Effect of Fe and Co substitution on the martensitic stability and the elastic, electronic, and magnetic properties of ${\mathrm{Mn}}_2\mathrm{NiGa}$: Insights from ab initio calculations

We investigate the effects of Fe and Co substitutions on the phase stability of the martensitic phase and mechanical, electronic, and magnetic properties of the magnetic shape memory system ${\mathrm{Mn}}_2\mathrm{NiGa}$ by first-principles density functional theory calculations. The evolution of these aspects upon substitution of Fe and Co at different crystallographic sites is investigated by computing the electronic structure, mechanical properties (tetragonal shear constant, Pugh ratio, and Cauchy pressure), and magnetic exchange parameters. We find that the austenite phase of ${\mathrm{Mn}}_2\mathrm{NiGa}$ gradually stabilizes with increase in concentration of Fe/Co due to the weakening of the minority spin hybridization of Ni and Mn atoms occupying crystallographically equivalent sites. The interplay between relative structural stability and the compositional changes is understood from the variations in the elastic moduli and electronic structures. We find that like in the ${\mathrm{Ni}}_2\mathrm{MnGa}$-based systems, the elastic shear modulus $C^{\prime }$ can be considered as a predictor of composition dependence of martensitic transformation temperature $T_m$ in substituted ${\mathrm{Mn}}_2\mathrm{NiGa}$, thus singling it out as the universally acceptable predictor for martensitic transformation in Ni-Mn-Ga compounds over a wide composition range. The magnetic properties of ${\mathrm{Mn}}_2\mathrm{NiGa}$ are found to be greatly improved by the substitutions due to stronger ferromagnetic interactions in the compounds. The gradually weaker (stronger) Jahn-Teller distortion (covalent bonding) in the minority spin densities of states due to substitutions leads to a half-metallic-like gap in these compounds resulting in materials with high spin polarization when the substitutions are complete. The substitutions at the Ga site result in the two compounds ${\mathrm{Mn}}_2\mathrm{NiFe}$ and ${\mathrm{Mn}}_2\mathrm{NiCo}$ with very high magnetic moments and Curie temperatures. Thus, our work indicates that although the substitutions destroy the martensitic transformation and thus the possibility of realization of shape memory properties in ${\mathrm{Mn}}_2\mathrm{NiGa}$, magnetic materials with very good magnetic parameters that are potentially useful for novel magnetic applications can be obtained. This can trigger interest in the experimental community in further research on substituted ${\mathrm{Mn}}_2\mathrm{NiGa}$.

Figure 1

Calculated total energy as a function of lattice constant for 25% Fe, Co, Ni, and Cu substituted at the Ga site in ${\mathrm{Mn}}_2\mathrm{NiGa}$(${\mathrm{Mn}}_2{\mathrm{NiGa}}_{0.75}{\mathrm{X}}_{0.25}$). “normal”: Fe, Co, Ni, or Cu occupy the Ga sublattice; “abnormal”: Fe, Co, Ni, or Cu occupy the MnI sites and remaining MnI atoms move to Ga sites.

Figure 2

Formation energy (eV/f.u.) as a function of Fe and Co content substituted at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$.

Figure 3

The variations of total energies as a function of $c/a$ ratio for Fe and Co substituted ${\mathrm{Mn}}_2\mathrm{NiGa}$ compounds. The zero energy is taken to be the energy of the austenite phase.

Figure 4

The calculated bulk modulus $B$ and shear elastic constants $C_{44}$ and $C^{\prime }$ as a function of Fe content at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$. The dashed lines represent variations of $\mathrm{\Delta }E$ with $x$; $\mathrm{\Delta }E$ is defined in Table 1.

Figure 5

The calculated bulk modulus $B$ and shear elastic constants $C_{44}$ and $C^{\prime }$ as a function of Co content at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$. The dashed lines represent variations of $\mathrm{\Delta }E$ with $x$; $\mathrm{\Delta }E$ is defined in Table 1.

Figure 6

Variations in the Cauchy pressure $C^p=(C_{12}–C_{44})$ with Pugh ratio $G_v/B$ are plotted for all the compounds. According to Ref. [72], $C^p>0,G_v/B<0.57$ indicates more ductility and more components of metallic bonding while $C^p<0,G_v/B>0.57$ indicates more brittleness and stronger covalent bonding.

Figure 7

Total density of states for Fe substituted at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$. The zero of the energy is set at Fermi energy ($E_F$).

Figure 8

Total density of states for Co substituted at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$. The zero of the energy is set at Fermi energy ($E_F$).

Figure 9

The calculated total (${\mu }_{\mathrm{B}}/\text{f.u.}$) and atomic magnetic moment as a function of Fe content for Fe-substituted ${\mathrm{Mn}}_2\mathrm{NiGa}$.

Figure 10

The calculated total (${\mu }_{\mathrm{B}}/\text{f.u.}$) and atomic magnetic moment as a function of Co content for Co-substituted ${\mathrm{Mn}}_2\mathrm{NiGa}$.

Figure 11

Calculated Curie temperatures as a function of substituent (a) Fe concentration and (b) Co concentration for substitutions at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$. Calculations are done by the MFA method.

Figure 12

Calculated Curie temperatures as a function of substituent (a) Fe concentration and (b) Co concentration for substitutions at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$. Calculations are done by the MCS method. Open symbols represent the experimental results which are adopted from Refs. [31, 32, 43, 80].

Figure 13

Effective exchange coupling constant ($J_{\mathrm{eff}}$) as a function of Fe content at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$.

Figure 14

Effective exchange coupling constant ($J_{\mathrm{eff}}$) as a function of Co content at different sites in ${\mathrm{Mn}}_2\mathrm{NiGa}$.