  The accretion of a terrestrial body and differentiation of its silicate/oxide
mantle from iron core provide abundant energy for heating its interior to
temperatures much higher than the present day Earth. The consequences of
differentiation on the structure and composition of planets are typically
addressed considering only the interaction of molten iron with an immiscible
`rocky' phase. We demonstrate that mixing in a representative system of liquid
or solid MgO and liquid iron to a single homogeneous liquid occurs at
sufficiently low temperature to be present in the aftermath of a giant impact.
Applying the thermodynamic integration technique to density functional theory
molecular dynamics simulations, we determine the solvus closure temperature for
the Fe-MgO system for pressures up to 400 GPa. Solvus closure occurs at
$\sim$4000 K at low pressure, and has a weak positive pressure dependence, such
that its gradient with respect to depth is less steep than an adiabatic
temperature profile. This predicts a new mode of core-mantle differentiation
following the most energetic giant impacts, with exsolution of iron from the
mixture beginning in the outer layers of the planet. We demonstrate that
high-temperature equilibration results in delivery of nominally insoluble
Mg-rich material to the early core. Since MgO is the least soluble major mantle
component in iron at low temperatures, these results may represent an upper
bound on temperature for mixing in terrestrial planets.
