Importance of spin–orbit coupling in M@Pb12 clusters (M = 3d and 4d atoms)

We investigated the effect of spin–orbit coupling (SOC) on symmetry and magnetism of M@Pb12 clusters (M = 3d and 4d transition-metal atoms) based on density functional theory. The symmetry of geometrical configurations may be enhanced with SOC. The SOC marginally affects the local spin magnetic moments of 3d atoms encapsulated in the Pb12 cages, whereas for 4d series, the spin moments of most impurities will remarkably decrease when SOC is considered due to the strong hybridization between M-4d and Pb-6p states. The considerable orbital moments can be obtained. The variation trend of orbital moments can well be explained based on Hund’s rule.