Spin dynamics and orbital state in LaTiO3

Evidence of Strong Orbital-Selective Spin-Orbital-Phonon Coupling in CrVO_{4}

Coupling of orbital degree of freedom with a spin exchange, i.e., Kugel-Khomskii-type interaction (KK), governs a host of material properties, including colossal magnetoresistance, enhanced magnetoelectric response, and photoinduced high-temperature magnetism. In general, KK-type interactions lead to deviation in experimental observables of coupled Hamiltonian near or below the magnetic transition. Using diffraction and spectroscopy experiments, here we report anomalous changes in lattice parameters, electronic states, spin dynamics, and phonons at four times the Néel transition temperature (T_{N}) in CrVO_{4}. The temperature is significantly higher than other d-orbital compounds such as manganites and vanadates, where effects are limited to near or below T_{N}. The experimental observations are rationalized using first-principles and Green's function-based phonon and spin simulations that show unprecedentedly strong KK-type interactions via a superexchange process and an orbital-selective spin-phonon coupling coefficient at least double the magnitude previously reported for strongly coupled spin-phonon systems. Our results present an opportunity to explore the effect of KK-type interactions and spin-phonon coupling well above T_{N} and possibly bring various properties closer to application, for example, strong room-temperature magnetoelectric coupling.

Two-Dimensional Superconductivity at the Titanium Sesquioxide Heterointerface

The study of exotic superconductivity in two dimensions has been a central theme in the solid state and materials research communities. Experimentally exploring and identifying exotic, fascinating interface superconductors with a high transition temperature (T_c) are challenging. Here, we report an experimental observation of intriguing two-dimensional superconductivity with a T_c of up to 3.8 K at the interface between a Mott insulator Ti₂O₃ and polar semiconductor GaN. At the verge of superconductivity, we also observe a striking quantum metallic-like state, demonstrating that it is a precursor to the two-dimensional superconductivity as the temperature is decreased. Our work shows an exciting opportunity to exploit the underlying, emergent quantum phenomena at the heterointerfaces via heterostructure engineering.

Orbital Order Melting at Reduced Dimensions

The orbital degree of freedom, strongly coupled with the lattice and spin, is an important factor when designing correlated functions. Whether the long-range orbital order is stable at reduced dimensions and, if not, what the critical thickness is remains a tantalizing question. Here, we report the melting of orbital ordering, observed by controlling the dimensionality of the canonical e_g¹ orbital system LaMnO₃. Epitaxial films are synthesized with vertically aligned orbital ordering planes on an orthorhombic substrate, so that reducing film thickness changes the two-dimensional planes into quasi-one-dimensional nanostrips. The orbital order appears to be suppressed below the critical thickness of about six unit cells by changing the characteristic phonon modes and making the Mn d orbital more isotropic. Density functional calculations reveal that the electronic energy instability induced by bandwidth narrowing via the dimensional crossover and the interfacial effect causes the absence of orbital order in the ultrathin thickness.

Orbital Isotropy of Magnetic Fluctuations in Correlated Electron Materials Induced by Hund's Exchange Coupling

Characterizing nonlocal magnetic fluctuations in materials with strong electronic Coulomb interactions remains one of the major outstanding challenges of modern condensed matter theory. In this Letter, we address the spatial symmetry and orbital structure of magnetic fluctuations in perovskite materials. To this aim, we develop a consistent multiorbital diagrammatic extension of dynamical mean-field theory, which we apply to an anisotropic three-orbital model of cubic t_{2g} symmetry. We find that the form of spatial spin fluctuations is governed by the local Hund's coupling. For small values of the coupling, magnetic fluctuations are anisotropic in orbital space, which reflects the symmetry of the considered t_{2g} model. Large Hund's coupling enhances collective spin excitations, which mixes orbital and spatial degrees of freedom, and magnetic fluctuations become orbitally isotropic. Remarkably, this effect can be seen only in two-particle quantities; single-particle observables remain anisotropic for any value of the Hund's coupling. Importantly, we find that the orbital isotropy can be induced both at half filling and for the case of four electrons per lattice site, where the magnetic instability is associated with different, antiferromagnetic and ferromagnetic, modes, respectively.

