Charge order and spin-singlet pairs formation in Ti4O7

TL;DR

This study investigates charge ordering in Ti4O7 using LDA+U calculations, revealing orbital order and spin-singlet pairing of Ti$^{3+}$ ions, with significant screening effects and negligible superexchange.

Contribution

It provides new insights into charge and orbital order, as well as spin-singlet formation, in Ti4O7, highlighting the role of screening and direct exchange over superexchange.

Findings

Orbital order parameter indicates charge ordering despite small charge separation.

Ti 4s and 4p states contribute to charge screening, eliminating charge disproportionation.

Ti$^{3+}$ ions form spin-singlet pairs via direct antiferromagnetic exchange.

Abstract

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 t2g occupancies of Ti$^{3+}$ and Ti$^{4+}$ cations is large and gives direct evidence for charge ordering. Ti 4s and 4p states make a large contribution to the static "screening" of the total 3d charge difference. This effective charge screening leads to complete loss of the disproportionation between the charges at 3+ and 4+ Ti sites. The occupied t2g states of Ti$^{3+}$ cations are predominantly of $d_{xy}$ character and form a spin-singlet molecular orbital via strong direct antiferromagnetic exchange coupling between neighboring Ti(1) and Ti(3) sites, whereas the role of superexchange is found to be negligible.