Initial- and final-state effects on screening and branching ratio in 2 p x-ray absorption of size-selected free 3 d transition metal clusters

A comprehensive study of size-dependent initial- and final-state effects in $2p$ x-ray absorption of free, homonuclear $3d$ transition metal clusters from titanium through nickel in a size range of 1--200 atoms is presented. From atom to bulk the $2p\\ensuremath{\\rightarrow}3d$ excitation in $3d$ transition metals shifts to higher photon energy, which can be explained by increasing valence electron delocalization in the initial state. A cluster-size-dependent decrease of the ${L}_{2,3}$ branching ratio at a constant $2p$ spin-orbit splitting can be attributed to core-hole screening effects for all investigated $3d$ transition metal clusters. For small manganese cluster ions, highly localized $3d$ orbitals with ferromagnetic spin coupling and a filled $3d$ majority spin subband are suggested by the experimental $2p$ x-ray absorption spectra.