Correlation between geometry, electronic structure, and magnetism of solids is both intriguing and elusive. This is particularly strongly manifested in small clusters, where a vast number of unusual structures appear. Here, we employ density functional theory in combination with a genetic search algorithm GGA + U and a hybrid functional to determine the structure of gas phase FexOy+/0 clusters. For FexOy+ cation clusters we also calculate the corresponding vibration spectra and compare them with experiments. We successfully identify Fe3O4+, Fe4O5+, Fe4O6+, Fe5O7+ and propose structures for Fe6O8+. Within the triangular geometric structure of Fe3O4+, a noncollinear, ferrimagnetic, and ferromagnetic state are comparable in energy. Fe4O5+ and Fe4O6+ are ferrimagnetic with a residual magnetic moment of 1 mu(B) due to ionization. Fe5O7+ is ferrimagnetic due to the odd number of Fe atoms. We compare the electronic structure with bulk magnetite and find Fe4O5+, Fe4O6+, Fe6O8+ to be mixed valence clusters. In contrast, in Fe3O4+ and Fe5O7+, all Fe are found to be trivalent.
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