# Magnetocaloric Properties and Critical Behaviour of the Sm\({}_{2}\)Ni\({}_{17}\) Compound
## 3 Results and Discussion
### Magnetocaloric Properties of Sm\({}_{2}\)Ni\({}_{17}\)
The magnetization sensitivity in the ordered magnetic state is represented by \(\frac{dM}{dT}|_{T<T_{\rm C}}\), while at \(T_{\rm C}\) it is denoted by \(\frac{dM}{dT}|_{T_{\rm C}}\). To obtain \(\Delta S_{M}\) of a compound undergoing adiabatic variation of the external magnetic excitation from 0 to a final value of the internal magnetic field (\(\mu_{0}H_{max}\)), the following equation can be used :  
\[\Delta S_{M}=-\alpha.\mu_{0}H_{max}\frac{M_{F}-M_{P}}{2}sech^{2}[(\alpha(T_{ \rm C}-T))]+(\frac{dM}{dT}|_{T<T_{\rm C}}).\mu_{0}H_{max} \tag{2}\]  
Equation (2) indicates that a large observed \(\Delta S_{M}\) is due to the presence of high magnetization for \(T<T_{\rm C}\) and a rapid decrease in magnetization for \(T=T_{\rm C}\). Therefore, the maxi  
Figure 5: Modelled and experimental magnetization measured under several \(\mu_{0}H\) plotted against temperature for Sm\({}_{2}\)Ni\({}_{17}\). mum value of \(\Delta S_{M}\), denoted as \(\Delta S_{M}^{max}\), can be derived using Equation (2). At \(T=T_{\text{C}}\), \(\Delta S_{M}\) is equivalent to \(\Delta S_{M}^{max}\), expressed as follows:  
Figure 2:0  
Furthermore, the determination of the half-value width, \(\delta T^{FWHM}\), of \(\Delta S_{M}\) can be determined using the following approach:  
Figure 2:1  
The relative cooling power (\(RCP\)) is a crucial parameter in the application of magnetocaloric materials, which is related to \(\Delta S_{M}^{max}\) and FWHM for the variation in \(\Delta S_{M}\) with temperature, as stated in [24]. The expression for \(RCP\) is given by the following equation:  
Figure 2:2  
Using the phenomenological model, it is possible to calculate key parameters such as \(\delta T^{FWHM}\), \(\Delta S_{M}^{max}\) and \(RCP\) for Sm\({}_{2}\)Ni\({}_{17}\) compounds while considering variations in the applied magnetic field. Another important parameter, known as the temperature-averaged entropy change (\(TEC\)), has been used in addition to \(RCP\) to evaluate the suitability of materials for magnetic refrigeration applications. Introduced by [PERSON] et al. in [57], \(TEC\) can be computed from the magnetic entropy change data according to the following expression:  
Figure 2:3  
\(\Delta T_{H-\text{C}}\) is the temperature range of the measurement apparatus and reflects the difference between hot and cold heat exchangers. \(T_{mid}\) is the temperature at the centre of \(\Delta T_{H-\text{C}}\) where \(TEC\) is maximized. The magnetic entropy variation obtained from the phenomenological model and [PERSON]'s relation for different applied magnetic fields is compared in Figure 6a. The agreement between the experimental and simulated curves is obvious. This suggests that the phenomenological model is a reliable tool for evaluating the magnetocaloric effect. Moreover, this model can predict the \(\Delta S_{M}\) curve based on a magnetization curve measured under a single low magnetic field value, saving time and cost in the measurement process. In Table 1, we compare the maximum entropy variation values with the \(RCP\) values for different magnetocaloric intermetallic materials. The Sm\({}_{2}\)Ni\({}_{17}\) compound studied in this work exhibits a \(\Delta S_{max}\) of 0.7 J(kg\(\cdot\)K)\({}^{-1}\) and a relatively large mean height width of 45 K. The product of these values yields an \(RCP\) of 37 J\(\cdot\)kg\({}^{-1}\). This is comparable with Pr(Co,Cu)\({}_{5}\) calculated around the spin reorientation temperature, higher than Er\({}_{2}\)Ni\({}_{17}\), SmNi\({}_{5}\), Pr\({}_{2}\)Co\({}_{7}\), PrCo\({}_{19}\), Fe\({}_{65}\)Ni\({}_{35}\), and GdFe\({}_{2}\). However, it is approximately four times lower than the PrCo\({}_{2}\)Cu\({}_{3}\) compound.