Multiband model for the electronic structure of Sr₂TiO₄

Abstract

We introduce and investigate the multiband d–p model for a TiO4 layer, such as realized in Sr2TiO4, with all t2g and eg orbitals (at titanium ions) and 2p orbitals (at oxygen ions). Complementary density functional theory ab initio computations are employed to determine the actual electron number per TiO4 unit and one finds perfect Sr ionization with Sr+2 ions and charged (TiO4)−2 layer. This system is predicted to be a robust nonmagnetic insulator, in agreement with experiment. The above charge distribution is crucial and when we deviate from it, even by a small amount, the system becomes conducting or very close to conducting and various magnetic structures compete with one another. This finding is generic, that is, it holds in a broad range of d–p Hamiltonian parameters. As expected, d–p hybridization strongly redistributes electrons and leads to titanium ions between d1 and d2 ionic configurations. Surprisingly, Sr22+false(TiO4 false)2− is not a simpleminded t2g system but instead electron densities are finite and roughly the same in all different 3d orbitals (of t2g and eg symmetry) and the electron densities within O(2p) orbitals are within the range 5.4–5.9. By selecting the charge‐transfer energy, Δ=ϵd−ϵp, we reproduce the experimental band gap of 3.8 eV. We emphasize that a realistic treatment of electronic distribution requires local Coulomb interactions at 2p oxygen orbitals and we show that the Coulomb interactions at titanium ions are strongly renormalized when the Coulomb interactions at oxygen ions are neglected.

d−p model and spin-orbital order in vanadium perovskites

“…The purpose of this paper is to investigate the spinorbital order in vanadium perovskites within the multiband d-p model, i.e., to go beyond the usually used picture of a Mott insulator with S = 1 spins and t 2g orbital degrees of freedom or effective degenerate Hubbard model of t 2g electrons. The d−p model includes non-zero on-site Coulomb interactions defined both on oxygen and on transition metal ions and takes into account the possibility of finite self-doping, explained below and applied before to ruthenium, iridium, and titanium oxides [31][32][33]. The d−p model was developed in these papers into a realistic method, capable of computationally cheap and fast realistic investigation of the electronic structure of complex transition metal oxides.…”

On the Neglect of Local Coulomb Interaction on Oxygens in Perovskites Described by the Multiband d-p Model

“…Any reasonable parameter set leads to nonmagnetic insulator as the ground state. The experimental band gap in Sr 2 TiO 4 is 3.8 eV [27] and it is reproduced when the Hamiltonian parameters are properly tuned to U d = 9.0 eV, J d = 0.8 eV and ∆ 6.5 eV [8].…”

“…We decided to study several possibilities, namely U d = 4, 6, 8, 9, and 10 eV according to the data in the literature [14]: (U d ∈ [7,8] eV) [15][16][17]; (U d ∼ 8 eV); and U d ∼ 6 eV [18,19]). The Hund exchange elements are less screened than intraorbital Coulomb elements and are closer to their atomic values.…”

“…The result is that Sr 2 TiO 4 is a robust non-magnetic insulator. The experimental band gap of 3.8 eV was recovered from the computations for: U d = 9.0 eV, U p = 4.4 eV and charge-transfer gap ∆ = ε d − ε p = 6.5 eV (defined for bare energy levels) [8]. The d-electron count on Ti ion is n d 1.2, almost equally distributed over e g and t 2g orbitals.…”

Spin-orbital order in LaMnO3 : d−p model study

“…The technical implementation is the same as that described in Refs. [6,32,33,38] featuring the averages d † mα,↑ d mα,↑ and p † iµ,↑ p iµ,↑ (in the HF Hamiltonian) which are treated as order parameters. We use the 4 × 4 × 4 clusters which are sufficient for the present d − p model with only nearest neighbor hopping terms.…”