How chemistry controls electron localization in 3d 1 perovskites: A Wannier-function study

Abstract

In the series of 3d(t 2g) 1 perovskites, SrVO 3-CaVO 3-LaTiO 3-YTiO 3, the transition-metal d electron becomes increasingly localized and undergoes a Mott transition between CaVO 3 and LaTiO 3. By defining a low-energy Hubbard Hamiltonian in the basis of Wannier functions for the t 2g LDA band and solving it in the single-site dynamical mean-field (DMFT) approximation, it was recently shown (Pavarini et al (2004) Phys. Rev. Lett. 92 176403) that simultaneously with the Mott transition there occurs a strong suppression of orbital fluctuations due to splitting of the t 2g levels. The present paper reviews and expands this work, in particular in the direction of exposing the underlying chemical mechanisms by means of ab initio LDA Wannier functions generated with the Nth order muffintin orbital (NMTO) method. The Wannier functions for the occupied oxygen-p band illustrate the importance of oxygen-p to large cation-d covalency for the progressive GdFeO 3-type distortion along the series. The oxygen-p orbitals which pdσ-bond to the cations are the same as those which pdπ-bond to the transitionmetal t 2g orbitals. As a consequence, the Wannier functions for the t 2g band exhibit residual covalency between the transition-metal t 2g, the large cation-d, and the oxygen-p states. This residual covalency, which increases along the series, turns out to be responsible not only for the splittings, Δ, of the t 2g levels, but also for non-cubic perturbations of the hopping integrals, both of which are decisive for the Mott transition. We find good agreement with the optical and photoemission spectra for all four materials, with the crystal-field splittings and orbital polarizations recently measured for the titanates, and with the metallization volume (pressure) for LaTiO 3. The metallization volume for YTiO 3 is predicted and the role of the Jahn-Teller (JT) distortion is discussed. For use in future many-body calculations, we tabulate the t 2g on-site and hopping matrix elements for all four materials and give an analytical expression for the orthorhombic Hamiltonian in the k + Q representation. Using conventional super-exchange theory, our on-site and hopping matrix elements reproduce the observed magnetic orders in LaTiO 3 and YTiO 3, but the results are sensitive to detail, in particular for YTiO 3 where, without the JT distortion, the magnetic order would be antiferromagnetic C- or A-type, rather than ferromagnetic. It is decisive that upon increasing the GdFeO 3-type distortion, the nearest-neighbour hopping between the lowest and the upper-level Wannier functions becomes stronger than the hopping between the lowest-level Wannier functions. Finally, we show that the non-cubic perturbations responsible for this behaviour make it possible to unfold the orthorhombic t 2g LDA bandstructure to a pseudo-cubic zone. In this zone, the lowest band is separated from the two others by a direct gap and has a width, W I, which is significantly smaller than that, W, of the entire t 2g band. The progressive GdFeO 3-type distortion thus favours electron localization by decreasing W, by increasing Δ / W, and by decreasing W I / W. Our conclusions concerning the roles of GdFeO 3-type and JT distortions agree with those of Mochizuki and Imada (2003 Phys. Rev. Lett. 91 167203). © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.