Simple Model for the Electronic Density of States near Transition-Metal Surfaces: Application to Ferromagnetic Ni

A semiquantitative model based on the Heine—Hubbard Hamiltonian is proposed to describe the distribution of $s$ and $d$ electron energies in the vicinity of a clean transition-metal-vacuum interface. It is shown that, as a result of the tunneling of $s$ electrons into the vacuum, the $d$ band near the surface lies lower and is narrower than that in the bulk. This is expected to have implications for numerous surface-related experiments. Specifically, it is demonstrated that near a Ni surface the $d$-electron density of states at the Fermi energy satisfies the Stoner criterion for paramagnetic stability. This suggests that the surface layer is locally nonmagnetic in agreement with recent experiments. The present theoretical approach is original in that it incorporates both many-body effects and the important features of transition-metal band structure. Interelectronic $s$-band interactions are treated in the Thomas-Fermi approximation. Renormalized-atom theory is used to describe how the nearly localized $d$ electrons respond to the tunneling of $s$ electrons into the vacuum and to treat $s-d$ Coulomb interactions. Finally, intra-atomic $d-d$ Coulomb interactions are treated in the Hartree-Fock approximation and are assumed to be spin dependent.