Complementary to the recent experimental finding that the orbital magnetic moment is strongly quenched in small Fe clusters [M. Niemeyer, K. Hirsch, V. Zamudio-Bayer, A. Langenberg, M. Vogel, M. Kossick, C. Ebrecht, K. Egashira, A. Terasaki, T. Möller, B. v. Issendorff, and J. T. Lau, Phys. Rev. Lett. 108, 057201 (2012)], we provide the theoretical understanding of the spin and orbital moments as well as the electronic properties of neutral and cation Fen clusters (n = 2-20) by taking into account the effects of strong electronic correlation, spin-orbit coupling, and noncollinearity of inter-atomic magnetization. The generalized gradient approximation (GGA)+U method is used and its effluence on the magnetic moment is emphasized. We find that without inclusion of the Coulomb interaction U, the spin (orbital) moments have an average value between 2.69 and 3.50 μB/atom (0.04 and 0.08 μB/atom). With inclusion of U, the magnetic value is between 2.75 and 3.80 μB/atom (0.10 and 0.30 μB/atom), which provide an excellent agreement with the experimental measurements. Our results confirm that the spin moments are less quenched, while the orbital moments are strongly quenched in small Fe clusters. Both GGA and GGA+U functionals always yield collinear magnetic ground-state solutions for the fully relaxed Fe structures. Geometrical evolution, as a function of cluster size, illustrates that the icosahedral morphology competes with the hexagonal-antiprism morphology for large Fe clusters. In addition, the calculated trends of ionization potentials, electron affinities, fragment energies, and polarizabilities generally agree with respective experimental observations.

Gadolinium-oxide clusters in various sizes and stoichiometries have been systematically studied by employing the density functional theory with the generalized gradient approximation. The clusters in bulk stoichiometry are relatively more stable and their binding energies increase with the increasing size. Stoichiometric (Gd2O3)n clusters of n = 1–3 prefer cage-like structures, whereas the clusters of n = 4–30 prefer compact structures layered by wedge-like units and exhibit a rough feature toward the bulk-like arrangement with small disorders of atomic positions. The polyhedral-cages analogous to carbon-fullerenes are stable isomers yet not the minimum energy configurations. Their stabilities can be improved by embedding one oxygen atom or a suitable cage to form core-shell configurations. The mostly favored antiferromagnetic couplings between adjacent Gd atoms are nearly degenerated in energy with their ferromagnetic couplings, resulting in super-paramagnetic characters of gadolinium-oxide clusters. The Ruderman-Kittel-Kasuya-Yosida (RKKY)-type mechanism together with the superexchange-type mechanism plays cooperation role for the magnetic interactions in clusters. We present, as a function of n, calculated binding energies, ionization potential, electron affinity, and electronic dipole moment.