  By applying a genetic algorithm in a cascade approach of increasing accuracy,
we calculate the composition and structure of MgMOx clusters at realistic
temperatures and oxygen pressures. The stable and metastable systems are
identified by ab initio atomistic thermodynamics. We find that small clusters
(M <= 5) are in thermodynamic equilibrium when x > M. The non-stoichiometric
clusters exhibit peculiar magnetic behavior, suggesting the possibility of
tuning magnetic properties by changing environmental pressure and temperature
conditions. Furthermore, we show that density-functional theory (DFT) with a
hybrid exchange-correlation (xc) functional is needed for predicting accurate
phase diagrams of metal-oxide clusters. Neither a (sophisticated) force field
nor DFT with (semi)local xc functionals are sufficient for even a qualitative
prediction.