Density Functional Theory Calculations of Structural, Electronic, and Magnetic Properties of the 3d Metal Trifluorides MF3 (M = Ti-Ni) in the Solid State

We employ density functional theory with Hubbard U correction or hybrid functionals to study the series of magnetic 3d metal trifluorides MF₃ (M = Ti-Ni). Experimental lattice parameters are reproduced with an error margin of 0.5%-4.3%. Cooperative Jahn-Teller distortions are reproduced for MnF₃ , but also found in TiF₃ and CoF₃ at smaller levels compared to MnF₃ . Trends in electronic structure with respect to positions of the d bands are linked to the magnetic properties where M = Ti-Cr are weak magnetic Mott-Hubbard insulators, M = Fe-Ni are strong magnetic charge-transfer insulators and MnF₃ falls in between. Our work contributes to the characterization of the relatively unknown NiF₃ , since FeF₃ and CoF₃ have similar electronic and magnetic properties. However, NiF₃ does not show a Jahn-Teller distortion as present in CoF₃ . © 2019 Wiley Periodicals, Inc.

Floquet Engineering of Multiorbital Mott Insulators: Applications to Orthorhombic Titanates

We consider driving multiorbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory in the strong interaction limit. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonian are highly tunable via variations of the frequency, amplitude, and polarization of the laser. We also take the effect of a finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO_{3} and LaTiO_{3} based on first-principles calculations, and we find that the spin exchange interactions in these compounds can be engineered to a large extent by tuning the frequency and electric-field amplitude of the laser.

Identification of ground-state spin ordering in antiferromagnetic transition metal oxides using the Ising model and a genetic algorithm

We identify ground-state collinear spin ordering in various antiferromagnetic transition metal oxides by constructing the Ising model from first-principles results and applying a genetic algorithm to find its minimum energy state. The present method can correctly reproduce the ground state of well-known antiferromagnetic oxides such as NiO, Fe₂O₃, Cr₂O₃ and MnO₂. Furthermore, we identify the ground-state spin ordering in more complicated materials such as Mn₃O₄ and CoCr₂O₄.

Investigation of the multiplet structures and crystal field effects of a TiO6 3d 1 cluster based on configuration interaction calculations

Configuration interaction cluster calculation can effectively reproduce the experimentally measured Ti L 23-edge absorption spectrum for the TiO6 cluster LaTiO3. A further investigation of the hybridization strength and charge-transfer energy effects on the multiplet structures suggests that LaTiO3 should be classified as an intermediate state between the charge-transfer and Mott–Hubbard regimes. Detailed temperature-dependent simulations of absorption spectra support the lifting of Ti t 2g orbital degeneracy and crystal field splitting. The spin–orbit coupling scenario is ruled out, even though 3d spin–orbit coupling can reproduce the experimental spectrum without including temperature. A combined polarization- and crystal-field-splitting-dependent analysis indicates asymmetric ΔCF–orbital interactions for the TiO6 cluster [Ti3+:3d 1(t 2g 1)], different from the orbital–lattice interactions reported for the NiO6 cluster [Ni3+:3d 7(t 2g 6 eg 1)]. The orbital polarization is defined in terms of the normalized electron occupancies in orbitals with xy and xz(yz) symmetries, and nearly complete orbital polarization (more than 75%) is observed, indicating strongly reduced orbital fluctuations due to the correlation effects. This is consistent with the density of states for titanates based on local density approximation plus dynamical mean-field theory calculations.

