G-type antiferromagnetism and orbital ordering due to the crystal field from the rare-earth ions induced by the GdFeO ₃-type distortion in RTiO ₃ where R = La, Pr, Nd and Sm

The origin of the antiferromagnetic order and puzzling properties of LaTiO ₃ as well as the magnetic phase diagram of the perovskite titanates are studied theoretically. We show that in LaTiO ₃, the t _2g degeneracy is eventually lifted by the La cations in the GdFeO ₃-type structure, which generates a crystal field. This allows the description of the low-energy structure of LaTiO ₃ by a single-band Hubbard model as a good starting point. The lowest-orbital occupation in this crystal field stabilizes the AFM(G) state, and well explains the spin-wave spectrum of LaTiO ₃ obtained by the neutron scattering experiment. The orbital-spin structures for RTiO ₃ where R = Pr, Nd and Sm are also accounted for by the same mechanism. We point out that through generating the R crystal field, the GdFeO ₃-type distortion has a universal relevance in determining the orbital-spin structure of the perovskite compounds in competition with the Jahn-Teller mechanism, which has been overlooked in the literature. Since the GdFeO ₃-type distortion is a universal phenomenon as is seen in a large number of perovskite compounds, this mechanism may also play important roles in other compounds of this type.