4.3 Results and Discussions
4.3.4 Magnetic exchange interactions
Chapter 4. Understanding the origin of the magnetocaloric effects in substitutional Ni-Mn-Sb-Z (Z=Fe, Co, Cu) compounds
phase stability due to Fe substitution is dependent on the atom that is being sub- stituted. For both cases, no changes in magnetic structures have been observed near the structural phase transition, and as a result, ∆M are also found to be very small. Substitution of Cu, in place of either Ni or Mn, does not affect the rela- tive phase stability significantly. As the Fig. 4.3(c) and Fig. 4.3(f) suggest, ∆E does not change appreciably with y, implying that TM remains almost unchanged even when concentration of the substituents are high. In both cases, the magnetic structures do not change across phases, as is clear from the results in Table 4.2.
Co-substitution turns out to be very interesting as compared to the other two cases.
With increase of Co concentration substituting Mn, ∆E first increases moderately in the lower concentration range (y ≤ 0.25), and no changes in magnetic structure across phases are observed, resulting in a lower value of ∆M. Further increase in Co concentration brings in a change in the magnetic structure in austenite phase as was discussed in the previous section; however, the magnetic structure remains same in the martensitic phase with Mn spins still aligned anti-parallel, leading to a
∆M value of 4.44 µB/f.u.. Simultaneously, we find a substantial increase in ∆E, implying a greater martensitic instability in the system. Large ∆M coupled with a largeTM indicate better prospect for MCE. Similar jump in ∆M is observed in case of Co substituting Ni. However, the ∆E decreases in this case withy. This is consis- tent with the experimental observation in Ni2−yCoyMn1.52Sb0.48 with y= 0.2 [135].
Incidentally, large MCE has been found in this compound. Thus, our results in Co-substituted compounds indicate that they are potential materials for large MCE near a magneto-structural transition of the first order.
4.3 Results and Discussions
-8 -4 0 4
Mn1-Mn1 Mn1-Mn2 Mn1-Ni1
-8 0 8 16
Mn2-Ni1 Ni1-Z1 Z1-Z1
0 0.1 0.2 0.3 0.4 0.5
-8 -4 0 4
Mn1-Z1 Mn2-Mn2 Mn2-Z1
-8 0 8 16
Exchange Prameter J ij (meV)
Concentration (y)
Z=Fe
Z=Co
Z=Cu
-8 -4 0 4 8
-8 0 8 16
0 0.1 0.2 0.3 0.4 0.5
-8 -4 0 4 -8 0 8 16
Concentration (y)
Z=Fe
Z=Co
Z=Cu
Exchange Parameter J ij (meV)
Figure 4.4: The dependence of the inter-atomic magnetic exchange parameters in the first coordination shell (for different pair of atoms) for (left panel) Ni2Mn1.52−yZySb0.48(Z@Mn) and (right panel) Ni2−yZyMn1.52Sb0.48(Z@Ni) with Z=Fe, Co and Cu systems in their austenite phases. Calculations in each case are done at the ground state magnetic config- uration. The composition of the parent compound (y= 0), in each case, is considered to be the ones in the experiments [134,135,140,142,289,294], and are nominally different from that of Ni2Mn1.5Sb0.5. For Co-substituted systems, magnetic exchange parameters both for “C3”(closed symbols) and “C4”(open symbols) magnetic configurations for y > 0.25 are shown.