Dielectric characteristics of Fe-doped LaTiO3+δ and visible light modulation

Fe-doped La_1−xFe_xTiO_3+δ (x = 0.05, 0.1, and 0.3, 0.4) ceramic samples were prepared via traditional solid-state reaction route, in which the dielectric properties of visible light modulation were found at room temperature in the measured frequency range.

Spin-Orbital Excitation Continuum and Anomalous Electron-Phonon Interaction in the Mott Insulator LaTiO_{3}

Raman scattering experiments on stoichiometric, Mott-insulating LaTiO_{3} over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of ~800 cm^{-1} upon cooling below the Néel temperature T_{N}=146 K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for T>T_{N}, but become sharp and symmetric for T<T_{N}. The electronic continuum and the marked renormalization of the phonon lifetime by the onset of magnetic order are highly unusual for Mott insulators and indicate liquidlike correlations between spins and orbitals.

Phototunable magnetism in copper octacyanomolybdate

We introduce copper molybdenum cyanides of general formula Cu₂[Mo(CN)₈]·nH₂O, which can serve as optofunctional magnetic devices. Their ground states generally stay paramagnetic down to temperatures of the K order but exhibit a spontaneous magnetization upon photoirradiation usually below a few tens of K. To interest us still further, such a ferromagnetic stateinduced by blue-laser irradiation is demagnetized step by step through further application of red or near-infrared laser pulses. We solve this intriguing photomagnetism. The ground-state properties are fully revealed by means of a group-theoretical technique. Taking account of experimental observations, we simulate applying pump laser pulses to a likely ground state and successfully reproduce both the magnetization and demagnetization dynamics. We monitor the photorelaxation process through angle-resolved photoemission spectroscopy. Electrons are fully itinerant in any of the photoinduced steady states, forming a striking contrast to the initial equilibrium state of atomic aspect. The fully demagnetized final steady state looks completely different from the initial paramagnetism but bears good analogy to one of the possible ground states available with the Coulomb repulsion on Cu sites suppressed.

Two-dimensional confinement of 3d{1} electrons in LaTiO_{3}/LaAlO{3} multilayers

We report spectroscopic ellipsometry measurements of the anisotropy of the interband transitions parallel and perpendicular to the planes of (LaTiO3)n(LaAlO3)5 multilayers with n=1-3. These provide direct information about the electronic structure of the two-dimensional (2D) 3d{1} state of the Ti ions. In combination with local density approximation, including a Hubbard U calculation, we suggest that 2D confinement in the TiO2 slabs lifts the degeneracy of the t{2g} states leaving only the planar d{xy} orbitals occupied. We outline that these multilayers can serve as a model system for the study of the t{2g} 2D Hubbard model.

Momentum dependence of orbital excitations in Mott-insulating titanates

High-resolution resonant inelastic x-ray scattering has been used to determine the momentum dependence of orbital excitations in Mott-insulating LaTiO(3) and YTiO(3) over a wide range of the Brillouin zone. The data are compared to calculations in the framework of lattice-driven and superexchange-driven orbital ordering models. A superexchange model in which the experimentally observed modes are attributed to two-orbiton excitations yields the best description of the data.

Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models

We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr2IrO4.

High-spin magnetic states in the two-orbital Hubbard model on a tetrahedron

We present a study of the two-orbital degenerate Hubbard model in which the exact numerical solution on a regular tetrahedron is obtained via suitable implementation of the symmetries generated by the spin, the pairing and the orbital pseudospin operators. In particular, we show that a large variety of high-spin magnetic ground states can develop away from half filling, depending on the values of the electron density and the parameters of the model. As the tetrahedron is the simplest finite-size cluster where hopping processes connect all pairs of sites with constant probability, the study is extended by providing the exact analytical solution of the model on an infinite lattice in the unconstrained hopping limit.

