We have studied the phase diagram and excitations of the spin-orbital model derived for a three-dimensional perovskite lattice, as in KCuF 3 . The results demonstrate that the orbital degeneracy drastically increases quantum fluctuations and suppresses the classical long-range order near the multicritical point in the mean-field phase diagram. This indicates the presence of a quantum liquid state, and we present explicit evidence for valence bond type correlations in three dimensions. [S0031-9007(97)02824-X] PACS numbers: 71.27.+a, 75.30.Et It is common knowledge that macroscopic ensembles of interacting particles tend to behave classically. This is not always true, however, and the study of collective quantum systems starts to become a prominent theme in condensed matter physics. Central to this pursuit are low-dimensional quantum spin systems (spin chains and ladders [1]), and it proves difficult to achieve quantum melting of magnetic long-range order (LRO) in empirically relevant systems in higher dimensions. Here we suggest a class of systems in which quantum melting occurs even in three dimensions: small spin, orbital degenerate magnetic insulators, and the so-called KugelKhomskii (KK) systems [2]. There might already exist a physical realization of such a three-dimensional (3D) "quantum spin-orbital liquid": LiNiO 2 .Global SU͑2͒ by itself is not symmetric enough to defeat classical order in D . 1, and the pursuit has been open for some time to engineer more fluctuations into these systems. Three (related) strategies to realize quantum melting have proven to be successful: (i) adding zero-dimensional fluctuations as in the bilayer Heisenberg model which leads to an incompressible spin liquid [3,4], (ii) frustrating the system so that the classical sector gets highly degenerate, as in the case of the S 1͞2 square lattice with longer ranged antiferromagnetic (AF) interactions (J 1 -J 2 -J 3 models [5,6]). These systems involve fine-tuning of parameters and are therefore hard to realize by chemistry. (iii) Finally, the third strategy would be to reduce the number of magnetic bonds, as in the 1͞5-depleted square lattice, where the resulting plaquette resonating valence bond (PRVB) state explains the spin gap observed in CaV 4 O 9 [7]. In this Letter we show that orbital degeneracy operates through the same basic mechanisms to produce quantum melting in the KK systems. The novelty is that these systems tend to "self-tune" to (critical) points of high classical degeneracy. There are interactions which may lift the classical degeneracy, but they are usually weak.An interaction of this kind is the electron-phonon coupling-the degeneracy is lifted by a change in crystal structure, the conventional collective Jahn-Teller (JT) instability. However, as was pointed out in the seminal work by Kugel and Khomskii [2], in orbital degenerate Mott-Hubbard insulators one has to consider in the first instance the purely electronic problem. Because of the large local Coulomb interactions (Hubbard U), a low energy Hilbert spa...

We derive a spin-orbital model for insulating LaMnO3 which fulfills the SU (2) symmetry of S = 2 spins at Mn 3+ ions. It includes the complete eg and t2g superexchange which follows from a realistic Mn 2+ multiplet structure in cubic site symmetry, and the Jahn-Teller induced orbital interactions. We show that the magnetic ordering observed in LaMnO3 is stabilized by a purely electronic mechanism due to the eg-superexchange alone, and provide for the first time a quantitative explanation of the observed transition temperature and the anisotropic exchange interactions.PACS numbers: 71.27.+a, 75.30.Et, 75.70.Pa.The fascinating properties of doped manganites R 1−x A x MnO 3 , where R is a rare earth element, and A is a divalent element, were discovered almost half a century ago [1], but the various phase transitions occurring under doping and in particular the phenomenon of 'colossal magnetoresistance' (CMR) are still not fully understood. The phase diagrams of La 1−x (Ca,Sr) x MnO 3 [2] show a complex interplay between magnetic, charge, and structural order, so that all these ordering phenomena may affect CMR at least indirectly. It is therefore important to obtain first of all a full understanding of the mechanism(s) stabilizing the observed order in the undoped insulating parent compound LaMnO 3 . This will be an essential element in putting together a satisfactory description of the more complicated doped compounds, and recognizing which mechanism(s) other than or in addition to double exchange [3] might be