Orbital ordering in manganites in the band approach

We consider the orbital ordering in LaMnO₃ and similar systems, proceeding from the band picture. We show that for a realistic magnetic structure of A type there exists a complete nesting between two eg bands. As a result there occurs an instability toward an excitonic insulatorlike state---an electron-hole pairing with the wave vector Q=(π,π), which opens a gap in the spectrum and makes the system insulating. In the resulting state there appears an orbital ordering, the orbital density wave, the type of which coincides with those existing in LaMnO₃.