Stability and Meta-stability of Clusters in a Reactive Atmosphere: Theoretical Evidence for Unexpected Stoichiometries of Mg$_M$O$_x$

Applying genetic algorithm and replica exchange molecular dynamics in a cascade approach we calculate structure and composition of Mg$_M$O$_x$ clusters at realistic temperatures and oxygen pressures. The cascade starts with force field and goes up to density functional theory with exact exchange plus correlation in the random phase approximation\footnote{X. Ren, P. Rinke, C. Joas, and M. Scheffler, Invited Review: Random-phase approximation and its applications in computational chemistry and materials science. J. Mater. Sci. {\bf 47}, 21 (2012).}. The stable compositions are identified using \textit{ab initio} atomistic thermodynamics. We find that at realistic environmental conditions small clusters ($M$ = 1-5) are in thermodynamic equilibrium when $x > M$. Non-stoichiometric clusters are found to have in general higher spin multiplicity than stoichiometric ones. This suggests a possibility of tuning magnetic properties by changing environmental conditions.