Charge order and spin-singlet pair formation in Ti4O7

Charge ordering in the low-temperature triclinic structure of titanium oxide (Ti4O7) is investigated using the local density approximation (LDA) + U method. Although the total 3d charge separation is rather small, an orbital order parameter defined as the difference between t(2g) occupancies of Ti3+ and Ti4+ cations is large and gives direct evidence for charge ordering. Strong covalency of O 2p-Ti 3d sigma-type bonds, which results in partial occupation of Ti e(g) states, leads to almost complete loss of the disproportionation between the charges at 3+ and 4+ Ti sites. The occupied t(2g) states of Ti3+ cations are predominantly of d(xy) character and form a spin-singlet molecular orbital via strong direct antiferromagnetic exchange coupling between neighbouring Ti(1) and Ti(3) sites, whereas the role of superexchange is found to be negligible.