Spin and Orbital States and Their Phase Transitions of the Perovskite-Type Ti Oxides: Weak Coupling Approach

The magnetic phase diagram of the perovskite-type Ti oxides as a function of the GdFeO₃-type distortion is examined by using the Hartree-Fock analysis of a multiband d-p Hamiltonian from a viewpoint of competitions of the spin-orbit interaction, the Jahn-Teller (JT) level-splitting and spin-orbital superexchange interactions. Near the antiferromagnetic (AFM)-to-ferromagnetic (FM) phase boundary, A-type AFM [AFM(A)] and FM states accompanied by a certain type of orbital ordering are lowered in energy at large JT distortion, which is in agreement with the previous strong coupling study. With increasing the GdFeO₃-type distortion, their phase transition occurs. Through this magnetic phase transition, the orbital state hardly changes, which induces nearly continuous change in the spin coupling along the c-axis from negative to positive. The strong suppression of T_N and T_C, which is experimentally observed is attributed to the resulting strong two-dimensionality in the spin coupling near the phase boundary. On the other hand, at small GdFeO₃-type without JT distortions, which correspond to LaTiO₃, the most stable solution is not G-type AFM [AFM(G)] but FM. Although the spin-orbit interaction has been considered to be relevant at the small or no JT distortion of LaTiO₃ in the literature, our analysis indicates that the spin-orbit interaction is irrelevant to the AFM(G) state in LaTiO₃ and superexchange-type interaction dominates. On the basis of further investigations on the nature of this FM state and other solutions, this discrepancy is discussed in detail.