and that the Fermi level was pinned just at the middle of the gap. The fact that the Co$_2$ZrSi had an integer value for the magnetic moment, $2.000\;\mu_{\text{B}}$ per formula unit (f.u.), also indicated that this compound was half-metallic. Calculations for the compounds Co$_2$YSi and Co$_2$NbSi showed that they were not half-metals, but ferromagneic metals with magnetic moments of $1.002$ and $2.243\;\mu_{\text{B}}$/f.u., respectively. The Fermi level of Co$_2$YSi, located at the left edge of the minority spin gap, made the material nearly half-metallic while that of Co$_2$NbSi was positioned just below a large peak of minority Co $3d$ states.