## 3 Results and Discussion
### Magnetic Properties  
Figure 4 displays the temperature dependent magnetization measured under 0.01 T in heating and cooling processes for annealed La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) compounds (0 \(\leq\) x \(\leq\) 0.15). The \(T_{\mathrm{C}}\)s, determined from the point of the maximum of d\(M\)/d\(T\) in the heating process, were 188 K, 192 K, 188 K, 190 K, and 190 K for x = 0, 0.03, 0.07, 0.1, and 0.15 respectively. The measured \(T_{\mathrm{C}}\)s were not drastically modified with Y substitution. No regular changes were observed in \(T_{\mathrm{C}}\)s, probably due to formation of the Y\({}_{2}\)Fe\({}_{17}\) phase and \(\alpha\)-Fe.  
The magnetizations in paramagnetic regions did not approach zero due to the existence of ferromagnetic phases, such as \(\alpha\)-Fe and Y\({}_{2}\)Fe\({}_{17}\) phases, in the compounds. In addition, the magnetizations above \(T_{\mathrm{C}}\)s increased with the increase of x because the amount of the ferromagnetic phases increased with x increasing.  
Isothermal magnetization curves as a function of magnetic field up to 2 T for the annealed La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) (0 \(\leq\) x \(\leq\) 0.2) were measured under increasing and decreasing field strengths at various temperatures and are shown in Figure 5a-f. The magnetization curves at temperatures far above \(T_{\mathrm{C}}\) show a curvature at low fields, which is caused by the \(\alpha\)-Fe and Y\({}_{2}\)Fe\({}_{17}\) phases as shown in the red rectangle in Figure 5c-f.  
Figure 6 displays the magnetic hysteresis loss in the vicinity of \(T_{\mathrm{C}}\)s, derived from Figure 5, for the annealed La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) compounds. The solid line in Figure 6 is a guide for the eyes. The magnetic hysteresis loss of all Y-substituted compounds decreases compared with that of x = 0. Additionally, the hysteresis loss is obviously reduced with the increase of x. For x = 0.2, the hysteresis loss almost disappears, which is favorable for magnetic refrigeration.  
Figure 7 shows the Arrott plots in the vicinity of \(T_{\mathrm{C}}\) for La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) (0 \(\leq\) x \(\leq\) 0.2) compounds. The negative slopes decrease almost monotonically with the increase of the Y content from the beginning at x = 0 to x = 0.15, indicating that the feature of the first-order magnetic transition becomes weak after Y additions. A positive slope appears for x = 0.2, indicating that a second-order magnetic phase transition occurs.  
Figure 4: Temperature dependent magnetization measured under the applied magnetic field of 0.01 T on the heating and cooling processes for La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) (0 \(\leq\) x \(\leq\) 0.15) compounds.  
Figure 6: Magnetic hysteresis loss in the vicinity of \(T_{\rm CS}\) for La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) compounds.  
Figure 8 shows the temperature dependence of \(\Delta S_{M}\)(\(T\), \(\mu_{0}H\)) calculated by Equation (1) in a magnetic field change from 0 to 2 T for La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) compounds. The isothermal magnetic entropy change (\(\Delta S_{M}\)) for x = 0, 0.03, 0.07, 0.1, and 0.15 are \(-24.1\) J/kg\(\cdot\)K, \(-24.3\)J/kg\(\cdot\)K, \(-20.8\) J/kg\(\cdot\)K, \(-20.2\) J/kg\(\cdot\)K, and \(-16.9\) J/kg\(\cdot\)K respectively. No significant reduction was found in the magnetic entropy change \(\Delta S_{M}\) by the partial substitution of Y for La in La\({}_{1-x}\)Y\({}_{x}\)Fe\({}_{11.5}\)Si\({}_{1.5}\) for x \(\leq\) 0.07. As to x \(>\) 0.07, the \(\Delta S_{M}\) is significantly suppressed due to the formation of the \(\alpha\)-Fe and Y\({}_{2}\)Fe\({}_{17}\) phases.