Role of magnetic and atomic ordering in the martensitic transformation of Ni-Mn-In from a first-principles study

The composition-dependent lattice parameters, crystal structure, elastic properties, magnetic moment, and electronic structure of Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($0\le x\le 0.6$) are studied by using first-principles calculations. It is shown that the martensitic phase transition (MPT) from cubic $L{2}_1$ to tetragonal $L{1}_0$ accompanies the Mn${}_{\text{Mn}}$-Mn${}_{\text{In}}$ ferromagnetic (FM) to antiferromagnetic (AFM) transition, at around the critical composition $x=0.32$, in agreement with the experimental measurement. The Mn-In atomic disorder leads to decreasing stability of the martensite relative to the austenite, which depresses the MPT. The shear elastic constant $C^{\prime }$ of the parent phase first decreases slightly with increasing $x$ and then remains almost unchanged above $x=0.32$, indicating $C^{\prime }$ alone cannot account for the increase of the MPT temperature with $x$. The total magnetic moments for the $L{2}_1$ phase are in good agreement with those determined by experiments, whereas for the $L{1}_0$ phase they are slightly larger than the experimental data due to the possible Mn-In atomic disorder in the sample. The calculated density of states demonstrate that the covalent bonding between the minority spin states of Ni and In plays an important role in both the magnetic and structural stability.

Figure 1

Unit cells of standard stoichiometric Ni${}_2$MnIn with simple cubic $L{2}_1$ structure (a) and body-centered-tetragonal $L{1}_0$ structure (b) in the [1 1 0] direction.

Figure 2

Theoretical lattice parameters of the ordered $L{2}_1$-Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($0.0\le x\le 0.6$) in FM ($a_{\text{FM}}$) and AFM ($a_{\text{AFM}}$) states as well as the disordered alloys in the FM state ($a_{\text{FM}}^{\text{DIS}}$), with respect to $x$, in comparison with the experimental data cited from Refs. 5 and 6 (denoted by $a$[Ref. 5] and $a$[Ref. 6], respectively).

Figure 3

The total energy change with respect to $c/a$ in Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($x=0.0$, 0.3, and 0.6) with Mn${}_{\text{Mn}}$ and Mn${}_{\text{In}}$ FM coupling (a) and AFM coupling (b). For comparison, the corresponding theoretical result for the disordered system with $x=0.6$ is also shown. The reference state is the ordered FM cubic phase ($c/a=1$).

Figure 4

The energy difference between AFM $L{1}_0$ ($c/a=1.25$) and FM $L{2}_1$ ($c/a=1$) ordered ($\Delta E_{L{1}_0-L{2}_1}$) as well as disordered ($\Delta E_{L{1}_0-L{2}_1}^{\text{DIS}}$) Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($0\le x\le 0.6$) with respect to $x$.

Figure 5

The shear elastic constants ($C^{\prime }$ and $C_{44}$, in GPa) and the anisotropic ratio ($A=C^{\prime }/C_{44}$) of the FM $L{2}_1$-Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($0.0\le x\le 0.6$) with respect to $x$ as well as the number of valence electrons per atom ($e/a$).

Figure 6

The composition dependence of the total magnetic moment in FM $L{2}_1$ (${\mu }_{\text{tot}}^{{L{2}_1}_{\text{FM}}}$) and AFM $L{1}_0$ (${\mu }_{\text{tot}}^{{L{1}_0}_{\text{AFM}}}$) ordered, and FM $L{2}_1$ disordered (${\mu }_{\text{tot}}^{{L{2}_1}_{\text{FM}}^{\text{DIS}}}$) Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($0\le x\le 0.6$), in comparison with those of the experimental data in the two phases (${\mu }_{\text{tot}}^{L{2}_1}$[Ref. 6] and ${\mu }_{\text{tot}}^{L{1}_0}$[Ref. 6], respectively).

Figure 7

The total density of states (DOS) of $L{2}_1$-Ni${}_2$Mn${}_{1.6}$In${}_{0.4}$ in FM (${L{2}_1}_{\text{FM}}$), AFM (${L{2}_1}_{\text{AFM}}$), and FM disordered (${L{2}_1}_{\text{FM}}^{\text{DIS}}$) states (a), as well as those of the $L{1}_0$ system in AFM (${L{1}_0}_{\text{AFM}}$), FM (${L{1}_0}_{\text{FM}}$), and AFM disordered (${L{1}_0}_{\text{AFM}}^{\text{DIS}}$) states (b). The vertical lines indicate the Fermi level.

Figure 8

The local density of states (DOS) of Ni (panels a and b), Mn (panels c and d) on Mn sublattice, Mn (panels e and f) on In sublattice; and In (panels g and h) of Ni${}_2$Mn${}_{0.6}$In${}_{0.4}$ in FM $L{2}_1$ (panels a, c, e and g) and AFM $L{1}_0$ (panels b, d, f, and h). The vertical lines indicate the Fermi level.

Figure 9

The total density of states (DOS) of (a) FM $L{2}_1$- and (b) AFM $L{1}_0$-Ni${}_2$Mn${}_{1+x}$In${}_{1-x}$ ($x=0.0$, 0.3, and 0.6). The vertical lines indicate the Fermi level.