Figure4.4shows the trends in variations of various nearest neighbor inter-atomic magnetic exchange coupling strengths as a function of the substituents concentra- tion. Only the variations in the first coordination shells are considered as these are the dominant interactions. We find that, in each case of substitution, the overall ferromagnetic interactions increase due to the predominantly ferromagnetic inter- actions between the Ni-Z, Mn-Z, and Z-Z pairs. When Mn is substituted by Fe, there is a competition between the ferromagnetic coupling of Ni-Fe, Mn1-Fe, and antiferromagnetic coupling of Mn1-Mn2 pairs. The antiferromagnetic interaction of Mn1-Mn2 pairs increases with the concentration of Fe and compensates for the weak increase in the ferromagnetic interactions with y. The small negative changes
Chapter 4. Understanding the origin of the magnetocaloric effects in substitutional Ni-Mn-Sb-Z (Z=Fe, Co, Cu) compounds
in the magnetic moment withycan be correlated to such variations in the exchange interactions. In complete contrast to this, substitution of Fe at Ni sites amplify the ferromagnetic Mn-Fe interactions, along with a simultaneous weakening of the anti-ferromagnetic interactions(Mn1-Mn2, Fe-Fe) as y increases. The increase in the magnetic moment with y is an artifact of this. Almost no variations in the magnetic moment of compounds when Ni is substituted by Cu can be understood from the minimal variations in both ferromagnetic and anti-ferromagnetic exchange interactions with Cu concentration. In contrast, The significant strengthening in Ni-Mn ferromagnetic interactions when Cu substitutes Mn can be correlated to the increase in the magnetic moment of the corresponding compound. Co substitutions, both at Mn and Ni sites, give rise to the largest ferromagnetic coupling strengths, which is due to very strong ferromagnetic exchange interactions between the Co and Mn atoms. Ferromagnetic interactions between Mn-Ni and Co-Co pairs strengthen it further. For higher concentrations (y > 0.25) the parallel alignment of the Mn atoms (as in “C4” magnetic configuration) magnifies the ferromagnetic interactions further. This explains the large value of moment at high concentrations of Co. Over- all, it can be concluded that substitutions of magnetic 3d-elements in Ni2Mn1.5Sb0.5
magnify ferromagnetic exchange interactions in the system, and thus in general, leads to a higher value of magnetic moment with respect to the parent compound.
We next focus on understanding of the occurrence of large ∆M and the possible connection to significant MCE in some of the substituted Mn-excess, Sb-deficient Ni2MnSb compounds. For this purpose, we consider Ni2Mn1.52Sb0.48 compound and investigate the behavior of magnetic exchange interactions, in both austenite and martensite phases, when Fe, Co and Cu substitute Ni and Mn with the concentration of the substituent being 0.24. The reason for picking this particular composition is the observation of large MCE for compositions close to this [142] in the compound where Co substitutes Ni. In Fig. 4.5, we show the results for parent composition Ni2Mn1.52Sb0.48 and Co substituted Ni1.76Co0.24Mn1.52Sb0.48 to interpret the experi- mental observations. In the parent composition Ni2Mn1.52Sb0.48, the austenite phase is dominated by the Mn1-Mn2 nearest-neighbor antiferromagnetic (AFM) interac- tions. In the tetragonal martensite phase, this AFM interaction gets almost four times magnified and shows an oscillatory behavior in the second and third coordina- tion shells. As a result, not much difference between the magnetic moments in the two phases is expected to occur. This proposition is consistent with the results on Ni2Mn1.5Sb0.5 (Table 4.2). When Co substitutes Ni, the Mn1-Mn2 AFM interaction strength remains the same as the pristine compound in the martensitic phase, while
4.3 Results and Discussions
0.4 0.6 0.8 1 1.2 1.4
d/a0 -8
-4 0 4 8
J ij (meV) Mn2-Mn2
Mn2-Mn1 Mn2-Ni1 Mn1-Mn1 Mn1-Ni1 Ni1-Ni1
(a) y=0.00 Cubic
0.4 0.6 0.8 1 1.2 1.4
d/a0 -8
-4 0 4 8
0.4 0.6 -35
-30 -25 -20
Tetra (b) y=0.00
0.4 0.6 0.8 1 1.2 1.4
d/a0 -8
0 8 16
J ij (meV)
Mn2-Mn2 Mn2-Mn1 Mn2-Ni1 Mn2-Co1 Mn1-Mn1 Mn1-Ni1 Mn1-Co1 Ni1-Ni1 Ni1-Co1 Co1-Co1
Cubic (c) y=0.24
0.4 0.6 0.8 1 1.2 1.4
d/a0 -8
0 8 16
0.4 0.6 -35 -30 -25 -20
Tetra (d) y=0.24
Figure 4.5: Inter-atomic magnetic exchange interactions in (a)-(b)parent composition Ni2Mn1.52Sb0.48 and (c)-(d) Ni2−yCoyMn1.52Sb0.48 with y = 0.24 in the cubic (c/a = 1) and tetragonal (c/a6= 1) phases as a function of distance d(in units of lattice constant a0) between the pair of atoms.
