  We investigate the effects of Fe and Co substitutions on the phase stability
of the martensitic phase, mechanical, electronic and magnetic properties of
magnetic shape memory system Mn$_{2}$NiGa by first-principles Density
functional theory(DFT) calculations. The evolution of these aspects upon
substitution of Fe and Co at different crystallographic sites are investigated
by computing the electronic structure, mechanical properties and magnetic
exchange parameters. We find that the martensitic phase of Mn$_{2}$NiGa
gradually de-stabilises with increase in concentration of Fe/Co due to the
weakening of the minority spin hybridisation of Ni and Mn atoms occupying
crystallographically equivalent sites. The interplay between relative
structural stability and the compositional changes are understood from the
variations in the elastic modulii and electronic structures. We find that the
elastic shear modulus C$^{\prime}$ can be considered as a predictor of
composition dependence of martensitic transformation temperature in substituted
Mn$_{2}$NiGa. The magnetic properties of Mn$_{2}$NiGa are found to be greatly
improved by the substitutions due to stronger ferromagnetic interactions in the
compounds. The gradually weaker(stronger) Jahn-Teller distortion (covalent
bonding) in the minority spin densities of states due to substitutions lead to
a half-metallic like gap in these compounds resulting in materials with high
spin-polarisation when the substitutions are complete. The substitutions at the
Ga site result in two new compounds Mn$_{2}$NiFe and Mn$_{2}$NiCo with very
high magnetic moments and Curie temperatures. Thus, our work indicates that
although the substitutions de-stabilise the martensitic phase in Mn$_{2}$NiGa,
new magnetic materials with very good magnetic parameters and potentially
useful for novel magnetic applications can be obtained.
