VOLUME 73, NUMBER 23 PHYSICAL REVIEW LETTERS 5 DECEMBER 1994 Quasiparticle Band Structure of NiO: The Mott-Hubbard Picture Regained F. Manghi, C. Calandra, and Stefano Ossicini Dipartirnento di Fisica, Universita di Modena, Via Campi 213/a, I 4II-OO Modena, Italy (Received 15 April 1994) We demonstrate that the Hubbard correlation among Ni 3d electrons is able to reproduce the insulating character of NiO, the correct value of the gap, the orbital character of the valence band edge, and the presence of satellite structures. We have determined the quasiparticle spectra starting from the complex single particle band structure of NiO and including the on-site Hubbard repulsion according to a recently developed three-body scattering theory which allows us to treat highly correlated and highly hybridized systems. The calculated quasiparticle band structure is in excellent agreement with photoemission data. PACS numbers: 71. 10. +x, 71. 28.+d, 71. 30. +h NiO is the prototype of transition metal oxides which exhibit a radical breakdown of conventional band theory. According to standard single particle approaches NiO is predicted to be a metal or at most a small gap insulator, while from electrical, optical, and combined direct-inverse photoemission it is known to be an insulator with a gap of few electron volts [1]. During the last decades various and controversial interpretations of the nature of the insulating gap of NiO have been proposed which emphasize (a) the role of electron-electron correlation [2], (b) the covalency of the chemical bond with oxygen [3, 4], (c) the importance of antiferromagnetic order [5], and (d) of self-interaction [6, 7] or U-corrected [8] energy functionals. The problem is far from being solved: Theories (c) and (d), which interpret NiO as a band insulator, either underestimate the gap or poorly reproduce the observed spectra; Mott-Hubbard theory (a) in its simplest form fails in reproducing the observed orbital character of the gap edges [4,9]; finally theories (b), which describe NiO as a charge transfer insulator, rely on a rather crude description of the band structure. The breakdown of the single particle description in NiO is evident also from the presence of well-defined satellite features in the excitation spectra [10,11], a clear signal of strong electron-electron correlation. A satisfactory description of the electronic structure of NiO, inclusive of many-body effects, must therefore reproduce quantitatively both the insulating gap and the detailed satellite structure. We demonstrate that this can be achieved in the Mott-Hubbard picture, pro- vided that the complexity of the band structure is fully included. The Hubbard Hamiltonian has often been used to mod- ify single particle eigenvalues, the implicit assumption being that among the various many-body terms responsi- ble for e-e correlation, the Coulomb repulsion U between electrons sitting on the same atom is the one which is erst treated by band theories based on mean field ap- proaches such as local density functional approximation (LDA). Most of the studies on the Hubbard Hamilton- ian are based, however, either on a simplified descrip- tion of the single particle states or on perturbative ap- proaches to treat the electron-electron correlation. None of these approximations are adequate for NiO where nickel d electrons are highly hybridized with p electrons of the ligand and where the value of the Hubbard pa- rameter U is known to be much larger than the d-band width [12]. We have recently developed a method which allows us to treat correlation effects through an approximate nonperturbative solution of the Hubbard Hamiltonian [13]. This approximation consists of a configuration- interaction expansion of the many-body states of the interacting system where the various configurations differ for the number of electron-hole pairs. The method has a rather wide range of validity since it is not limited to particular band filling and can be applied for any value of U. The interactions between configurations with the same number of electron-hole pairs are represented by a set of two-body scattering t matrices, which can be calculated exactly. The Fadeev three-body scattering theory [14,15] is used to determine the total scattering matrix and the resolvent giving the energy of the many-body system. All the details for a single-band Hamiltonian are reported in Ref. [13], the generalization to the multiband case requiring only minor changes and an explicit use of the so-called local approximation [16, 17]. The method allows us to obtain the energy of the in- teracting system with one removed or one added elec- tron, the reference energy being the ground state of the interacting system. Since in the present approach the configuration expansion is truncated to included just one electron-hole pair, the energy of the interacting N particle system coincides with the noninteracting one [13]: The band eigenvalues and eigenvectors must be calculated once and for all, and no self-consistent loop is required. The quasiparticle spectrum for electron and hole states is obtained starting from the single particle density of states and for a given value of the intrasite correlation. The hole state self-energy for a multiband system is 0031-9007/94/73(23)/3129(4)$06. 00 1994 The American Physical Society 3129