Peierls-like distortion drives anion ordering in rutile TiOF

Using first principles density functional theory calculations, we examine the effect of multiple anions on the Peierls distortion in rutile compounds with the oxyfluoride TiOF. We use a structure enumeration approach and obtain the ground state for TiOF and identify the driving force behind the experimentally observed two-dimensional chemical ordering along rutile (110) planes. We find that the anion bridge connecting adjacent edge-shared octahedra comprises like atoms with an –O-O/F-F/O-O/F-F– pattern along the rutile [001] direction and a Peierls-like distortion leading to the formation of a singlet state. This anion ordering arising from the competition between electrostatic interactions from the Ti-F cation-anion pairs and the tendency of the d¹ Ti³⁺ cation to form a metallic Ti-Ti dimer. We find that the addition of strong on-site Coulombic interactions suppresses the formation of the singlet state. By increasing the correlation strength, we uncover two first-order phase transitions: first, from a nonmagnetic insulator to a ferromagnetic half-metal, and then second to a ferromagnetic Mott insulator. Our work shows that anion ordering in oxyfluorides can be driven by cation-cation interactions, enabling design of ordered heteroanionic materials exhibiting collective phenomena through cation sublattice control.