Reference states of Cr-doped Ni-Co-Mn-(In, Sn) alloys: insights from first principles study

In this paper we report on the equilibrium magnetic and structural reference states of complex Cr-doped Ni-Co-Mn-(In, Sn) Heusler alloys, which are studied from first-principles within the density functional theory. The off-stoichiometric compositions were treated by using the supercell approach with different atomic distributions of excess Mn and In atoms. Supercells of 16 and 32 atoms were used. Three different ferrimagnetic and one ferromagnetic spin configurations were considered. The results of energy relaxation calculations have been averaged over different atomic distributions. It is found that for 16 atoms supercell the ferromagnetic (ferrimagnetic) state in austenite and a ferrimagnetic state in martensite are favorable for Ni$_7$Co$_1$Mn$_5$Cr$_1$In(Sn)$_2$, respectively. While for 32 atoms supercell of Ni$_{14}$Co$_2$Mn$_{11}$Cr$_1$(In, Sn)$_4$ the ferromagnetic (a ferrimagnetic) spin configuration in austenite (martensite) is energetically stable, respectively.