Muon spin relaxation study of LaTiO(3) and YTiO(3)

We report muon spin relaxation (μSR) measurements on two Ti(3+) containing perovskites, LaTiO(3) and YTiO(3), which display long-range magnetic order at low temperature. For both materials, oscillations in the time dependence of the muon polarization are observed which are consistent with three-dimensional magnetic order. From our data we identify two magnetically inequivalent muon stopping sites. The μSR results are compared with the magnetic structures of these compounds previously derived from neutron diffraction and μSR studies on structurally similar compounds.

Transition from orbital liquid to Jahn-Teller insulator in orthorhombic perovskites RTiO3

Following the same strategy used for RVO3, thermal conductivity measurements have been made on a series of single-crystal perovskites RTiO3 (R=La,Nd,...,Yb). Results reveal explicitly a transition from an orbital liquid to an orbitally ordered phase at a magnetic transition temperature, which is common for both the antiferromagnetic and ferromagnetic phases in the phase diagram of RTiO3. This spin/orbital transition is consistent with the mode softening at T_{N} in antiferromagnetic LaTiO3 and is supported by an anomalous critical behavior at T_{c} in ferromagnetic YTiO3.

Absence of hole confinement in transition-metal oxides with orbital degeneracy

We investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t(2g) electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry. The orbital model describes also propagation of a hole in some e(g) compounds, and we argue that orbital degeneracy alone does not lead to hole self-localization.

Doping variation of orbitally induced anisotropy in the electronic structure of La1-xSrxVO3

The variation of anisotropic charge dynamics in the course of a filling-control insulator-metal transition (IMT) in La(1-x)Sr(x)VO3 has been investigated by measurements of optical conductivity spectra with the focus on the role of the t(2g)-orbital degree of freedom. The orbitally induced anisotropic feature of the Mott-gap excitation as well as of the doping-induced midinfrared excitation is suppressed with increasing x, and instead the isotropic and incoherent dynamics of the doped hole dominates over the low-energy excitation near and above the IMT point.

Raman scattering in the Mott insulators LaTiO3 and YTiO3: evidence for orbital excitations

Raman scattering is used to observe pronounced electronic excitations around 230 meV--well above the two-phonon range--in the Mott insulators LaTiO3 and YTiO3. Based on the temperature, polarization, and photon energy dependence, the modes are identified as orbital excitations. The observed profiles bear a striking resemblance to magnetic Raman modes in the insulating parent compounds of the superconducting cuprates, indicating an unanticipated universality of the electronic excitations in transition metal oxides.

Spin-orbital entanglement and violation of the Goodenough-Kanamori rules

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.

One-dimensional orbital excitations in vanadium oxides

The d electron orbital is a hidden but important degree of freedom controlling novel properties of transition-metal oxides. A one-dimensional orbital system is especially intriguing due to its enhanced quantum fluctuation. We present a combined experimental and theoretical study on the Raman scattering spectra in perovskite oxides NdVO(3) and LaVO(3) to prove that the quasi-one-dimensional orbital chain described by fermionic pseudospinons bears orbital excitations exchanging occupied orbital states on the neighboring sites, termed a two-orbiton in analogy with two-magnon.

Determination of the orbital moment and crystal-field splitting in LaTiO3

Utilizing a sum rule in a spin-resolved photoelectron spectroscopic experiment with circularly polarized light, we show that the orbital moment in LaTiO3 is strongly reduced from its ionic value, both below and above the Ne el temperature. Using Ti L2,3 x-ray absorption spectroscopy as a local probe, we found that the crystal-field splitting in the t2g subshell is about 0.12-0.30 eV. This large splitting does not facilitate the formation of an orbital liquid.

Directional ordering of fluctuations in a two-dimensional compass model

In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in orbital space and in real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.

