  The electronic band structures, density of states plots and magnetic moments
of Fe$_{2 }$MnSi, Fe$_{2 }$MnAl, and Co$_{2 }$MnGe are studied by using the
first principles calculations. The FM solutions using LSDA without \textit{U}
show the presence of half-metallic ferromagnetic (HFM) ground state in Fe$_{2
}$MnSi, whereas the ground state of Fe$_{2 }$MnAl is found to be metallic. In
both compounds the maximum contribution to the total magnetic moment is from
the Mn atom, while the Fe atom contributes very less. The electronic structures
and magnetic moments of Fe-based compounds affected significantly by
\textit{U}, whereas its effect is very less on Co$_{2}$MnGe. The magnetic
moment of Fe atom in Fe$_{2 }$MnSi (Fe$_{2 }$MnAl), increased by $\sim$ 70 %
($\sim$ 75 %) and in Mn atom it decreases by $\sim$ 50 % ($\sim$ 70 %) when the
value of \textit{U} is increased from 1 to 5 eV. The Hund's like exchange
interactions are increasing in Fe atom while decreasing in Mn atom with
increase in \textit{U}. The Fe and Mn moments are ferromagnetically coupled in
Fe$_{2 }$MnSi for all values of \textit{U}, whereas in Fe$_{2 }$MnAl they
coupled antiferromagnetically below \textit{U} = 2 eV and ferromagnetically
above it. Above \textit{U} = 2 eV the metallic ground state of Fe$_{2 }$MnAl
changes to semiconducting ground state and the ferromagnetic coupling between
Fe and Mn atoms appears to be responsible for this.
