Band picture of the spin-Peierls cuprate CuGeO 3 Z ˇ eljko V. S ˇ ljivanc ˇ anin, Zoran S. Popovic ´ , and Filip R. Vukajlovic ´ Laboratory for Theoretical Physics and Physics of Condensed Matter (020), Institute of Nuclear Sciences-‘‘Vinc ˇa,’’ P.O. Box 522, 11001 Belgrade, Yugoslavia Received 29 January 1997 The electronic structure for the cuprate CuGeO 3 has been studied by the generalization of the local-density- approximation method for the systems with strong Coulomb correlations. The stable insulating antiferromag- netic solution with an energy gap of 3.02 eV and a magnetic moment of 0.89  B is obtained. According to our results the strong copper on-site Coulomb interaction of U=9.66 eV is the most important quantity for the gap opening in this inorganic spin-Peierls compound. S0163-18299706732-5 I. INTRODUCTION Since Hase, Terasaki, and Uchinokura 1 discovered that cuprate or copper metagermanate CuGeO 3 is the first ion- organic compound containing linear spin- 1 2 CuO 2 chains along the orthorhombic c axis, which undergoes a spin- Peierls SP transition, very intensive experimental and the- oretical investigations of various physical properties of this compound were completed cf. some recent experimental 2–11 and theoretical works, 2,12–16 and references cited therein.A distinctive feature of a large variety of phase transitions in quasi-one-dimensional compounds is their broad regime of one-dimensional fluctuations, precursor to the true critical point. The SP transition is a kind of magnetoelastic transition occurring in a system of one-dimensional spin- 1 2 chains coupled to three-dimensional phonons. At low temperatures it leads to a dimerization of the magnetic lattice, the forma- tion of a gap in the spectrum of magnons, and an exponential temperature decrease of the magnetic susceptibility. The opening of the magnetic gap is usually accompanied by a structural transition. Studies of SP systems not only increase our understanding of the competition between magnetic and superconducting ground states, but they allow for a compari- son of phase transition mechanisms in magnetic systems as well. 17 In spite of the presence of non-negligible interchain inter- actions, most experiments concerning the magnetic proper- ties of CuGeO 3 are shown to be well described by a spin- 1 2 antiferromagnetic AF Heisenberg model with alternating nearest-neighbor interactions 14 and additional uniform second-neighbor interactions. 15b Single crystals of CuGeO 3 are translucent blue in color, and transport measurement shows that these samples exhibit an insulating behaviour with a room-temperature resistivity as high as  ( T =300 K) 10 13  cm. 12 The transmission measure- ments of polarized light gave gap values of 3.25 and 3.55 eV, depending on the direction of the polarization of incoming light relative to the crystal axes. 18a Recent absorp- tion measurements with polarized light in the energy range 1–4 eV Ref. 18b gave similar results. These facts justified the picture that the spins and magnetic moments, whose alignments lead to magnetic effects, are certainly localizable, so that phenomenologically, at least, they can be described by a spin Hamiltonian which contains spin operators and exchange terms of the Heisenberg type. On the other hand, trying to solve the problem of elec- tronic motion which should answer the question whether the cuprate CuGeO 3 in crystalline phase is an insulator, a semi- conductor, or a metal, one will encounter the problem. Stan- dard band calculations, the spin-restricted linear-augmented- plane-wave method 12 and the linear-muffin-tin-orbital LMTO method in the atomic-sphere approximation ASA, both spin-restricted and spin-polarized calculations, 13 predict a metallic state for the copper metagermanate. Both theoret- ical band calculations 12,13 showed that dimerization of CuO 2 chains can open a very small band gap at E F ( 0.15 eV), provided that Cu displacements in neighboring chains are out of phase. We already have the situation seen in the transition-metal oxides and high-temperature superconductors. 19 An important prerequisite for understanding the nature of optical, electrical, magnetic, and other properties of the cop- per metagermanate is a detailed knowledge of its electronic structure. The present failure of standard density-functional methods in the local-density approximation LDA and in the local-spin-density approximation LSDA to give better quantitative results should be taken as an indication of the importance of electron correlation effects in the CuGeO 3 sys- tem. It is commonly accepted that strongly correlated systems are well described by multiband Hubbard or Anderson- lattice-type models cf. Ref. 19. One can use the LDA and LSDA to calculate parameters of these models. The method introduced by Anisimov et al. 20 includes the leading terms for on-site Coulomb and exchange interactions U and J al- lowing for orbital ordering to develop around the mean-field solution in systems containing localized orbitals. This method conciliates a paradox which one faces at first sight. On one hand, the standard the LSDA is unable to describe magnetic insulators. On the other hand, all the necessary in- formation is apparently there. It turns out that, for a variety of strongly correlated systems, rare-earth compounds, 3 d -transition metal Mott insulators, and high-T c supercon- ductors, this LDA-parameter Hubbard-model approach is surprisingly accurate. The fruitfulness of the idea to introduce a modified total- energy functional (LDA+U), 20 which produces a one- electron orbitally dependent potential, has been proved in PHYSICAL REVIEW B 15 AUGUST 1997-II VOLUME 56, NUMBER 8 56 0163-1829/97/568/44327/$10.00 4432 © 1997 The American Physical Society