Quantum versus Jahn-Teller orbital physics in YVO3 and LaVO3

We argue that the large Jahn-Teller (JT) distortions in YVO3 and LaVO3 should suppress the quantum orbital fluctuation. The unusual magnetic properties can be well explained based on local density approximation + Hubbard U calculations using experimental structures, in terms of the JT orbital. The observed splitting of the spin-wave dispersions for YVO3 in a C-type antiferromagnetic state is attributed to the inequivalent VO2 layers in the crystal structure, instead of the "orbital-Peierls state." Alternative stacking of ab-plane exchange couplings produces the c-axis spin-wave splitting; thus, the spin system is highly three dimensional rather than quasi-one-dimensional. Similar splitting is also predicted for LaVO3, although it is weak.

Mott transition and suppression of orbital fluctuations in orthorhombic 3d1 perovskites

Using t(2g) Wannier functions, a low-energy Hamiltonian is derived for orthorhombic 3d(1) transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO3-type distortions) is found to suppress orbital fluctuations in LaTiO3 and even more in YTiO3, and to favor the transition to the insulating state.

Spin and orbital frustration in MnSc2S4 and FeSc2S4

Crystal structure, magnetic susceptibility, and specific heat were measured in the normal cubic spinel compounds MnSc2S4 and FeSc2S4. Down to the lowest temperatures, both compounds remain cubic and reveal strong magnetic frustration. Specifically the Fe compound is characterized by a Curie-Weiss (CW) temperature ThetaCW = -45 K and does not show any indications of order down to 50 mK. In addition, the Jahn-Teller ion Fe2+ is orbitally frustrated. Hence, FeSc2S4 belongs to the rare class of spin-orbital liquids. MnSc2S4 is a spin liquid for temperatures T>TN approximately 2 K.

Optical-spectroscopic detection of spin-exchange interaction pyrochlore molybdates

Optical spectroscopy was used to determine nearest-neighbor spin correlations in pyrochlore molybdates R2Mo2O7 (R=Y, Sm, and Nd), which exhibit ferromagnetic metal to spin-glass insulator transition as the R ion size decreases. Using an analysis based on the orbitally degenerate Hubbard model, we could estimate important physical parameters, such as the effective on-site Coulomb energy U(eff) and the Hund rule exchange coupling J(H). We demonstrated experimentally and theoretically that the effective superexchange interaction between the Mo ions depends on J(H)/U(eff), which determines the phase boundary of the magnetic ground states.

Dimerization versus orbital-moment ordering in a Mott insulator YVO3

We use exact diagonalization combined with mean-field theory to investigate the phase diagram of the spin-orbital model for cubic vanadates. The spin-orbit coupling competes with Hund's exchange and triggers a novel phase, with the ordering of t(2g) orbital magnetic moments stabilized by the tilting of VO6 octahedra. It explains qualitatively spin canting and reduction of magnetization observed in YVO3. At finite temperature, an orbital instability in the C-type antiferromagnetic phase induces modulation of magnetic exchange constants even in the absence of lattice distortions. The calculated spin structure factor shows a magnon splitting at q-->=(0,0,pi / 2) due to the orbital dimerization.

Orbital-spin structure and lattice coupling in RTiO3 where R=La, Pr, Nd, and Sm

The origin of the G-type antiferromagnetism [AFM(G)] and puzzling properties of RTiO3 with R=La are studied. We clarify that the crystal field from La caused by the GdFeO3-type distortion lifts the t(2g) degeneracy at Ti 3d orbitals. The lift stabilizes the AFM(G) with spin-exchange constant in agreement with neutron-scattering results. The orbital-spin structures for R=Pr, Nd, and Sm are also consistent with experiments. We propose that the GdFeO3-type distortion has a universal mechanism of controlling orbital-spin structure competing with the Jahn-Teller (JT) mechanism.

Presence of 3d quadrupole moment in LaTiO3 studied by 47,49Ti NMR

47,49Ti NMR spectra of LaTiO3 are reexamined and the orbital state of this compound is discussed. The NMR spectra of LaTiO3 taken at 1.5 K under zero external field indicate a large nuclear quadrupole splitting. This splitting is ascribed to the presence of the rather large quadrupole moment of 3d electrons at Ti sites, suggesting that the orbital liquid model proposed for LaTiO3 is inappropriate. The NMR spectra are well explained by the orbital ordering model expressed approximately as 1/square root of 3(d(xy)+d(yz)+d(zx)) originating from a crystal field effect. It is also shown that most of the orbital moment is quenched.

