Origin of G-type antiferromagnetism and orbital-spin structures in LaTiO₃

The possibility of the D_3d distortion of TiO₆ octahedra is examined theoretically in order to understand the origin of the G-type antiferromagnetism [AFM(G)] and experimentally observed puzzling properties of LaTiO₃. By utilizing an effective spin and pseudospin Hamiltonian with the strong Coulomb repulsion, it is shown that the AFM(G) state is stabilized through the lift of the t_2g-orbital degeneracy accompanied by a tiny D_3d-distortion. The estimated spin-exchange interaction is in agreement with that obtained by the neutron-scattering experiment. Moreover, the level-splitting energy due to the distortion can be considerably larger than the spin-orbit interaction even when the distortion becomes smaller than the detectable limit under the available experimental resolution. This suggests that the orbital momentum is fully quenched and the relativistic spin-orbit interaction is not effective in this system, in agreement with the result of a recent neutron-scattering experiment.