VOLUME 74, NUMBER 12 PHYSICAL REVIEW LETTERS 20 MARcH 1995 Band-Structure Picture for MnA Reexplored: A Model GW Calculation S. Massidda Dipartimento di Scienze Fisiche, Universita degli Studi di Cagliari, I-09124 Cagliari, 1taly A. Continenza Dipartimento di Fisica, Universita degLi Studi dell'Aquila, I 6701-0 Coppito (Aq), Italy M. Posternak and A. Baldereschi Institut Romand de Recherche Numerique en Physique des Materiaux (IRRMA), PHB Ecublens, CH 1015 -Lausanne, Switzerland (Received 1 June 1994) We calculate ab initio the quasiparticle energies of MnO with a self-energy model derived from the GW approximation. We obtain good values of the energy gap (4. 2 eV), magnetic moment (4. 5p, s), and on-site interaction U (-8 eV) and reproduce both energy and intensity of all one-particle features of the photoemission spectra. The highest occupied states are 0 2p — Mn 3d (eg) antibonding combinations. The lowest empty state is delocalized with strong ( — 30%) Mn 4s character. PACS numbers: 71. 27.+a, 79. 60. Bm The ab initio prediction of the electronic structure of transition-metal monoxides (TMO's) remains a challeng- ing problem even after decades of activity [1]. The con- ventional local-spin-density (LSD) scheme [2] gets into difficulties with the localized TM d orbitals, and incor- rectly predicts their spectral weights and energies relative to 0 2p states. The configuration-interaction (CI) cluster method [3] is semiempirical and does not describe prop- erly the delocalized 0 2p orbitals and energy dispersions. Nevertheless, the CI method has been quite successful in interpreting spectroscopic results and, in spite of its drawbacks, has been used extensively for TMO's. Band- widths, however, can be substantial in these materials as, e. g. , in NiO where a d-band dispersion of 0.7 eV (possi- bly 1. 5 eV considering anticrossings) has been observed recently [4]. The deficiencies of LSD, therefore, have been investigated lately and extended LSD approaches, such as the self-interaction corrected (SIC) density func- tional theory [5] and the model LSD + U method [6], have been proposed. These schemes have led to improve- ments of the LSD band gaps and moment values. A more ab initio scheme within many-body perturba- tion theory, the GW approximation [7], provides a practi- cal method to calculate quasiparticle energies which differs from LSD-based schemes. It has been used for materi- als ranging from metals and semiconductors [8,9], where screening is strong, to large-gap ionic insulators, such as LiC1 [10]. Furthermore, GW calculations for an exactly solvable model [11] have shown that sensible results can be obtained even when the on-site interaction U is larger than the bandwidth. GW calculations would be, therefore, very valuable for TMO's, but the computational implementation of the method is heavy for these materials. Exploratory work in this direction for NiO [12] has provided encour- aging results. In this Letter, we propose to study TMO's with a model GW approach [13] which is expected to reproduce the results of a full GW calculation with much reduced ef- fort. We consider the paradigmatic case of MnO, the simplest among rocksalt TMO's, since the Mn2+ ion has a half-filled shell (3d ) and the spin subbands are either completely full or completely empty. Its electronic struc- ture has been investigated extensively by photoemission spectroscopy [14 — 17] and discussed in terms of ligand- field theory [18], the CI cluster method [16, 17], the LSD band scheme [2, 19], the SIC [5], and the LSD + U [6] methods. The CI scheme reproduces most experimen- tal data with three adjustable parameters. The LSD band calculations, because of the exchange stabilization of the half-ulled d shell, predict the insulating character of anti- ferromagnetic MnO [2], although the corresponding gap (1. 0 eV) and magnetic moment (4.3p, e) are too small compared to experiment. Better values of these quanti- ties are obtained with the SIC [5] and the LSD + U [6] schemes. Our pioneering application of a high-level many-body scheme to MnO will show that a realistic ab initio band approach is capable of predicting the basic electronic properties of this highly correlated system, as the semiem- pirical CI-cluster method does, and also provides informa- tion on the effects of translational symmetry. Our work on MnO should therefore open the way to rigorous ab ini- tio investigations of a larger class of materials. The self-energy operator in the GW approximation is QGw = iGW, where G is the interacting one-particle Green' s function and W is the dynamically screened Coulomb potential [7, 9]. Following [13], we separate W as W(r, r', E) = W (r, r', E) + BW(r, r', E), where W'Eo is the (short-range) potential of a metallic in- homogeneous electron gas and gives rise, in the quasipar- ticle equation, to a term which can be approximated [20] 0031-9007/95/74(12)/2323(4)$06. 00 1995 The American Physical Society 2323