Magnetic properties of4dtransition-metal clusters

We analyze the stability of magnetic states obtained within the tight-binding model solved by molecular dynamics for cubo-octahedral (fcc) and icosahedral clusters of $3d$ (Ni and Co) and $4d$ (Pd, Rh, and Ru) transition metals. The magnetic states are stabilized by the Hund's rule exchange interaction between the $d$ orbitals. Taking realistic parameters deduced from band structure calculations and spectroscopic data, we obtained saturated ferromagnetism for ${\mathrm{Ni}}_{13}$, ${\mathrm{Co}}_{13}$, and ${\mathrm{Pd}}_{13}$ clusters, while ${\mathrm{Rh}}_{13}$ fcc and ${\mathrm{Ru}}_{13}$ clusters are partially magnetic, with an antiferromagnetic orientation of the moments on the central atoms in Ru clusters. Our results for $4d$ transition-metal clusters agree qualitatively with the recent experimental data and with other calculations. Metastable magnetic clusters were identified in several situations. We found a dependence of the equilibrium lattice constant on the magnetization in the considered clusters which may be explained by the character of wave functions in the cluster electronic structure.