  A major bottleneck for the development of Mg batteries is the identification
of liquid electrolytes that are simultaneously compatible with the Mg-metal
anode and high-voltage cathodes. One strategy to widen the stability windows of
current non-aqueous electrolytes is to introduce protective coating materials
at the electrodes, where coating materials are required to exhibit swift Mg
transport. In this work, we use a combination of first-principles calculations
and ion-transport theory to evaluate the migration barriers for nearly 27
Mg-containing binary, ternary, and quaternary compounds spanning a wide
chemical space. Combining mobility, electronic band gaps, and stability
requirements, we identify MgSiN$_2$, MgI$_2$, MgBr$_2$, MgSe, and MgS as
potential coating materials against the highly reductive Mg metal anode, and we
find MgAl$_2$O$_4$ and Mg(PO$_3$)$_2$ to be promising materials against
high-voltage oxide cathodes (up to $\sim$3~V).
