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intraand inter-sublattice) in these two alloys. The results on inter-sublattice exchange parameters suggest that the decisive factor is the Mn–Mn interactions between sublattice II and sublattice III. The Ni–Mn interactions for both systems are quantitatively smaller than the Mn–Mn ones and are nearly same in magnitude. On the other hand, the dominant Mn– Mn contribution is from the first-neighbor exchange parameter, which has a larger negative value as one goes from Ni52 to Ni49, thereby decreasing the magnetization. The same trend is seen in the case of the intra-sublattice Mn–Mn parameters. A comparison of results in figures 1 and 2 clearly shows that in Ni49, the Mn–Mn exchange parameters for sublattice 1 is large and antiferromagnetic for the second neighboring shell while the others are close to zero; the exchange parameters for sublattice III are quantitatively slightly larger than the ones for Ni52 (configuration 1). One can, thus, conclude that the decrease in overall magnetization in going from Ni52 to Ni49 can be explained by the presence of the antiferromagnetic alignment of Mn spins and hence cancelation of moments.

4. Conclusions

In conclusion, the trends in magnetization observed in experiments with varying compositions of Mn and with varying occupancies of the sublattices are explained by using the magnetic exchange parameters from ab initio theory for the experimentally suggested three off-stoichiometric NiMnGa alloys. The main observations are listed below.

(i)The inter-sublattice coupling between Mn atoms is predominantly antiferromagnetic. The same goes for the intra-sublattice coupling between Mn atoms occupying sublattices other than the original Mn ones.

(ii)The experimentally observed trend of decreasing magnetization with increasing Mn concentration can be explained by the qualitative and quantitative features of the interand intra-sublattice Mn–Mn exchange parameters. For the Ni49 alloy, excess Mn atoms occupy both Ni and Ga sublattices while for the Ni52 alloy, excess Mn atoms occupy only the Ga sublattice. Thus, the significantly larger negative values of Mn–Mn exchange parameters between atoms in the Mn and Ga sublattices in the Ni49 alloy lead to an overall decrease of the net magnetization with respect to the Ni52 alloy. This is reinforced by the larger negative values of intra-sublattice Mn–Mn exchange parameters in Ni and Ga sublattices in the Ni49 sample. Since the inter-sublattice exchange parameters are larger in magnitude than the intra-sublattice parameters, the dominant effect in the trends of magnetization must come from the inter-sublattice parameters.

(iii)The Mn–Mn intra-sublattice coupling in the original Mn sublattice does not change significantly upon variation of the occupancies in the sublattice while it is sensitive to variations of chemical occupancies in the case of offsublattice Mn atoms. This is observed in the case of two different configurations considered for Ni52 alloy. Although total energy calculations were inconclusive about the stable configuration, the values of the Mn– Mn exchange parameters differed substantially between

the two configurations. The configuration 1 had smaller and more antiferromagnetic components in the exchange interaction between Mn moments in the Ga sublattice in comparison to the ones in configuration 2. On the other hand, the Mn–Mn inter-sublattice exchange parameters between Mn and Ga sublattices were found to be insensitive to the changes in the atomic ordering, as is seen in case of Ni52 alloy. Thus, in case of this alloy, a smaller overall magnetization in configuration 1 with respect to that in configuration 2, which is in accordance with the experimental results [9], can be related to the intra-sublattice exchange parameters alone.

(iv)The Ni–Mn interactions play no role in understanding the trends in magnetization. For all three alloys studied, the Ni–Mn interactions are ferromagnetic and are quantitatively nearly same. They are also much smaller in magnitude than the Mn–Mn exchange parameters, thus producing no effect on the relative changes in magnetization with change of composition or atomic ordering.

These results present a complete understanding of the nature of magnetic interactions among atomic specie pairs in off-stoichiometric NiMnGa alloys. Although these calculations were done for the cubic austenite phase, an understanding of the detailed magnetic structures in disordered NiMnGa alloys in the martensitic phase can also be explored along similar lines. Such an understanding of the magnetic properties in these alloys would pave the way for tailoring the magnetically related properties of these technologically important systems.

Acknowledgments

BS acknowledges Goran¨ Gustafssons Stiftelse, Carl Tryggers Stiftelse, STINT and the Swedish Research Council (VR) for financial support. We thank UPPMAX, NSC and HPC2N computing centers within the Swedish National Infrastructure for Computing (SNIC) for granting computer time. Also, we acknowledge Professors Igor Abrikosov and Andrei Ruban for providing the KKR-ASA code for the computations.

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