Quantized Ferromagnetism in Free Cobalt and Iron Clusters

The magnetic moments $\mu$$_{N}$ for cobalt clusters \textit{Co}$_{N}$ (20$\le N\le $200) measured in a cryogenic molecular beam are found to be quantized both in the ground state: $\mu _{N}\sim $2$N$µ$_{B}$ and in the metastable excited state: $\mu _{N}^{\ast }\sim N\mu _{B}$ in contrast with the bulk where it is fractional: $\mu _{N=\infty }$=1.7$N\mu _{B}$. For $N$=30, the ionization potentials of the excited state is about 0.1 eV lower than of the ground state while this difference diminishes with increasing size, which implies that the two states become degenerate at large sizes. The evolution from localized moments in small clusters to itinerant moments in the bulk appears to be related to the closing of this energy gap which results in a fluctuating ground state. These effects can be understood in terms of the Falicov-Kimball model. Two states are also observed in iron clusters, with $\mu _{N}\sim $3$N\mu _{B}$ for \textit{Fe}$_{N}$, and $\mu _{N}^{\ast }$ $\sim N\mu _{B}$ for \textit{Fe}$_{N}^{\ast }$ (20$\le N\le $150).