  Re-entrant melting (in which a substance's melting point starts to decrease
beyond a certain pressure) is believed to be an unusual phenomenon. Among the
elements, it has so far only been observed in a very limited number of species,
e.g., the alkali metals. Our density functional theory calculations reveal that
this behavior actually extends beyond alkali metals to include magnesium, which
also undergoes re-entrant melting, though at the much higher pressure of ~300
GPa. We find that the origin of re-entrant melting is the faster softening of
interatomic interactions in the liquid phase than in the solid, as pressure
rises. We propose a simple approach to estimate pressure-volume relations and
show that this characteristic softening pattern is widely observed in metallic
elements. We verify this prediction in the case of aluminum by finding
re-entrant melting at ~4000 GPa. These results suggest that re-entrant melting
may be a more universal feature than previously thought.
