# Jahn-Teller transition in TiF_{3} investigated using density-functional theory

## Abstract

We use first-principles density-functional theory to calculate the electronic and magnetic properties of TiF3 using the full-potential-linearized augmented-plane-wave method. The local density approximation (LDA) predicts a fully saturated ferromagnetic metal and finds degenerate energy minima for high- and low-symmetry structures. The experimentally observed Jahn-Teller phase transition at Tc=370K cannot be driven by the electron-phonon interaction alone, which is usually described accurately by the LDA. Electron correlations beyond the LDA are essential to lift the degeneracy of the singly occupied Ti t2g orbital. Although the on-site Coulomb correlations are important, the direction of the t2g-level splitting is determined by dipole-dipole interactions. The LDA+U functional predicts an aniferromagnetic insulator with an orbitally ordered ground state. The input parameters U=8.1eV and J=0.9eV for the Ti 3d orbital were found by varying the total charge on the TiF62− ion using the molecular NRLMOL code. We estimate the Heisenberg exchange constant for spin 1/2 on a cubic lattice to be approximately 24 K. The symmetry lowering energy in LDA+U is about 900 K per TiF3 formula unit. © 2004 The American Physical Society.