Orbital Ordering and Orbital Fluctuations in Transition Metal Oxides

We summarize some characteristic features of the frustrated magnetic interactions in spin-orbital models adequate for cubic transition metal oxides with orbital degeneracy. A generic tendency towards dimerization, found already in the degenerate Hubbard model, is confirmed for t2g but not for eg systems. In the t2g case the quantum orbital fluctuations are more pronounced and contribute to a stronger competition between different magnetic and orbital states. Therefore the orbital liquid states exist in some undoped t2g systems, while in the manganites such states can be triggered only by doping. Journal reference: A. M. Oleś, Phys. Stat. Sol. (b) 236, 281 (2003). The physical properties of transition metal oxides are dominated by large on-site Coulomb interactions ∝ U which suppress charge fluctuations. Therefore, such systems are either Mott or charge-transfer insulators, and the metallic behavior might occur only as a consequence of doping. Here we will discuss first the undoped systems with localized d electrons which interact by effective superexchange (SE) interactions. An interesting situation occurs when d electrons occupy partly degenerate orbital states, and one has to consider orbital degrees of freedom in the SE at equal footing with electron spins [1]. Competition between different states is then possible, holes may couple to orbital excitations [2], and the quantum effects are enhanced already in undoped systems [3]. The first models of SE in such situations were proposed almost three decades ago [4], either by considering the degenerate Hubbard model [5, 6], or for realistic situations encountered in cuprates (KCuF3 and K2CuF4) and in V2O3 [7]. Then it was realized that the SE which is usually antiferromagnetic (AF) might become ferromagnetic (FM) when Hund’s exchange interaction JH is finite, but only in recent years the phenomena which originate from the orbital physics are investigated in a more systematic way. The SE which involves the orbital degrees of freedom is described by the so-called spinorbital models [8], and is typically highly frustrated on a cubic lattice where it might even lead to the collapse of magnetic long-range order by strong spin or orbital fluctuations [3]. However, in real eg systems such quantum phenomena are usually quenched by finite JH which induces a structural phase transition and thus helps to stabilize a particular ordering of occupied orbitals which supports A-type AF order, as observed when degenerate orbitals are filled either by one hole (KCuF3) [9], or by one electron (LaMnO3) [10]. The coupling to the lattice due to the Jahn-Teller (JT) effect also helps to stabilize the orbital ordering, and quantitative models of the structural transition have to include both these effects [10]. The essential feature of the SE described by spin-orbital models is the frustration of magnetic interactions: the FM terms occur next to the AF ones, and it depends on the physical 1) E-mail: [email protected] phys. stat. sol. – 2 –