the ferromagnetic interactions gain slightly. But, in the austenite phase, the Mn-Co ferromagnetic interactions amplify more than five times in comparison to the domi- nant ferromagnetic interactions in the pristine compound. As a result, the magnetic moments in the two phases would differ substantially, in comparison to that in the pristine compound. This, therefore, perfectly explains the experimentally observed large ∆M and large MCE. Another highlight of these calculations is observation of a correlation between the qualitative nature of the variations in the exchange interactions and relative stabilities of the structural phases. Experimentally it was observed that for Co-substitution at Ni site in Ni2Mn1.52Sb0.48, TM decreases with the substituent concentration implying that this substitution stabilizes the austenite phase. The nature of magnetic exchange interactions in Fig. 4.5(c) suggests that the strong ferromagnetic interactions stabilize the austenite phase.
Analysis of the figures4.6-4.8lead to the following: (i) for Fe substitution at Mn site, AFM couplings are stronger in the austenite phase, in comparison to the parent
Chapter 4. Understanding the origin of the magnetocaloric effects in substitutional Ni-Mn-Sb-Z (Z=Fe, Co, Cu) compounds
0.4 0.8 1.2 1.6 2
d/a0
-10 -5 0 5 10
Jij (meV)
Mn2-Mn2 Mn2-Mn1 Mn2-Fe1 Mn2-Ni1 Mn1-Mn1 Mn1-Fe1 Mn1-Ni1 Fe1-Fe1 Fe1-Ni1 Ni1-Ni1
(a) Cubic
0.4 0.8 1.2 1.6 2
d/a0 -10
-5 0 5 10
0 0.5 1
-35 -30 -25 -20
Tetra (b)
0.4 0.8 1.2 1.6 2
d/a0
-10 -5 0 5 10
Jij (meV)
Mn2-Mn2 Mn2-Mn1 Mn2-Ni1 Mn2-Fe1 Mn1-Mn1 Mn1-Ni1 Mn1-Fe1 Ni1-Ni1 Ni1-Fe1 Fe1-Fe1
(c) Cubic
0.4 0.8 1.2 1.6 2
d/a0
-10 -5 0 5 10
0 0.5 1
-35 -30 -25 -20
Tetra (d)
Figure 4.6: Inter-atomic magnetic exchange interactions in (a)-(b) Ni2Mn1.52−yFeySb0.48
(y = 0.24) and (c)-(d) Ni2−yFeyMn1.52Sb0.48 (y = 0.24) in the cubic (c/a = 1) and tetragonal (c/a 6= 1) phases as a function of distance d(in units of lattice constant a0) between the pair of atoms.
0.4 0.8 1.2 1.6 2
d/a0
-8 0 8 16
J ij (meV)
Mn2-Mn2 Mn2-Mn1 Mn2-Ni2 Mn2-Ni1 Mn2-Co1 Mn1-Mn1 Mn1-Ni2 Mn1-Ni1 Mn1-Co1 Ni2-Ni2 Ni2-Ni1 Ni2-Co1 Ni1-Ni1 Ni1-Co1 Co1-Co1
(a) Cubic
0.4 0.8 1.2 1.6 2
d/a0
-8 0 8 16
0 0.5 1
-35 -30 -25 -20
Tetra (b)
Figure 4.7: Inter-atomic magnetic exchange interactions in Ni2Mn1.52−yCoySb0.48 (y = 0.24) in the (a) cubic (c/a = 1) and (b) tetragonal (c/a 6= 1) phases as a function of distance d(in units of lattice constant a0) between the pair of atoms.
