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Transition metals (ex. metallic Ni):

strongly-correlated d-band electrons

The on-site electron-electron Coulomb repulsion obtained from Hartree-Fock or LDA atomic calculations is also of the order of 10eV.

For the solid, the state-of-the-art modified LDA and LSD calculations provide a quantitatively accurate description of the bandstructure, but fail in describing the multiplet splittings observed in core spectroscopies.

The Falicov 4-sites model, with periodic boundary conditions, accounts for the two points and X of a fcc lattice bandstructure. Ni metal is represented in this model by 4 d shells at the 4 lattice sites, filled with 38 or 37 electrons (i.e. 2 or 3 holes). Atomic electron-electron correlations are treated exactly, and the bands are described at the two available points in terms of tight-binding integrals dd, dd, dd.

Menchero has applied recently this Ni₄ cluster model to the dichroism in core photoemission spectroscopy (XPS) [Phys. Rev. Lett. 76, 3208 (1996)], with apparently good results, but...

Dichroism in absorption

We tried to improve these properties changing the number of holes and tuning the bandstructure, getting closer to experimental observation. The final spectra are, however, in no better accord with experiment than what we could get out of a much simpler impurity model à la Anderson. In the figure at the right, the lower part shows the isotropic and circular dichroic L2,3 x-ray absorption spectra (XAS) and the upper part gives the sum and the difference of the minority (up) and majority (down) 2p XPS spectra, in the same geometry as in the work by Menchero. Calculations are done for the Ni4 cluster with two X5 (dotted) and three X2 (solid) holes.

Those interested may read more in Manini, van Veenendaal, and Altarelli, Phys. Rev. Lett. 79, 2594 (1997).