Correlated Electrons, Phase Transitions and Frustrated Magnetism in TiF₃

Transition metal trifluorides are known to exhibit fascinating physical properties such as the negative thermal expansion observed in ScF₃ and several coupled structural and magnetic phase transitions. In this work, we focus on the electronic and magnetic properties of TiF₃ (Ti carrying an extra valence d-electron compared to Sc) which is reported to have strongly correlated d electrons. At low temperature, TiF₃ has a rhombohedral structure while above 370 K, it has the cubic perovskite structure AMX₃ with no cation A present.

It has been reported (PRB 69, 115102 (2004)) that the local density approximation (LDA) predicts a fully saturated ferromagnetic metal for TiF₃ with degenerate energy minima for high- and low-symmetry structures. LDA+U and introduction of a large U (=8 eV) led to a prediction of an antiferromagnetic insulator with moments of the order of 0.5 μ_B. We have examined the above statements carefully with larger unit cells and allowing for atomic relaxations with non-collinear magnetism which were not included in the above work. Our VASP calculations with GGA+U for a unit cell of Ti₆F₁₈ give rise to mixed internal magnetic orders with different (Ti) moments at smaller U (=3 eV) values. Such U values are directly responsible for opening a gap at the Fermi level and the resulting insulating behavior. In addition, Monte Carlo studies were carried out in order to examine the magnetic phase transitions at low temperature which reveal a competition between an anti-ferromagnetic and a ferromagnetic order with a potential spin-liquid phase at the phase boundary.