We perform spin-polarized density-functional theory simulations within the generalized gradient approximation (GGA) and $\text{GGA}+\text{U}$ method on nanometer-sized iron-oxide atomic clusters in different stoichiometries. By comparing total energies of structures with different symmetries and selected collinear magnetic configurations we find that low symmetry and, in general, ferrimagnetic structures exhibiting low total magnetic moment are energetically favorable. For the oxygen-rich ${\text{Fe}}_{25}{\text{O}}_{30}$ cluster we obtain a cagelike geometry with a few ions within the cage that seem to stabilize the structure. Considering the ${\text{Fe}}_{33}{\text{O}}_{32}$ cluster of nanometer-size we propose the formation of a rocksalt type structure, which is characteristic of bulk FeO. Based on data of iron $d$ shell electron occupancies, we exclude double exchange from possible magnetic interactions between iron ions, and we point to a competition between direct exchange and superexchange, where the dominant interaction is determined by the cluster topology. For the smaller ${\text{Fe}}_{13}{\text{O}}_8$ cluster we find ferromagnetic energetically favorable geometries of lower symmetry than previously reported. Our results demonstrate the importance of going beyond GGA, in particular, physical properties obtained within $\text{GGA}+\text{U}$ description are found to be remarkably different from those using GGA. In order to confirm our theoretical predictions, cluster experiments in this size regime are desirable.

• Received 4 June 2009

DOI:https://doi.org/10.1103/PhysRevB.81.075403