  Effect of Co substitution on Mn$_3$Ga is investigated using first-principles
study for structural and magnetic properties. Without Co, ferrimagnetic Heusler
compound Mn3Ga is in tetragonal phase. With Co substitution, depending on Co
concentration (x) Mn$_3$Ga prefers tetragonal (cubic) phase when x \leq 0.5 (x
\geq 0.5). Ferrimagnetism is robust regardless of x in both phases. While
magnetic moments of two Mn do not vary significantly with x, Co magnetic moment
in two phases exhibit different behaviors, leading to distinct features in
total magnetic moment (M_{tot}). When x \leq 0.5, in tetragonal phase, Co
magnetic moment is vanishingly small, resulting in a decrease of M_{tot} with
x. In contrast, when x \geq 0.5, in cubic phase, Co magnetic moment is roughly
1$\mu_B$, which is responsible for an increase of Mtot. Electronic structure is
analyzed with partial density of states for various x. To elucidate the
counterintuitively small Co moment, the magnetic exchange interaction is
investigated where exchange coefficient between Co and Mn is much smaller in x
\leq 0.5 case than x \geq 0.5 one.
