The effective Hamiltonian for perovskite titanates is derived by taking into account the threefold degeneracy of t2g orbitals and the strong electron-electron interactions. The magnetic and orbital ordered phases are studied in the mean-field approximation applied to the effective Hamiltonian. A large degeneracy of the orbital states in the ferromagnetic phase is found in contrast to the case of the doubly degenerate eg orbitals. Lifting of this orbital degeneracy due to lattice distortions and spin-orbit coupling is examined. A general form for the scattering cross section of the resonant x-ray scattering is derived and is applied to the recent experimental results in YTiO₃. The spin wave dispersion relation in the orbital ordered YTiO₃ is also studied.
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Ishihara et al. (2002) studied this question.
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