## 3 Results
### Magnetic Properties  
To determine the magnetic properties of the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound, the temperature-dependent magnetic susceptibility \(M\) (T) was measured in the temperature range of 2-300 K under an applied magnetic field of 0.01 T using both zero-field-cooled (ZFC) and field-cooled (FC) modes, as shown in Figure 3a. With decreasing temperature, the magnetic susceptibility gradually increases, and no inflection point is observed down to 2 K, indicating that the magnetic ordering temperature of this compound is below 2 K. The d\(M\)/d\(T\) curve also confirms that no magnetic ordering transition occurs in the compound above 2 K. The Curie-Weiss fitting of the magnetic susceptibility data in the temperature range of 2-300 K yields an effective magnetic moment of 8.1 \(\mu_{B}\) for Gd\({}^{3+}\), which is close to the theoretical value (7.96 \(\mu_{B}\)) [24]. Furthermore, the fitted paramagnetic Curie temperature (\(\theta\)) is \(-\)8.17 K, indicating that the Gd\({}^{3+}\) ions exhibit typical antiferromagnetic characteristics. However, the magnetic measurements collected above 2 K did not observe a magnetic ordering temperature. When considering only the nearest-neighbor interactions (\(J_{1}\)) of Gd\({}^{3+}\), the Hamiltonian for the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound can be expressed as \(H_{\rm ex}=J_{1}\sum_{\langle i,\ j\rangle}S_{i}S_{j}\). Hence, the magnitude of the \(J_{1}\) can also be used to evaluate the magnetic ordering temperature. For the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound, with \(z=4\) and \(S=7/2\), the experimental fit of the Curie-Weiss temperature is \(-\)8.17 K, which leads to a \(J_{1}\) value of 390 mK through \(\theta_{\rm CW}=-J_{1}zS(S+1)/3k_{B}\). Since the magnetic transition temperature in magnetic materials is significantly influenced by \(J_{1}\), the magnetic transition temperature in is below 2 K. To further understand the magnetism of the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound, the d\(M\)/d\(T\) results of its susceptibility as a function of temperature under different magnetic fields are presented in Figure 3b. At magnetic fields below 3 T, no inflection point is observed in the d\(M\)/d\(T\) curves. As the magnetic field increases, the inflection point appears and moves to higher temperatures. Therefore, based on the present results, several characteristics of the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound can be inferred: the magnetic transition temperature is below 2 K, and an induced transition from antiferromagnetic to ferromagnetic states occurs in magnetic fields exceeding 3 T.  
Figure 2: The XRD pattern of Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound obtained by refinement at room temperature. Black squares represent experimental values, while red, cyan, and blue lines represent refined fitted values, interpolations between experimental and fitted values, and positions of standard peaks for the refined indices, respectively. Figure 4a shows the isothermal magnetization curves \(M\) (H) of the Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound at different temperatures under magnetic fields ranging from 0 to 7 T. As the magnetic field increases, the magnetization intensity increases almost linearly and does not reach saturation even at a high field of 7 T, which can be attributed to the typical frustrated structure in this compound. In Figure 4b, the Brillouin function for a free Heisenberg spin of \(S=7/2\) at \(T=2\) K is plotted. A significant difference can be clearly observed between the Brillouin function and the \(M\) (H) curve of Gd\({}_{7}\)(BO\({}_{3}\))(PO\({}_{4}\))\({}_{2}\)O\({}_{6}\) compound at 2 K. Relatively speaking, the Brillouin function curve tends to saturate at lower magnetic fields, indicating that the magnetic interactions in this compound are dominated by superexchange or dipolar antiferromagnetic interactions.