Spin-wave spectrum of the Jahn-Teller system LaTiO₃

We present an analytical calculation of the spin-wave spectrum of the Jahn-Teller system LaTiO₃. The calculation includes all superexchange couplings between nearest-neighbor Ti ions allowed by the space-group symmetries: The isotropic Heisenberg couplings and the antisymmetric (Dzyaloshinskii-Moriya) and symmetric anisotropies. The calculated spin-wave dispersion has four branches, two nearly degenerate branches with small zone-center gaps and two practically indistinguishable high-energy branches having large zone-center gaps. The two lower-energy modes are found to be in satisfying agreement with neutron-scattering experiments. In particular, the experimentally detected approximate isotropy in the Brillouin zone and the small zone-center gap are well reproduced by the calculations. The higher-energy branches have not been detected yet by neutron scattering but their zone-center gaps are in satisfying agreement with recent Raman data.