## 3 Results and Discussion
### Magnetocaloric Properties of Fe\({}_{65}\)Ni\({}_{35}\) and Fe\({}_{65}\)Mn\({}_{35}\)
Additionally, this could be another possible reason that the modification of Fe-Ni exchange interac  
Figure 5: Temperature response of isothermal magnetic entropy change (\(\Delta\)S\({}_{\rm M}\)) at different applied field: (**a**) \(\Delta\)S\({}_{\rm M}\) vs. T curve for Fe\({}_{65}\)Ni\({}_{35}\); (**b**) \(\Delta\)S\({}_{\rm M}\) vs. T curve for Fe\({}_{65}\)Mn\({}_{35}\). value. The small magnetic hysteresis and second-order nature of such alloys have suitable properties of a magnetic refrigerant, which are helpful for practical application. The small magnetic hysteresis and second-order nature of such alloys have suitable properties for a magnetic refrigerant which are helpful for practical application. In the research area of magnetocaloric material, it is necessary to draw a comparison regarding the experimental results for various compounds since all magnetocaloric parameters exhibit an applied magnetic field-dependent behavior; also, these parameters vary from material to material. Therefore, the magnetic field-dependent investigation of the isothermal magnetic entropy change is necessary for the preferable comprehension of the intrinsic nature of the magnetocaloric effect [10; 11; 12; 48; 49]. The applied magnetic field response of isothermal magnetic entropy change (\(\Delta\)S\({}_{\text{M}}\)) is characterized by power law behavior, i.e., (\(\Delta\)S\({}_{\text{M}}\)\(\sim\)H\({}^{\text{m}}\)), where m is the exponent. This exponent explains the nature of the magnetic state of the material. Here, we fit the magnetic field response of \(\Delta\)S\({}_{\text{M}}\) near the maximum entropy change temperature for both compounds. Figure 6a,b represent the resulting curves of field-dependent \(\Delta\)S\({}_{\text{M}}\) at peak temperature for Fe\({}_{65}\)Ni\({}_{35}\) and Fe\({}_{65}\)Mn\({}_{35}\), respectively. For Fe\({}_{65}\)Ni\({}_{35}\), it is explored that the \(\Delta\)S\({}_{\text{M}}\) obeys a power law, and the obtained value of m is 0.57. Similarly, in Fe\({}_{65}\)Mn\({}_{35}\), \(\Delta\)S\({}_{\text{M}}\) furthermore observes the power law, whereas the value of m is 1.2 more elevated than those obtained in Fe\({}_{65}\)Ni\({}_{35}\). For the antiferromagnetic correlation, the value of the exponent found was 2 [10; 11], while in the case of ferromagnetic correlation it was 0.6 [49; 50]. Therefore, in our case study, Fe\({}_{65}\)Ni\({}_{35}\) compounds exhibit ferromagnetic correlations; however, Fe\({}_{65}\)Mn\({}_{35}\) display the higher value of the exponent, confirming the antiferromagnetic correlation within the ferromagnetic correlations. Such a kind of antiferromagnetic correlation is also found in FeMn systems (earlier reported magnetization studies) [41]; additionally, the change in nature of the magnetization and \(\Delta\)S\({}_{\text{M}}\) curves also support that. Figure 6: Field response of isothermal magnetic entropy change (\(\Delta\)S\({}_{\text{M}}\)) at maximum entropy temperature: (**a**) \(\Delta\)S\({}_{\text{M}}\) vs. H curve for Fe\({}_{65}\)Ni\({}_{35}\); (**b**) \(\Delta\)S\({}_{\text{M}}\) vs. H curve for Fe\({}_{65}\)Mn\({}_{35}\). The plot through the points is fit to the power law behavior (\(\Delta\)S\({}_{\text{M}}\)\(\sim\)H\({}^{\text{m}}\)).