The spin and orbital moment of Fen (n = 2–20) clusters

Abstract

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.