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Using first-principles based Density Functional Theory (DFT), we haveinvestigated the structural instabilities in the austenite phases ofMn$_{2}$Ni{\it X} ({\it X}= Al, Ga, In, Sn) magnetic shape memory alloys(MSMA). A complete softening is observed in the acoustic TA$_{2}$ branches forall the materials along [$\xi\xi$0] directions leading to the instability inthe austenite structure which effectively stabilizes into martensiticstructure. The reasons behind this softening are traced back to the repulsionfrom the optical T$_{2g}$ branches and to the nesting features in the Fermisurfaces. The vibrational density of states, the force constants and theelastic moduli are also computed and analyzed, which reconfirm the underlyingmechanism behind the instabilities. The results indicate that the phononanomalies are related to the occurrence of possible pre-martensitic phaseswhich can be quite complex.

First-principles study of the lattice instabilities in Mn$_{2}$Ni{\it X} ({\it X}= Al, Ga, In, Sn) magnetic shape memory alloys