Site occupancy, magnetic moments, and elastic constants of off-stoichiometricNi2MnGafrom first-principles calculations

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The site occupancy and elastic modulus of off-stoichiometric ${\text{Ni}}_{2}\text{MnGa}$ alloys are investigated by the use of the first-principles exact muffin-tin orbital method in combination with coherent-potential approximation. The stable site occupancy at 300 K is determined by comparing the free energies of the alloys with different site-occupation configurations. It is shown that, for most of the off-stoichiometric ${\text{Ni}}_{2}\text{MnGa}$, the ``normal'' site occupation is favorable, i.e., the excess atoms of the rich component occupy the sublattice(s) of the deficient one(s). Nevertheless, for the Ga-rich alloys, the excess Ga atoms have strong tendency to take the Mn sublattice no matter if Mn is deficient or not. Based on the determined site occupancy, the elastic moduli of the off-stoichiometric ${\text{Ni}}_{2}\text{MnGa}$ are calculated. We find that, in general, the bulk modulus increases with increasing $e/a$ ratio (i.e., the number of valence electrons per atom). The shear moduli ${C}^{\ensuremath{'}}$ and ${C}_{44}$ change oppositely with $e/a$ ratio: ${C}^{\ensuremath{'}}$ decreases but ${C}_{44}$ increases with increasing $e/a$. However, the Mn-rich Ga-deficient alloys deviate significantly from this general trend. The correlation of calculated elastic moduli and available experimental martensitic transformation temperatures $({T}_{M})$ demonstrates that the alloy with larger ${C}^{\ensuremath{'}}$ than that of the perfect ${\text{Ni}}_{2}\text{MnGa}$ generally possesses lower ${T}_{M}$ except for ${\text{Ni}}_{2}{\text{Mn}}_{1+x}{\text{Ga}}_{1\ensuremath{-}x}$.