Geometric, electronic and magnetic structure of Fe$_{x}$O$_{y}^{+}$ clusters

Abstract: 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 Fe${x}$O${y}^{+/0}$ clusters. For Fe${x}$O${y}$ cation clusters we also calculate the corresponding vibration spectra and compare them with experiments. We successfully identify Fe${3}$O${4}^{+}$, Fe${4}$O${5}^{+}$, Fe${4}$O${6}^{+}$, Fe${5}$O${7}^{+}$ and propose structures for Fe${6}$O${8}^{+}$. Within the triangular geometric structure of Fe${3}$O${4}^{+}$ a non-collinear, ferrimagnetic and ferromagnetic state are comparable in energy. Fe${4}$O${5}^{+}$ and Fe${4}$O${6}^{+}$ are ferrimagnetic with a residual magnetic moment of 1~\muB{} due to ionization. Fe${5}$O${7}^{+}$ is ferrimagnetic due to the odd number of Fe atoms. We compare the electronic structure with bulk magnetite and find Fe${4}$O${5}^{+}$, Fe${4}$O${6}^{+}$, Fe${6}$O${8}^{+}$ to be mixed valence clusters. In contrast, in Fe${3}$O${4}^{+}$ and Fe${5}$O${7}^{+}$ all Fe are found to be trivalent.