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High-pressure Mg-Sc-H phase diagram and its superconductivity from first-principles calculations

In this work, global search for crystal structures of ternary Mg-Sc-H hydrides (Mg$_x$Sc$_y$H$_z$) under high pressure ($100 \le P \le 200$ GPa) were performed using the evolutionary algorithm and first-principles calculations. Based on them, we computed the thermodynamic convex hull and pressure-dependent phase diagram of Mg$_x$Sc$_y$H$_z$ for $z/(x+y) < 4$. We have identified the stable crystal structures of four thermodynamically stable compounds with the higher hydrogen content, i.e., $R\bar{3}m$-MgScH$_{6}$, $C2/m$-Mg$_{2}$ScH$_{10}$, $Immm$-MgSc$_{2}$H$_{9}$ and $Pm\bar{3}m$-Mg(ScH$_{4}$)$_{3}$. Their superconducting transition temperatures were computationally predicted by the McMillan-Allen-Dynes formula combined with first-principles phonon calculations. They were found to exhibit superconductivity; among them, $R\bar{3}m$-MgScH$_{6}$ was predicted to have the highest $T_{c}$ (i.e. 23.34 K) at 200 GPa.