Antiferromagnetic-like coupling in the cationic iron cluster of thirteen atoms

Abstract

We explore, within the density functional theory in the generalized gradient approximation to exchange and correlation, the map of spin isomers of the cationic Fe13(+) cluster in connection with recent X-ray magnetic circular dichroism spectroscopy experiments [M. Niemeyer et al., Phys. Rev. Lett. 2012, 108, 057201] which showed an anomalous low magnetic moment per number of 3d holes in this cluster. We systematically explore the low-lying magnetic excitations and correlate them with structural rearrangements and stability indicators. We obtain the observed low magnetic moment per 3d hole as the ground state of Fe13(+) and we demonstrate that, as supposed by the experimentalists, the cluster undergoes a magnetic transition from a ferromagnetic-like configuration to an antiferromagnetic-like one upon ionization. We unravel this unexpected magnetic behavior showing that it is concomitant with a Th-deformation of the icosahedral structure together with the electronic filling of this particular iron cluster. The spin-orbit interaction preserves this magnetic configuration which is essentially due to the spin. Our computed magnetic anisotropy energy supports the experimental interpretation of the cluster as fluxional due to the very weak coupling of the magnetic moment to an easy axis.

Spin and orbital magnetic moments of size-selected iron, cobalt, and nickel clusters

“…In this process, 3d states are predominantly probed because of the large transition matrix element 70,71 , which leads to x-ray absorption cross sections that are larger by one order of magnitude than transitions into higher ns and nd (n > 3) states. This excitation scheme allows to probe the magnetic moments of iron, cobalt, and nickel clusters, which are carried by the 3d electrons while magnetic contributions from 4s and 4p states are negligible for clusters with more than 10 atoms 72 as well as in the bulk [73][74][75][76] . The 2p core hole that is created in the x-ray absorption process relaxes via Auger decay cascades.…”

“…Table II lists the average experimental 3d spin and orbital magnetic moments per atom and per cluster. Even though XMCD spectroscopy at the L 2,3 edges of 3d transition elements is only sensitive to the 3d magnetic moments, these values will be close to the total magnetic moments because 4s and 4p electron contributions to the spin magnetic moment are expected to be negligible [72][73][74][75][76] .…”

“…In contrast to iron, the situation is different for cobalt and nickel clusters. Here, our data give spin magnetic moments of Co find either an antiferromagnetically coupled spin magnetic moment of the central atom 74,76 or a ferromagnetic alignment of the 3d spins at all atoms but a nearly quenched spin magnetic moment of the central atom 75,90 . In spite of these differences, all these studies predict the same average magnetic moment of µ S = 2.69 µ B per atom [74][75][76]90 for Fe [74][75][76]90 determine identical spin magnetic moments as can be seen from Fig.…”

“…3 and 4) that is required to obtain the magnetic moment per atom. For the cluster ions investigated here, n h for each element has been taken from the available theoretical values for the number of unoccupied 3d states in iron, cobalt, and nickel bulk metals 73,82,84,85,[92][93][94] , clusters 74,75,[86][87][88][89] , and diatomic molecular cations 91 . Calculations for iron clusters 88 have shown that n h is close to the bulk value and does not undergo significant variations over a large range of cluster sizes.…”

“…To illustrate the situation in free transition metal clusters, Fig. 2 shows a series of xray absorption spectra of Fe 82,84,85 ; iron (n = 2 − 89), cobalt (n = 1 − 5), and nickel (n = 2 − 6) clusters 74,75,[86][87][88][89][90] ; and cationic diatomic molecules 91 . In this work, we assume n h as given in the last column.…”