We have performed density-functional calculations on the ${\text{Ti}}_4{\text{O}}_7$ Magnéli phase. Our results provided a consistent description of the high-temperature $\left(T\ge 298\text{K}\right)$ phase, the intermediate-temperature $\left(120\text{K}\le T\le 140\text{K}\right)$ phase, and the low-temperature $\left(T\le 120\text{K}\right)$ phase. The established model for the electronic structure of the low- and intermediate-temperature phases of ${\text{Ti}}_4{\text{O}}_7$ states that ${\text{Ti}}^{3+}{\text{-Ti}}^{3+}$ pairs, bonded through nonmagnetic metal-metal bonds, form ordered bipolarons in the low-temperature phase, and that these bipolarons exist but are disordered in the intermediate-temperature phase. In this work we propose a different picture for the ${\text{Ti}}_4{\text{O}}_7$ low- and intermediate-temperature electronic structure. We argue that, in the low-temperature phase, a combination of a strong on-site Coulomb repulsion and electron-phonon coupling results in the localization of unpaired electrons in the ${\text{Ti}}^{3+}$ ions forming the pairs. The electrons are accommodated in specific ${\text{t}}_{2g}$-like orbitals for two reasons: to minimize the direct Coulomb repulsion, and to minimize the indirect interaction that results from lattice distortion. The localized electrons are antiferromagnetically coupled, producing bipolarons with zero spin. This orbital ordering results in the widening of the gap between the fully occupied and unoccupied levels. This is a bipolaronic state, but there is no bond in between the ${\text{Ti}}^{3+}$ forming the pairs. In the intermediate phase, a subset of the bipolarons dissociate but the electrons remain strongly localized: this state consists of a mixture of polarons and bipolarons placed in a superstructure with long-range order. This model provides a consistent explanation of the observed electric and magnetic properties of ${\text{Ti}}_4{\text{O}}_7$.

• Received 21 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.245133