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Orbital Physics in the Perovskite Ti Oxides
In the perovskite Ti oxide RTiO3 (R=rare-earth ions), the Ti t2g orbitals and
spins in the 3d^1 state couple each other through the strong electron
correlations, resulting in a rich variety of orbital-spin phases. The origin
and nature of orbital-spin states of these Mott insulators have been
intensively studied. In this article, we review the studies on orbital physics
in the perovskite titanates. 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 YTiO3, (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. We
also show that the Ti t2g degeneracy is inherently lifted in the titanates,
which allows the single-band descriptions of the ground-state and low-energy
electronic structures as a good starting point. Our analyses indicate that
these compounds offer touchstone materials described by the single-band Hubbard
model on the cubic lattice. From this insight, we also reanalyze the hole-doped
titanates. Experimentally revealed filling-dependent and bandwidth-dependent
properties and the critical behavior of the metal-insulator transitions are
discussed in the light of theories based on the single-band Hubbard models.Comment: Review article, 26 pages, to appear in New Journal of Physic