Spin and orbital magnetic moments of size-selected iron, cobalt, and nickel clusters

Abstract

Spin and orbital magnetic moments of cationic iron, cobalt, and nickel clusters have been determined from x-ray magnetic circular dichroism spectroscopy. In the size regime of $n=10--15$ atoms, iron and cobalt clusters show fully spin-polarized unoccupied $3d$ states with maximized spin magnetic moments of $1\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ per hole because of completely filled $3d$ majority-spin bands. The notable exception is ${\mathrm{Fe}}_{13}^{+}$ where an unusually low average spin magnetic moment of $0.73\ifmmode\pm\else\textpm\fi{}0.12$ ${\ensuremath{\mu}}_{B}$ per unoccupied $3d$ state is detected, an effect which is neither observed for ${\mathrm{Co}}_{13}^{+}$ nor ${\mathrm{Ni}}_{13}^{+}$. This distinct behavior can be linked to the existence and accessibility of antiferromagnetic, paramagnetic, or nonmagnetic phases in the respective bulk phase diagrams of iron, cobalt, and nickel. Compared to the experimental data, available density functional theory calculations generally seem to underestimate the spin magnetic moments significantly. In all clusters investigated, the orbital magnetic moment is quenched to $5%--25%$ of the atomic value by the reduced symmetry of the crystal field. The magnetic anisotropy energy in this size range is well below $65\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{eV}$ per atom.