Spin–orbit Splitting and Magnetism of Icosahedral M@Ag12 Clusters (M = 3d and 4d atoms)

Abstract

The spin–orbit splitting and magnetism of a single 3d, 4d impurity (Sc–Zn, Y–Cd) encapsulated in an icosahedral Ag12 cage (M@Ag12) are explored by using methods based on density functional theory. The large spin–orbit splittings of HOMO levels can be found in the clusters with heavy impurities in each series, especially for 4d case. The total and local spin magnetic moments of 3d series are hardly affected by spin–orbit coupling (SOC). The similar scenario can take place for the first clusters of 4d series (Y–Mo@Ag12). For Tc–Pd@Ag12, the total and local spin magnetic moments remarkably decrease when SOC is considered. The magnetism of Ag@Ag12 and Cd@Ag12 hardly changes when the SOC is included despite large atomic number of the centric Ag and Cd, which can be ascribed to the closed d orbitals of Ag and Cd atoms. The densities of states of some typical clusters and orbital components for HOMO levels of all clusters have been calculated in order to understand these phenomena. The calculated spin and orbital magnetic moments can be comprehended in accordance with the Hund’s rule of superatom model. The closed-shell electron configuration is formed in Mo@Ag12 cluster according to 18-electron rule, quenching both its spin and orbital moments.