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The electronic structure of selected rare-earth atoms adsorbed on a free-standing graphene was investigated using methods beyond the conventional density functional theory (DFT+U, DFT+HIA and DFT+ED). The influence of the electron correlations and the spin-orbit coupling on the magnetic properties has been examined. The DFT+U method predicts both atoms to carry local magnetic moments (spin and orbital) contrary to a nonmagnetic $f^6$ ($J=0$) ground-state configuration of Sm in the gas phase. Application of DFT${}+{}$Hubbard-I (HIA) and DFT${}+{}$exact diagonalization (ED) methods cures this problem, and yields a nonmagnetic ground state with six $f$ electrons and $J=0$ for the Sm adatom. Our calculations show that Nd adatom remains magnetic, with four localized $f$ electrons and $J=4.0$. These conclusions could be verified by STM and XAS experiments., Comment: REVTeX 4-1, 8 pages, 4 figures

We present the results obtained by superconducting quantum interference device (SQUID) magnetometry, specific heat, and M\"ossbauer spectroscopy measurements carried out on ${\mathrm{Np}}_{2}{\mathrm{Ni}}_{17}$ polycrystalline samples. We show that long-range magnetic order, with a moment ${\ensuremath{\mu}}_{(2b)}\ensuremath{\sim}2.25$ ${\ensuremath{\mu}}_{B}$, occurs below ${\mathrm{T}}_{N}=17.5$ K on the Np $(2b)$ sites. A nontrivial situation is observed in that the other Np sites $(2d)$ do not take part to the order transition and carry only an induced moment of about 0.2 ${\ensuremath{\mu}}_{B}$ below ${\mathrm{T}}_{N}$. A combined analysis of the different experimental data sets allowed us to determine key parameters associated with the electronic structure of the system. The experimental results are discussed against first-principles electronic structure calculations based on the spin-polarized local spin density approximation plus Hubbard interaction.