  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 intra-site Coulomb interactions, based on a non-degenerate orbital
ground state due to the static crystal field. The latter corresponds to an
orbital order which recently has been confirmed experimentally. Using
perturbation theory we calculate, in addition to the Heisenberg coupling,
antisymmetric and symmetric anisotropy terms of the superexchange spin
Hamiltonian which are caused by the spin-orbit interaction. Employing our
superexchange Hamiltonian, we deduce the magnetic order at low temperatures
which is found to be in good agreement with experiment.
