The magnetic coupling between Mn atoms on Ga sublattice $\left({\text{Mn}}_{\text{Ga}}\right)$ and Mn atoms on Mn sublattice $\left({\text{Mn}}_{\text{Mn}}\right)$ in ${\text{Ni}}_2{\text{Mn}}_{1+x}{\text{Ga}}_{1-x}$ alloy and its effect on the elastic modulus of the alloy are investigated by the use of first-principles methods. It is shown that, for $x=0.25$, the state with antiparallel ${\text{Mn}}_{\text{Ga}}{\text{-Mn}}_{\text{Mn}}$ magnetic coupling is slightly more stable than that with parallel coupling, whereas for $x=0.10$, both magnetic states are almost degenerated. For both antiparallel and parallel ${\text{Mn}}_{\text{Ga}}{\text{-Mn}}_{\text{Mn}}$ magnetic couplings, the bulk modulus $\left(B\right)$ of ${\text{Ni}}_2{\text{Mn}}_{1+x}{\text{Ga}}_{1-x}$ deviates from the general $e/a\text{−}B$ relationship with $e/a$ being the number of valence electrons per atom. The shear modulus $C^{\prime }$ versus the martensitic transformation temperature $T_M$ for ${\text{Ni}}_2{\text{Mn}}_{1+x}{\text{Ga}}_{1-x}$ with antiparallel ${\text{Mn}}_{\text{Ga}}{\text{-Mn}}_{\text{Mn}}$ magnetic coupling is in line with the general $C^{\prime }\text{−}{T}_M$ relationship for ${\text{Ni}}_2\text{MnGa}$-based alloys, in contrast to the case of parallel ${\text{Mn}}_{\text{Ga}}{\text{-Mn}}_{\text{Mn}}$ magnetic coupling.

• Received 11 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.064108