Iron clusters: Electronic structure and magnetism

Abstract

Self-consistent-field $X\alpha$ -scattered-wave molecular-orbital calculations have been performed for iron clusters containing four, nine, and fifteen atoms. The convergence of several properties toward the values for bulk iron has been examined. The dominance of magnetic effects on the electronic structure is quickly established; even the four-atom cluster displays the large exchange splitting and high magnetic moment characteristic of bulk iron. Some other quantities, such as the $d$- and especially the $s$-band width, converge more slowly. For ${\mathrm{Fe}}_{15}$ all of the major features of the bulk density of states (DOS) are present in the cluster DOS. The energy positions of the DOS peaks are sufficiently near those of bulk iron that a qualitative discussion of the binding in bulk iron may be given in terms of the nature of the cluster wave functions. Spin-density maps have been generated for ${\mathrm{Fe}}_{15}$ and these bear a striking resemblance to those derived from neutron scattering experiments on bulk iron. Values of the contact hyperfine field have been calculated and, for the peripheral atoms, reasonable agreement with band theory and with experimental results is found. The experimentally observed increase in the magnetic moment of iron at high temperature is rationalized on the basis of the cluster calculation for ${\mathrm{Fe}}_{15}$. While one is able to obtain much insight into the properties of bulk iron by examining those of ${\mathrm{Fe}}_{15}$, there are also some clear differences due to the finite size of the cluster. The central atom has an excess negative charge of about one, and most of this extra charge is of minority spin, leading to a magnetic moment which is much smaller than those for the peripheral atoms. The local density of states at the central atom is also atypical as is the detailed form of the spin density and the value of the contact hyperfine field. Overall the peripheral atoms are more bulklike than the central atom despite the fact that they are missing some nearest neighbors. Non-spinpolarized calculations for ${\mathrm{Fe}}_{15}$ lead to a better understanding of why iron is ferromagnetic through a Stoner-type analysis. For paramagnetic ${\mathrm{Fe}}_{15}$ the Fermi level is situated very near the overall maximum of the DOS. Moreover the cluster wave functions at ${\epsilon }_F$ are antibonding and hence highly localized in space, which would lead to a large value for the cluster "Stoner integral." Thus a rationalization for the instability of paramagnetic iron has been obtained in terms of quantum chemical concepts.