Size and structural dependence of the magnetic properties of rhodium clusters

Abstract

The size and structural dependence of the magnetic properties of ${\mathrm{Rh}}_{\mathrm{N}}$ clusters (9\ensuremath{\leqslant}N\ensuremath{\leqslant}55) are studied by using a d-electron tight-binding Hamiltonian including Coulomb interactions in the unrestricted Hartree-Fock approximation. Three main different types of cluster geometries are considered (viz., fcc, bcc, and icosahedral). In each case the equilibrium bond length R is optimized by maximizing the cohesive energy ${\mathrm{E}}_{\mathrm{coh}}$(N). The geometries yielding the largest ${\mathrm{E}}_{\mathrm{coh}}$(N) alternate as a function of N. These structural changes, together with the variation of R, play a crucial role in the determination of the average magnetic moment \ensuremath{\mu}-${\mathrm{bar}}_{\mathrm{N}}$ of ${\mathrm{Rh}}_{\mathrm{N}}$. The calculated size dependence of \ensuremath{\mu}-${\mathrm{bar}}_{\mathrm{N}}$ corresponding to the most stable geometries presents oscillations which are in good qualitative agreement with experiment. The magnetic properties of ${\mathrm{Rh}}_{\mathrm{N}}$ clusters show a remarkable structural dependence which is characteristic of weak (unsaturated) itinerant ferromagnetism. The relation between the observed \ensuremath{\mu}-${\mathrm{bar}}_{\mathrm{N}}$ and the cluster geometry is analyzed. The role of nonuniform geometry relaxation, sp electrons, and sp-d hybridization effects are quantified for representative examples. Perspectives of extensions of this study are also discussed.