Revisiting YH$_9$ Superconductivity and Predicting High-T$_c$ in GdYH$_5$

The discovery of superconductivity in $\mathrm{YH_{9}}$ with a critical temperature of approximately $T_c\sim 243 \ K$ has opened a new window toward room temperature superconductivity. In this work, we employ the lowest order constrained variational method to investigate the thermodynamic and magnetic properties of the $\mathrm{YH_{9}}$ structure, obtaining results in good agreement with experimental data. % Based on the robustness of the LOCV approach for describing high-$T_c$ superconductors, we further extend our analysis to the gadolinium-yttrium-hydrogen system across various stoichiometries. The key finding of this study is the prediction of a superconducting phase transition at $T_c = 223.2~\mathrm{K}$ for $\mathrm{GdYH_{5}}$ under a critical pressure of approximately $157~\mathrm{GPa}$. This compound crystallizes in a tetragonal structure with space group $P4/mmm$. Moreover, the calculated gap ratio confirms that $\mathrm{GdYH_{5}}$ is a type-II superconductor with a critical current density suitable for potential industrial applications.