Magnetic structure of the Jahn-Teller system LaTiO₃

We investigate the effect of the experimentally observed Jahn-Teller distortion of the oxygen octahedra in LaTiO₃ on the magnetic exchange. We present a localized model for the effective hopping between nearest-neighbor Ti ions and the intrasite Coulomb interactions, based on a nondegenerate orbital ground state due to the static crystal field. The latter corresponds to an orbital order which has recently been confirmed experimentally. Using perturbation theory we calculate, in addition to the Heisenberg coupling, antisymmetric (Dzyaloshinskii-Moriya) and symmetric anisotropy terms of the superexchange spin Hamiltonian, which are caused by the spin-orbit interaction. Employing this spin Hamiltonian, we deduce that at low temperatures the spins have predominantly a G-type antiferromagnetic ordering along the crystallographic a axis, accompanied by a weak ferromagnetic moment along the c axis and by a weak A-type antiferromagnetic moment along the b axis. The first two components are found to be in good agreement with experiment.