First-principle studies of the tendency towards segregation in heusler alloys Ni$_{2}$Mn$_{1+x}$Sb$_{1-x}$ with different atomic ordering

Using ab initio calculations, the stability issues of a series of Heusler alloys Ni$_{2}$Mn$_{1+x}$Sb$_{1-x}$ ($x$ = 0, 0.25, 0.5, 0.75, 1) with staggered and layer-by-layer ordering of Mn atoms are investigated. It is shown that compositions with an excess of Mn are stable with respect to decomposition into constituent elements and unstable with respect to decomposition into a two-phase system consisting of a ferromagnetic cubic L2$_{1}$ phase Ni$_{2}$MnSb and an antiferromagnetic tetragonal L1$_{0}$ phase NiMn. Thus, all nonstoichiometric compositions in the austenite and martensitic phases, taking into account different magnetic and atomic ordering, tend to segregate. Stability of alloys is possible only in stoichiometric compositions ($x$ = 0 and 1).