Understanding the origin of the magnetocaloric effects in substitutional $\text{Ni-Mn-Sb-}Z(Z=\mathrm{Fe},\mathrm{Co},\mathrm{Cu})$ compounds: Insights from first-principles calculations

Ni-Mn based ternary Heusler compounds have drawn attention lately as significant magnetocaloric effects in some of them have been observed. Substitution of Ni and Mn by other $3d$-transition metals in controlled quantity has turned out to be successful in enhancing the effect and bring the operational temperatures closer to room temperature. Using density functional theory calculations, in this work, we have systematically explored the roles of various factors such as site occupancies, magnetic interactions, and compositions associated with the constituents of Mn-excess ${\mathrm{Ni}}_2\mathrm{MnSb}$ Heusler compounds upon substitution of Ni and/or Mn by $3d$-transition metals Fe, Co, and Cu. Our calculations unveiled the physics behind the variations of physical properties associated with the magnetocaloric effects, and thus interpreted the available experimental results successfully. The work also provided important information on the compounds and the composition ranges where significant magnetocaloric effects may be realized, and further experimental investigations need to be done.

Figure 1

Calculated total magnetic moment and atomic magnetic moments (in ${\mu }_{\mathrm{B}}/f.u.$) (for atom-name convention see Table 1) as a function of concentration $y$ of substituting elements, $Z$=Fe, Co, and Cu for (a) ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.50-y}{Z}_y{\mathrm{Sb}}_{0.50}(Z$@Mn) and (b) ${\mathrm{Ni}}_{2-y}{Z}_y{\mathrm{Mn}}_{1.50}{\mathrm{Sb}}_{0.50}(Z$@Ni) systems in their lowest energy magnetic configurations as indicated in Table 1. Variations of total magnetic moments with $y$ calculated by sprkkr code [48], are presented by dashed lines with open symbols. For Co-substituted systems, magnetic moments both for “C3”(dashed lines with open circles) and “C4”(solid lines with marked circles) magnetic configurations for $y>0.25$ are shown.

Figure 2

The variations of total energy difference ($\mathrm{\Delta }E$) between the austenite ($\mathrm{L}{2}_1$) and the martensite (tetragonal) phases as a function of tetragonal distortion, i.e., $c/a$ ratio for [(a)–(c)] ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.50-y}{Z}_y{\mathrm{Sb}}_{0.50}$($Z$@Mn) and [(d)–(f)] ${\mathrm{Ni}}_{2-y}{Z}_y{\mathrm{Mn}}_{1.50}{\mathrm{Sb}}_{0.50}$($Z$@Ni) ($Z$=Fe, Co and Cu) systems for considered values of $y$ and at their ground-state magnetic configurations (as in Table 1). Results where the magnetic configurations are different in the martensitic phases (for Co substitution with $y=0.50$) are also shown.

Figure 3

The dependence of the interatomic magnetic exchange parameters in the first coordination shell (for different pair of atoms) for (left) ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.52-y}{Z}_y{\mathrm{Sb}}_{0.48}(Z$@Mn) and (right) ${\mathrm{Ni}}_{2-y}{Z}_y{\mathrm{Mn}}_{1.52}{\mathrm{Sb}}_{0.48}(Z$@Ni) with $Z$=Fe, Co and Cu systems in their austenite phases. Calculations in each case are done at the ground-state magnetic configuration. The composition of the parent compound ($y=0$), in each case, is considered to be the ones in the experiments [33, 34, 35, 36, 65, 71], and are nominally different from that of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.5}{\mathrm{Sb}}_{0.5}$. For Co-substituted systems, magnetic exchange parameters both for “C3”(closed symbols) and “C4”(open symbols) magnetic configurations for $y>0.25$ are shown.

Figure 4

Interatomic magnetic exchange interactions in (a) and (b) parent composition ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.52}{\mathrm{Sb}}_{0.48}$ and (c) and (d) ${\mathrm{Ni}}_{2-y}{\mathrm{Co}}_y{\mathrm{Mn}}_{1.52}{\mathrm{Sb}}_{0.48}$ with $y=0.24$ in the cubic ($c/a=1$) and tetragonal ($c/a\ne 1$) phases as a function of distance $d$ (in units of lattice constant ${\mathrm{a}}_0$) between the pair of atoms.

Figure 5

Calculated Curie temperatures ($T_c^A$) as a function of substituents ($Z=\text{Fe}$, Co, Cu) concentration for ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.52-y}{Z}_y{\mathrm{Sb}}_{0.48}(Z$@Mn) and ${\mathrm{Ni}}_{2-y}{Z}_y{\mathrm{Mn}}_{1.52}{\mathrm{Sb}}_{0.48}(Z$@Ni) systems. Closed symbols and Open symbols represent results calculated by Monte Carlo simulation (MCS) and mean field approximation (MFA) methods, respectively. For Co-substituted systems, Curie temperatures in “C4” magnetic configuration for $y>0.25$ are shown with marked circles.

Figure 6

Variations in the (a) total magnetic moments with $y$ for various site configurations (Table 5) for ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.50-y}{\mathrm{Fe}}_y{\mathrm{Sb}}_{0.50}$ system in their austenite phases calculated with vasp (closed symbols with solid line) and for ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.52-y}{\mathrm{Fe}}_y{\mathrm{Sb}}_{0.48}$ calculated by sprkkr (open symbols with dashed line). Experimental values of the total moment are added for comparison; (b) total energy differences ($\mathrm{\Delta }E$) between the austenite and martensite phases of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.50-y}{\mathrm{Fe}}_y{\mathrm{Sb}}_{0.50}$ with $y$, for select site configurations. Experimental values of $T_M$ [36] are given for comparing trends.

Figure 7

The dependence of the interatomic magnetic exchange parameters in the first coordination shell (for different pairs of atoms) for ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.52-y}{\mathrm{Fe}}_y{\mathrm{Sb}}_{0.48}$ in their austenite phases for site configurations (a) “S-b” and (b) “S-c”.