Effect of 3d transition elements substitution for Ni in Ni ₂Mn_1+xSn_1-x on the phase stability and magnetic properties: A first principle investigation

In hope of understanding the origin of the 3d-transition elements doping effect on the phase stability and magnetic properties of the ferromagnetic shape memory Heusler alloy Ni-Mn-Sn, the Ni-Z-Mn-Sn system with Z=Ni, Cu, Co, Fe, Mn and Cr is investigated using first-principles calculations. The calculated results show that the energetically favorable magnetic order of the L2 ₁ structure is antiferromagnetic for Z=Ni and Cu, and ferromagnetic for the Z=Co, Fe, Mn and Cr. However, for L1₀ structure, the antiferromagnetic state has an energetical preference for each alloy. Accordingly, a magnetic transition accompanies with the martensite phase transformation and a large change in the magnetic moment can be observed in the alloys with the L2₁ under the ferromagnetic state, which is mainly dependent on the coupling behaviors of the doped atoms. The weak ferromagnetic coupling between the Ni/Cu and Mn, the strong ferromagnetic coupling between Co/Fe and Mn and the antiferromagnetic coupling between Mn/Cr and Mn play an important role on the magnetic order of L2₁ structures. Furthermore, the Bethe-Slater model is employed to gain a further understanding and regulation of the coupling behaviors of different doping elements, which is very sensitive to the interatomic distance. These calculated results may help in gaining an insight into the doping behavior of these transition metals and provide some theoretical aid to the material design.