4.3 Results and Discussions
0.4 0.8 1.2 1.6 2
d/a0 -10
-5 0 5 10
J ij (meV)
Mn2-Mn2 Mn2-Cu1 Mn2-Mn1 Mn2-Ni1 Cu1-Cu1 Cu1-Mn1 Cu1-Ni1 Mn1-Mn1 Mn1-Ni1 Ni1-Ni1
(a) Cubic
0.4 0.8 1.2 1.6 2
d/a0
-10 -5 0 5 10
0 0.5 1
-35 -30 -25 -20
Tetra (b)
0.4 0.8 1.2 1.6 2
d/a0 -10
-5 0 5 10
J ij (meV)
Mn2-Mn2 Mn2-Mn1 Mn2-Ni1 Mn2-Cu1 Mn1-Mn1 Mn1-Ni1 Mn1-Cu1 Ni1-Ni1 Ni1-Cu1 Cu1-Cu1
(c) Cubic
0.4 0.8 1.2 1.6 2
d/a0 -10
-5 0 5 10
0 0.5 1
-35 -30 -25 -20
Tetra (d)
Figure 4.8: Inter-atomic magnetic exchange interactions in (a)-(b) Ni2Mn1.52−yCuySb0.48 (y = 0.24) and (c)-(d) Ni2−yCuyMn1.52Sb0.48 (y = 0.24) in the cubic (c/a = 1) and tetragonal (c/a 6= 1) phases as a function of distance d(in units of lattice constant a0) between the pair of atoms.
compound, due to AFM Mn2-Fe interactions on top of already existing Mn1-Mn2 one. In tetragonal phase, the AFM interactions magnify, mainly due to stronger Mn2-Fe interactions. Moreover, Mn1-Mn2 and Mn2-Fe interactions are oscillatory in nature. This implies that ∆M may not be very large in this system; (ii) Fe sub- stitution at the expense of Ni leads to substantial increase in the FM components in the exchange interactions in the austenite phase, due to strong Mn-Fe FM interac- tions. In the martensitic phase, the nature of the interactions are not too different from that in the parent compound; (iii) ferromagnetic interactions become domi- nant upon substitution of Co at Mn site, in both phases. The many-fold stronger FM interactions in austenite phases and the presence of large AFM interaction in martensitic phases can explain the reason behind large ∆M when Co is substituted;
(iv) nature of interactions in Cu substituted compounds are more or less similar to that in the parent compound. Combining these with the results on the relative stability of structural phases of various compounds, occurrence of large ∆M from our calculations and experimental observation of large MCE in Co-substituted (at Ni site) Ni2Mn1.48Sb0.52[130,132], we can infer that strong FM interactions stabilize
Chapter 4. Understanding the origin of the magnetocaloric effects in substitutional Ni-Mn-Sb-Z (Z=Fe, Co, Cu) compounds
130 140 150 160
B (GPa) Z=Fe
Z=Co Z=Cu
77 88 99 110
C 44 (GPa)
0 0.1 0.2 0.3 0.4 0.5
Concentration (y) -15
0 15
C′ (GPa)
Figure 4.9: The variations in bulk modulus B, shear elastic constants C44 and C′ as a function of concentration y of substituents, Z=Fe, Co and Cu, in the austen- ite phases of the considered two systems: Ni2Mn1.50−yZySb0.50(closed symbols) and Ni2−yZyMn1.50Sb0.50(open symbols).
the austenite phase, reducing the TM and that the observed large MCE is due to strikingly different nature of dominant magnetic interactions across structural phase transitions, in these compounds.