Supplementary material from "Investigation of the structural competing and atomic ordering in Heusler compounds Fe₂NiSi and Ni₂FeSi under strain condition"

The structural competing and atomic ordering of the full Heusler compounds Fe₂NiSi and Ni₂FeSi under uniform and tetragonal strains have been systematically studied by the first-principles calculation. Both Fe₂NiSi and Ni₂FeSi have the XA structure in cubic phase and they show metallic band structures and large magnetic moments (greater than 3μ_B) at equilibrium condition. Tetragonal distortion can further decrease the total energy, leading to the possible phase transformation. Furthermore, different atom reordering behaviours have been observed: for Fe₂NiSi, atoms reorder from cubic XA-type to tetragonal L1₀-type; for Ni₂FeSi, there is only structural transformation without atom reordering. The total magnetic moments of Fe₂NiSi and Ni₂FeSi are mainly contributed by Fe atoms and Si atom can strongly suppress the moments of Fe atoms when it is present in the nearest neighbours of Fe atoms. With the applied strain, the distance between Fe and Si atoms play an important role for the magnetic moment variation of Fe atom. Moreover, the metallic band nature is maintained for Fe₂NiSi and Ni₂FeSi under both uniform and tetragonal strains. This study provides a detailed theoretical analysis about the full Heusler compounds Fe₂NiSi and Ni₂FeSi under strain conditions.