## 3 Results
### Magnetocaloric Effect  
Although the compound exhibits a high saturation magnetization of 180 Am\({}^{2}\)/kg, a significant portion of the magnetic entropy (-\(\Delta S_{M}\)) is lost due to strong antiferromagnetic interactions. Magnetic entropy change is an important parameter for evaluating the magnetocaloric effect. Based on the Maxwell relation, it is given by [25]. The temperature dependence of the magnetic entropy change -\(\Delta S_{M}\) (\(T\)) for the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound under different magnetic fields is shown in Figure 5. As the magnetic field increases, the peak value of the -\(\Delta S_{M}\) appears to gradually shift towards higher temperatures, which is particularly evident under 7 T. This suggests that the compound may undergo a field-induced metamagnetic transition from an antiferromagnetic state to a ferromagnetic state under the influence of the magnetic field. This conclusion is obtained because the peak value of the -\(\Delta S_{M}\) in ferromagnetic materials shifts towards higher temperatures with an increasing magnetic field. Although the compound has an antiferromagnetic ground state, the results of the -\(\Delta S_{M}\) are sufficient to prove the correctness of this hypothesis, and similar results have also been observed in other compounds with antiferromagnetic interactions [26]. Under a varying magnetic field of 0-7 T, the maximum magnetic entropy change (-\(\Delta S_{M}^{max}\)) of the compound reaches 35.2 J/kg K, exhibiting a relatively excellent low-temperature magnetocaloric effect. However, based on the theoretical magnetic entropy change calculation formula -\(\Delta S_{M}^{max}\) = nRIn(2\(S+1\))/\(M\), where n is the number of magnetic ions, R is the ideal gas constant, \(S\) is the spin quantum number of the magnetic ions, and \(M\) corresponds to the molar mass of the compound, the calculated theoretical magnetic entropy change is as high as 83.0 J/kg K. This is significantly higher than the currently observed experimental value. As mentioned above, due to the strong frustration, the magnetization increases linearly with the magnetic field, resulting in a significant reduction in -\(\Delta S_{M}\). The refrigerent capacity (RC) and temperature-averaged magnetic entropy change (TEC) are also important parameters for evaluating the magnetocaloric effect, as obtained from Equations (2) and (3) [27; 28], where \(T_{hot}\) and \(T_{cold}\) correspond to the temperatures at half of the \(\mid\)-\(\Delta S_{M}^{max}\mid\), respectively. For the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound, \(T_{cold}\) is determined to be 2.5 K, \(\Delta T_{1 ftf}\) is the desired temperature lift, and \(T_{mind}\) is the center temperature  
Figure 5: Magnetic entropy change as a function of temperature \(-\Delta S_{M}\) (\(T\)) for Gd\({}_{7}\)BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound under a varying magnetic field from 0 T to 7 T.  
at which the maximum TEC is expected to be obtained. Under a varying magnetic field of 0-7 T, the TEC (3) and RC of the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound are 33.2 J/kg and 288.6 J/kg, respectively. Table 2 compares the magnetocaloric parameters of other low-temperature magnetic refrigerant materials with similar magnetic transition temperatures. It should be emphasized that although the magnetocaloric effect of the current compound is not outstanding, its theoretical magnetic entropy changes of up to 83.0 J/kg K indicate that excellent magnetocaloric effects can be expected and achievable through further optimization. From the crystal structure of the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound, it can be observed that Gd\({}^{3+}\) forms a magnetic frustrated structure in the \(ab\)-plane, creating a two-dimensional structure, and these layers are stacked along the \(c\)-axis direction. Therefore, if partial non-magnetic ions occupy the Gd\({}^{3+}\) sites, it could disrupt some of the frustrated structures.