First-principles and Group-theoretical Analysis of the Magnetic Order in the Rare Earth Titanates

The low-temperature magnetic order in the rare earth titanate perovskites (RTiO3) transitions from ferromagnetic (FM) to antiferromagnetic (G-AFM) as the rare earth atom varies from Y to La. The nature of this transition, and in particular how this transition is intertwined with the structural distortions (which vary as a function of rare earth ion size) is unclear. We present a combined first-principles, group theoretical, and phenomenological analysis to elucidate the nature of the magnetic phases in strained (biaxial and uniaxial) and doped compounds. We discuss the competition between multiple magnetic phases and the sensitive dependence on the exchange anisotropies, as investigated using a next-nearest neighbor Heisenberg model fitted to first-principles calculations. We further present a general phenomenological theory based on a group theoretical analysis of the octahedral rotations, which couple different magnetic orders, and discuss its implication on the nature of the FM-AFM transition.