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We investigate relative stability, structural properties and electronicstructure of various modulated martensites of the magnetic shape memory alloyMn$_{2}$NiGa by means of density functional theory. We observe that theinstability in the high-temperature cubic structure first drives the system toa structure where modulation shuffles with a period of six atomic planes aretaken into account. The driving mechanism for this instability is found to bethe nesting of the minority band Fermi surface, in a similar way as establishedfor the prototype system Ni$_{2}$MnGa. In agreement with experiments, we find14M modulated structures with orthorhombic and monoclinic symmetries havingenergies lower than other modulated phases with same symmetry. In addition, wealso find energetically favourable 10M modulated structures which have not beenobserved experimentally for this system yet. The relative stability of variousmartensites is explained in terms of changes in the electronic structures nearthe Fermi level, affected mostly by the hybridisation of Ni and Mn states. Ourresults indicate that the maximum achievable magnetic field-induced strain inMn$_{2}$NiGa would be larger than in Ni$_{2}$MnGa. However, the energy costsfor creating nanoscale adaptive twin boundaries are found to be one order ofmagnitude higher than that in Ni$_{2}$MnGa.

Interplay of phase sequence and electronic structure in the modulated martensites of Mn$_2$NiGa from first-principles