Unusual symmetries in the Kugel-Khomskii Hamiltonian

The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between d(1) ions having threefold degenerate t(2g) orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to the orbital planes, the total number of electrons in |alpha> orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.

Evidence for Jahn-Teller distortions at the antiferromagnetic transition in LaTiO3

LaTiO3 is known as a Mott insulator which orders antiferromagnetically at T(N)=146 K. We report on results of thermal expansion and temperature dependent x-ray diffraction together with measurements of the heat capacity, electrical transport measurements, and optical spectroscopy in untwinned single crystals. At T(N) significant structural changes appear, which are volume conserving. Concomitant anomalies are also observed in the dc resistivity, in bulk modulus, and optical reflectivity spectra. We interpret these experimental observations as evidence of orbital order.

Quantum behavior of orbitals in ferromagnetic titanates: novel orderings and excitations

We investigate the collective behavior of orbital angular momentum in the spin ferromagnetic state of a Mott insulator with t(2g) orbital degeneracy. The frustrated nature of the interactions leads to an infinite degeneracy of classical states. Quantum effects select four distinct orbital orderings. Two of them have a quadrupolar order, while the other states show in addition weak orbital magnetism. Specific predictions are made for neutron scattering experiments which might help to identify the orbital order in YTiO3 and to detect the elementary orbital excitations.

Magnetic order and dynamics in an orbitally degenerate ferromagnetic insulator

Neutron scattering was used to determine the spin structure and the magnon spectrum of the Mott-Hubbard insulator YTiO3. The magnetic structure is complex, comprising substantial G-type and A-type antiferromagnetic components in addition to the predominant ferromagnetic component. The magnon spectrum, on the other hand, is gapless and nearly isotropic. We show that these findings are inconsistent with the orbitally ordered states thus far proposed for YTiO3 and discuss general implications for a theoretical description of exchange interactions in orbitally degenerate systems.

Pressure-induced quenching of the Jahn-Teller distortion and insulator-to-metal transition in LaMnO(3)

LaMnO(3) was studied by synchrotron x-ray diffraction, optical spectroscopies, and transport measurements under pressures up to 40 GPa. The cooperative Jahn-Teller (JT) distortion is continuously reduced with increasing pressure. There is strong indication that the JT effect and the concomitant orbital order are completely suppressed above 18 GPa. The system, however, retains its insulating state to approximately 32 GPa, where it undergoes a bandwidth-driven insulator-metal transition. Delocalization of electron states, which suppresses the JT effect but is insufficient to make the system metallic, appears to be a key feature of LaMnO(3) at 20-30 GPa.

Spin order due to orbital fluctuations: cubic vanadates

We investigate the highly frustrated spin and orbital superexchange interactions in cubic vanadates. The fluctuations of t(2g) orbitals trigger a novel mechanism of ferromagnetic interactions between spins S = 1 of V3+ ions along one of the cubic directions which operates already in the absence of Hund's rule exchange J(H), 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 YVO (3).

Orbital liquid in three-dimensional mott insulator: LaTiO3

We present a theory of spin and orbital states in Mott insulator LaTiO3. The spin-orbital superexchange interaction between d(1)(t(2g)) ions in cubic crystal suffers from a pathological degeneracy of orbital states at the classical level. Quantum effects remove this degeneracy and result in the formation of the coherent ground state, in which the orbital moment of t(2g) level is fully quenched. We find a finite gap for orbital excitations. Such a disordered state of local degrees of freedom on unfrustrated, simple cubic lattice is highly unusual. Orbital liquid state naturally explains observed anomalies of LaTiO3.