Investigation on the preference of the martensitic structure in off-stoichiometric Ni-Mn-In alloys by first-principle calculations

•The tetragonal distortion was employed to predict the preferred stable structure under the effect of the excess Mn in the Ni-Mn-In alloys by first-principle calculations using EMTO-CPA with magnetic structure optimization.•To find out more accurate preference of the martensite structure in off-stoichiometric Ni-Mn-In alloys, the formation energy of the tetragonal L10 structure was calculated by the chemical disordered method using EMTO-CPA, and that of the orthorhombic structure was calculated by supercell method using VASP. In order to figure out the effect of excess Mn atoms on the preference of the martensite structure, the tetragonal distortion was employed in the off-stoichiometric Ni-Mn-In alloys with different Mn contents using the Extra Muffin-tin Orbital combined with the Coherent Potential Approximation (EMTO-CPA). The calculations were conducted with the optimization of the magnetic structure, where the stoichiometric Ni2MnIn alloy was served as the reference. The ground state-energy-resolved tetragonal distortion reveals that the excess Mn changes the preferred stable structure from the perfect cubic L21 structure to the tetragonally distorted structures. The stable tetragonal structure could shift from c/a 1 with the increase of the Mn concentration. Furthermore, to find out more accurate preference of the martensite structure, the formation energies were calculated using different relaxation methods. The chemical disorder method with a 4-atom cell was used for the tetragonal L10 structure by the EMTO-CPA, and the supercell method with a 96-atom cell was applied for the orthorhombic structure by the VASP at 0 K in their ferromagnetic state. The results show that, compared with the perfect cubic L21 structure of the stoichiometric Ni2MnIn alloy, the orthorhombic structure is preferred at lower Mn concentrations (between 29 at. % and 40 at. %), whereas the tetragonal L10 structure is more stable at the higher Mn concentrations (above 40 at. %). Moreover, the effect of the Mn concentration on the magnetic properties was also studied. With the increase of excess Mn content, the magnetic moment increases linearly in the ferromagnetic cubic L21 structure, whereas it varies in the two kinds of martensite. The excess Mn could lead to the coexistence of ferromagnetism and antiferromagnetism. The appearance of the antiferromagnetism could be attributed to the Ni-Mn antiferromagnetic interaction in the tetragonal martensite.