High-$T\rm_{c}$ superconductivity of clathrate Y$_{3}$EuH$_{24}$

Recent progress on theoretical predictions of ternary superhydrides and their subsequent experimental confirmations have introduced us with a new generation of superconductors, having the potential to realize the synthesis of the most anticipated room temperature superconductors. Motivated by the recent high pressure experiment on YH$_6$ and EuH$_6$, we have theoretically examined the stability as well as superconductivity by mixing the two compounds. Here we identified four phases capable of maintaining thermodynamic stability in the pressure range of 150-300 GPa, namely $Fm\bar{3}m$-Y$_{3}$EuH$_{24}$, $Cmmm$-YEuH$_{12}$, $Cmmm$-YEu$_{3}$H$_{24}$,$Immm$-YEu$_{3}$H$_{24}$. Among them, only $Fm\bar{3}m$-Y$_{3}$EuH$_{24}$ can maintain dynamically stability in the searched pressure range. The Allen-Dynes modified McMillan formula was used to further check the superconductivity of this phase, and the results reveal that the predicted superconducting transition temperature $T\rm_{c}$ of Y$_{3}$EuH$_{24}$ is approaching 220 K at 200 GPa. $Fm\bar{3}m$-Y$_{3}$EuH$_{24}$ has a nearly identical logarithmic average phonon frequency $\omega_{log}$ to YH$_{6}$, but its electron-phonon coupling (EPC) constant $\lambda$ is somewhat smaller than YH$_{6}$'s 2.56, resulting in a lower ultimate $T_{c}$ value.