## 3 Results and Discussion
### Magnetocaloric Properties of Fe\({}_{65}\)Ni\({}_{35}\) and Fe\({}_{65}\)Mn\({}_{35}\)  
To determine the magnetocaloric effect in these particular Fe\({}_{65}\)_T\({}_{35}\)_ (_T_ = Ni and Mn) alloys, the magnetocaloric effect is derived from the virgin magnetic isotherms (M-H) in the range of 200 K to 400 K. From this procedure, the magnetocaloric effect is usually measured in terms of the change in isothermal magnetic entropy (\(\Delta\)S\({}_{\rm M}\)), produced by the change in the applied magnetic field. In the present study, we have taken each isotherm after cooling the respective compound from the maximum operating temperature (400 K) to the measured temperature. The isothermal magnetic entropy change has been computed by using the following expression [11,47]: \(\Delta\)S\({}_{\rm M}\) = \(\Sigma\) [(M\({}_{\rm n}\) - M\({}_{\rm n+1}\))/(T\({}_{\rm n+1}\) - T\({}_{\rm n}\))] \(\Delta\)H\({}_{\rm n}\), where M\({}_{\rm n}\) and M\({}_{\rm n+1}\) are the magnetization values measured at field H\({}_{\rm n}\) and H\({}_{\rm n+1}\) at temperature T\({}_{\rm n}\) and T\({}_{\rm n+1}\), respectively. Figure 5a,b display the temperature-dependent \(\Delta\)S\({}_{\rm M}\) curve for  
Figure 4: Applied field response of isothermal magnetization curves at 50 K and 300 K: (**a**) M\(-\)H isotherms for Fe\({}_{65}\)Ni\({}_{35}\); inset: M(H) curves expanded in the low-field region; (**b**) M\(-\)H isotherms for Fe\({}_{65}\)Mn\({}_{35}\); inset: M(H) curves expanded in the low-field region. different applied magnetic fields (5 kOe to 30 kOe) of Fe\({}_{65}\)Ni\({}_{35}\) and Fe\({}_{65}\)Mn\({}_{35}\), respectively. For Fe\({}_{65}\)Ni\({}_{35}\), it is observed from the results that \(\Delta\)S\({}_{\rm M}\) showed a broad peak and gained the maximum value of \(-\)\(-\)0.35 J/kg-K near 262 K for a 30 kOe applied magnetic field. However, in the case of Fe\({}_{65}\)Mn\({}_{35}\), the value of \(\Delta\)S\({}_{\rm M}\) reduces to \(-\)0.27 J/kg-K for the same applied magnetic field near 318 K. Here, we noticed that for both the compounds, the peak temperature of \(\Delta\)S\({}_{\rm M}\) matches well with the magnetic transition temperature, as observed in temperature-dependent magnetization results. From the viewpoint of \(\Delta\)S\({}_{\rm M}\) value, we get a slightly lower value than those reported literature report [20; 22; 23; 24]; such a lower value may arise due to the competitive nature of the magnetic state, which actually originates from the mixed crystallographic phase in these compounds. Though such a mixed phase affects the magnetocaloric parameters, it may broaden the magnetic entropy change. Therefore, such investigations could provide better insights into the fundamental magnetism of such systems. Interestingly, it is noticed from the \(\Delta\)S\({}_{\rm M}\) curve's nature that both the compounds exhibit different characteristics of the curves; such behavior is analogous to the temperature and magnetic field-dependent magnetization results, where both curves change their nature as Ni replaces the Mn in Fe\({}_{65}\)T\({}_{35}\) alloy. Hence, it can be concluded that, in these alloys, the observed MCE is owing to the magnetic entropy variation arising from iron transition metal sub-lattice interactions along with the competition between the \(\alpha\) and \(\gamma\) phase. Additionally, the \(\Delta\)S\({}_{\rm M}\) peak's broadness indicates the magnetic transition's second-order nature; the nature of magnetic transition investigation by \(\Delta\)S\({}_{\rm M}\) data has already been reported in the literature [7; 8]. These alloys have significant MCE in a broad temperature range near room temperature. In the case of Fe\({}_{65}\)Ni\({}_{35}\), it exhibits greater magnetization change; consequently, it has more MCE than Fe\({}_{65}\)Mn\({}_{35}\).