responsible for CMR [4].In this Letter we therefore reconsider the problem of the microscopic origin of the experimentally observed type of antiferromagnetic (AF) order in LaMnO 3 [5], which consists of ferromagnetic (FM) planes ordered antiferromagnetically in the third direction (A-AF phase). As the magnetic order in LaMnO 3 couples to orbital order [6], one possible explanation might be the occurrence of a cooperative Jahn-Teller (JT) effect [7] which induces a particular order of the singly occupied e g orbitals [8]. However, while the JT effect plays a crucial role in charge transport [9], we show here that a purely electronic mechanism drives orbital and magnetic ordering in the manganites near the Mott-Hubbard transition [10].The local Coulomb interaction U is the dominating energy scale in late transition metal oxides. If partly filled orbitals are degenerate, as in KCuF 3 or in LaMnO 3 , this leads to an effective low-energy Hamiltonian, where spin and orbital degrees of freedom are interrelated [8,11]. In the simplest case of d 9 ions in KCuF 3 , such a model describes spins S = 1/2 of e g holes coupled to the discrete orbital variables. Finite Hund's rule exchange J H removes the classical degeneracy of magnetically ordered phases [8,12], and stabilizes the A-AF phase in conjunction with the particular orbital order observed in KCuF 3 . Here we show that a similar state follows from a realistic S = 2 spin-orbital model for the d 4 ions in LaMnO 3 . We include also the t 2g superexchange and the JT...

We investigate the highly frustrated spin and orbital superexchange interactions in cubic vanadates. The fluctuations of t2g orbitals trigger a novel mechanism of ferromagnetic interactions between spins S = 1 of V 3+ ions along one of the cubic directions which operates already in the absence of Hund's rule exchange JH , and leads to the C-type antiferromagnetic phase in LaVO3. The Jahn-Teller effect can stabilize the orbital ordering and the G-type antiferromagnetic phase at low temperatures, but large entropy due to orbital fluctuations favors again the C-phase at higher temperatures, as observed in YVO3.PACS numbers: 75.30. Vn, 71.27.+a, 75.30.Et, Large Coulomb interactions play a crucial role in transition metal oxides, and are responsible for the collective behavior of strongly correlated d electrons which localize in Mott-Hubbard (or charge-transfer) insulators [1]. Such localized electrons may occupy degenerate orbital states which makes it necessary to consider orbital degrees of freedom at equal footing with electron spins, and leads to the effective (superexchange) spin-orbital models to describe the low-energy physics [2][3][4]. A remarkable feature of these models is that the superexchange interaction is highly frustrated on a cubic lattice, which was recognized as the origin of novel quantum effects in transition metal oxides [5]. In case of e g orbital systems this frustration is likely removed by orbital order due to order-out-ofdisorder mechanism, which maximizes the energy gain from quantum spin fluctuations [6]. Moreover, quantum effects among e g orbitals are largely suppressed by the Jahn-Teller (JT) effect in real systems, which together with superexchange often leads to structural phase transitions accompanied by a certain ordering of occupied orbitals, supporting particular magnetic structures. Some well known examples are systems with degenerate e g orbitals filled either by one hole (KCuF 3 ), or by one electron (LaMnO 3 ), which order antiferromagnetically well below the structural transition.The transition metal oxides with partly filled t 2g orbitals exhibit different and more interesting phenomena. This occurs due to the relative weakness of the JT coupling in this case, and due to the higher degeneracy and additional symmetry of t 2g orbitals [7]. As a result, the orbitals may form the coherent orbital-liquid ground state stabilized by quantum effects, as observed in the spin S = 1/2 Mott-insulator LaTiO 3 [8]. It is puzzling what happens when the t 2g orbitals are filled by two electrons, as in vanadium oxides. On one hand, the occupied t 2g orbitals are known to order in non-cubic vanadium compounds, such as LiVO 2 [9] and V 2 O 3 [10]. In fact, the first spin-orbital model for V 2 O 3 with spins s = 1/2 was proposed over twenty years ago [11], but later it was realized that J H at V 3+ (d 2 ) ions is large [12], and the relevant model has to involve S = 1 spins [10]. On the other hand, the situation in cubic systems might be very different as all the bonds are a priori magnetica...