The spin and orbital contributions to the total magnetic moments of free Fe, Co, and Ni clusters

We present size dependent spin and orbital magnetic moments of cobalt (Co$_{n}$$^{+}$, 8 ≤ n ≤ 22), iron (Fe$_{n}$$^{+}$, 7 ≤ n ≤ 17), and nickel cluster (Ni$_{n}$$^{+}$, 7 ≤ n ≤ 17) cations as obtained by X-ray magnetic circular dichroism (XMCD) spectroscopy of isolated clusters in the gas phase. The spin and orbital magnetic moments range between the corresponding atomic and bulk values in all three cases. We compare our findings to previous XMCD data, Stern-Gerlach data, and computational results. We discuss the application of scaling laws to the size dependent evolution of the spin and orbital magnetic moments per atom in the clusters. We find a spin scaling law “per cluster diameter,” ~n$^{−1/3}$, that interpolates between known atomic and bulk values. In remarkable contrast, the orbital moments do likewise only if the atomic asymptote is exempt. A concept of “primary” and “secondary” (induced) orbital moments is invoked for interpretation.