Core-level x-ray photoemission on NiO in the impurity limit

We present a core level X-ray photoelectron spectroscopy study of ${\mathrm{Ni}}_x{\mathrm{Mg}}_{1-x}\mathrm{O}$ crystals with $0.03<x<\mathrm{}1\mathrm{}$. We show that nonlocal effects involving inter-Ni-site fluctuations strongly influence the Ni $2p$ core-level spectra for higher Ni concentrations including NiO itself. It is only in the very dilute Ni limit that the core-level spectra can be described in terms of an Anderson impurity model which also must include a realistic band structure for the O $2p$. Moreover, it is only in this limit that a single-site model can explain the core-level and valence-band spectra as well as the optical data by using one consistent set of parameter values. These results consolidate the concepts of nonlocal screening and provide a better understanding of the electronic structure of NiO.