Ab initio studies of effect of copper substitution on the electronic and magnetic properties of Ni${}_2$MnGa and Mn${}_2$NiGa

Using first-principles density functional theory based calculations, we study systematically the effect of medium to large Cu substitution at the Mn, Ga as well as Ni sites on the geometric, bulk mechanical, electronic, and magnetic properties of Ni${}_2$MnGa and Mn${}_2$NiGa. The calculations have been carried out for possible austenite and martensite phases using a supercell approach. Partial Cu substitutions at Mn and Ga sites show promises in terms of the electronic and magnetic properties for both Ni${}_2$MnGa and Mn${}_2$NiGa alloys from an application point of view. Our calculations predict that for certain partial substitutions, the austenite to martensite transition temperature is likely to increase and the system remains magnetic in nature. On the other hand, a significantly large amount of Cu substitution at the Ni site seems to stabilize the austenite phase in both of these alloy systems rendering a martensite transition unlikely. Interestingly, the overall trend in the changes in the structural, bulk mechanical, electronic, and magnetic properties of these two different types of alloy systems, Ni${}_2$MnGa and Mn${}_2$NiGa, as a result of substantial Cu substitution in all the three different sites, is found to be the same.

Figure 1

(a) Mixing energy in eV/f.u. as a function of Cu substitution at different sites in Ni${}_2$MnGa. The line is only guide to the eyes. (b) Energy in meV/atom as a function of $c/a$ for different Cu-doped Ni${}_2$MnGa systems. The energy (E) of the martensite phase is normalized with respect to the austenite phase. $c/a=1$ corresponds to the austenite phase.

Figure 2

Total density of states as a function of energy for different amounts of Cu substitution (a) at the Ni site, (b) at the Mn site, and (c) at the Ga site in Ni${}_2$MnGa. The zero on the $x$ axis corresponds to the Fermi energy.

Figure 3

(a) Mixing energy in eV/f.u. as a function of Cu substitution at different sites in Mn${}_2$NiGa. The line is only guide to the eyes. (b) Energy in meV/atom as a function of $c/a$ for different Cu-doped Mn${}_2$NiGa systems. The energy ($E$) of the martensite phase is normalized with respect to the austenite phase. $c/a=1$ corresponds to the austenite phase.

Figure 4

Total density of states as a function of energy for different amounts of Cu substitution (a) at the Ni site, (b) at the Mn site, and (c) at the Ga site in Mn${}_2$NiGa. The Fermi level is at 0 eV.

Figure 5

Heisenberg exchange parameters $J_{ij}$ of Mn atom with its neighbors as a function of normalized distance, $d$/$a$, where $a$ is the respective lattice constants of the austenite phases for (a) Ni${}_2$MnGa and (b) Ni${}_2$MnCu. Based on the $J_{ij}$ parameters, the Curie temperatures within a mean-field approximation[48] have been calculated; for the former it is 390.6 K (experimental value is 376 K) and for the latter 413.7 K.