Titanate compounds have been recognized as key materials for understanding the coupling of magnetism and orbitals in strongly correlated electron systems. In the perovskite Ti oxide RTiO3 (where R represents the trivalent rare-earth ions), which is a typical Mott-Hubbard insulator, the Ti t 2g orbitals and spins in the 3d1 state couple each other through the strong electron correlations, resulting in a rich variety of orbital-spin phases. One way of controlling the coupling is to change the tiltings of the TiO6 octahedra (namely the GdFeO3-type distortion) by varying the R ions, through which the relative ratio of the electron bandwidth to the Coulomb interaction is controlled. With this control, these Mott insulators exhibit an antiferromagnetic-to-ferromagnetic (AFM-FM) phase transition, which has turned out to be a consequence of rich orbital physics in these materials. The origin and nature of orbital-spin structures of these Mott insulators have been intensively studied both experimentally and theoretically. When the Mott insulators are doped with carriers, the titanates show touchstone properties of the filling controlled Mott transition. In this paper, we first review the state of the art on the studies for understanding physics contained in the properties of the perovskite titanates. On the properties of the insulators, we focus on the following three topics: (1) the origin and nature of the ferromagnetism as well as the orbital ordering in the compounds with relatively small R ions such as GdTiO3 and YTiO 3, (2) the origin of the G-type antiferromagnetism and the orbital state in LaTiO3 and (3) the orbital-spin structures in other AFM(G) compounds with relatively large R ions (R = Ce, Pr, Nd and Sm). On the basis of these discussions, we discuss the whole phase diagram together with mechanisms of the magnetic phase transition. On the basis of the microscopic (understanding of the orbital-spin states, we show that the Ti t2g degeneracy is inherently lifted in the titanates, which allows the single-band descriptions of the ground-state and the low-energy electronic structures as a good starting point. Our analyses indicate that these compounds offer good touchstone materials described by the single-band Hubbard model on the cubic lattice. From this insight, we also re-analyse the hole-doped titanates R1-xA xTiO3 (where A represents the divalent alkaline-earth ions). Experimentally revealed filling- and bandwidth-dependent properties and the critical behaviour of the metal-insulator transitions are discussed in the light of theories based on the single-band Hubbard models.
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