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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...

The temperature dependence and anisotropy of optical spectral weights associated with different multiplet transitions is determined by the spin and orbital correlations. To provide a systematic basis to exploit this close relationship between magnetism and optical spectra, we present and analyze the spin-orbital superexchange models for a series of representative orbital-degenerate transition metal oxides with different multiplet structure. For each case we derive the magnetic exchange constants, which determine the spin wave dispersions, as well as the partial optical sum rules. The magnetic and optical properties of early transition metal oxides with degenerate t 2g orbitals ͑titanates and vanadates with perovskite structure͒ are shown to depend only on two parameters, viz. the superexchange energy J and the ratio of Hund's exchange to the intraorbital Coulomb interaction, and on the actual orbital state. In e g systems important corrections follow from charge transfer excitations, and we show that KCuF 3 can be classified as a charge transfer insulator, while LaMnO 3 is a Mott insulator with moderate charge transfer contributions. In some cases orbital fluctuations are quenched and decoupling of spin and orbital degrees of freedom with static orbital order gives satisfactory results for the optical weights. On the example of cubic vanadates we describe a case where the full quantum spin-orbital physics must be considered. Thus information on optical excitations, their energies, temperature dependence, and anisotropy, combined with the results of magnetic neutron scattering experiments, provides an important consistency test of the spin-orbital models, and indicates whether orbital and/or spin fluctuations are important in a given compound. I. SUPEREXCHANGE AND OPTICAL EXCITATIONS AT ORBITAL DEGENERACYThe physical properties of Mott ͑or charge transfer͒ insulators are dominated by large on-site Coulomb interactions ϰU which suppress charge fluctuations. Quite generally, the Coulomb interactions lead then to strong electron correlations which frequently involve orbitally degenerate states, such as 3d ͑or 4d͒ states in transition metal compounds, and are responsible for quite complex behavior with often puzzling transport and magnetic properties. 1 The theoretical understanding of this class of compounds, with the colossal magnetoresistance ͑CMR͒ manganites as a prominent example, 2,3 has substantially advanced over the last decade, 4 after it became clear that orbital degrees of freedom play a crucial role in these materials and have to be treated on equal footing with the electron spins, which has led to a rapidly developing field, orbital physics. 5 Due to the strong onsite Coulomb repulsion, charge fluctuations in the undoped parent compounds are almost entirely suppressed, and an adequate description of these strongly correlated insulators appears possible in terms of superexchange. 6 At orbital degeneracy the superexchange interactions have a rather rich structure, represented by the so-called spin-orbita...

The forward scattering f functions of the exact one-dimensional Landau theory are evaluated for the case of the Hubbard chain. The static charge and spin susceptibilities of the interacting system at arbitrary magnetic fields are derived as in a Fermi liquid. The connection to conformal Geld theory is studied in detail. All the critical exponents associated with the asymptotic behavior of the correlation functions are fully determined by the pseudoparticle interactions.

We point out that large composite spin-orbital fluctuations in Mott insulators with t(2g) orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules.

We consider a model of strongly correlated eg electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO3. It is found that the classical orbital order with alternating occupied eg orbitals has a full rotational symmetry at orbital degeneracy, and the excitation spectrum derived using the linear spin-wave theory is gapless. The quantum (fluctuation) corrections to the order parameter and to the ground state energy restore the cubic symmetry of the model. By applying a uniaxial pressure orbital degeneracy is lifted in a tetragonal field and one finds an orbital-flop phase with a gap in the excitation spectrum. In two dimensions the classical order is more robust near the orbital degeneracy point and quantum effects are suppressed. The orbital excitation spectra obtained using finite temperature diagonalization of two-dimensional clusters consist of a quasiparticle accompanied by satellite structures. The orbital waves found within the linear spin-wave theory provide an excellent description of the dominant pole of these spectra.

Introducing partial sum rules for the optical multiplet transitions, we outline a unified approach to magnetic and optical properties of strongly correlated transition metal oxides. On the example of LaVO3 we demonstrate how the temperature and polarization dependences of different components of the optical multiplet are determined by the underlying spin and orbital correlations dictated by the low-energy superexchange Hamiltonian. Thereby the optical data provides deep insight into the complex spin-orbital physics and the role played by orbital fluctuations.

The matrix elements of the up-spin and down-spin electronic density fluctuations taken between the ground state and the gapless elementary excitations of the Hubbard chain in a magnetic field are obtained. The small-ft> charge and spin conductivity spectra are derived. Our results clarify the physical character of the pseudoparticles of the new Landau liquid theory, and identify them as the transport carriers. A generalized adiabatic continuity principle concerning the elementary excitations at finite magnetic field in the limit where momentum and frequency tend to zero is established.