Orbital ordering transition in Ca2RuO4 observed with resonant X-ray diffraction

Resonant x-ray diffraction performed at the L(II) and L(III) absorption edges of Ru has been used to investigate the magnetic and orbital ordering in Ca2RuO4 single crystals. A large resonant enhancement due to electric dipole 2p-->4d transitions is observed at the wave-vector characteristic of antiferromagnetic ordering. Besides the previously known antiferromagnetic phase transition at T(N)=110 K, an additional phase transition, between two paramagnetic phases, is observed around 260 K. Based on the polarization and azimuthal angle dependence of the diffraction signal, this transition can be attributed to orbital ordering of the Ru t(2g) electrons. The propagation vector of the orbital order is inconsistent with some theoretical predictions for the orbital state of Ca2RuO4.     

X‐ray absorption spectroscopy analysis of Ru in La2RuO5

The compound La₂RuO₅ was examined by the x‐ray absorption spectroscopy (XAS) methods, x‐ray absorption near edge structure (XANES) and extended x‐ray absorption fine structure (EXAFS). XANES technique was used to probe directly the average valence of Ru atoms in the compound. The energy shift of the Ru K‐edge in the XANES signal gave the average Ru valence state as 4.0 ± 0.1. EXAFS analysis provided, by yielding directly the interatomic distances and coordination numbers, the first information on the Ru atom neighborhood, on which the model for the Rietveld refinement of the unit cell of the new compound was devised. Finally, the local structure around the Ru atoms from the refinement was used in the FEFF6 code for a model EXAFS spectrum. The very good quantitative agreement with the measured spectrum proves that the refined crystal structure contains no systematic defects in the vicinity of Ru atoms. This result, together with the valence obtained from XANES, strongly confirms the proposed La₂RuO₅ stoichiometry. Copyright © 2007 John Wiley & Sons, Ltd.     

Orbital ordering, new phases, and stripe formation in doped layered nickelates

Ground-state properties of layered nickelates are investigated based on the orbital-degenerate Hubbard model coupled with lattice distortions, by using numerical techniques. The Néel state composed of spin S=1 ions is confirmed in the undoped limit x = 0. At x = 1/2, novel antiferromagnetic states, called CE- and E-type phases, are found by increasing the Hund's coupling. (3x2-r2/3y2-r2)-type orbital ordering is predicted to occur in a checkerboard-type charge-ordered state. At x = 1/3, both Coulombic and phononic interactions are found to be important, since the former stabilizes the spin stripe, while the latter leads to the striped charge order.     

Orbital ordering in CuGeO3

The combined effect of the ligand crystal field and the exchange interaction on the Cu²⁺ cation in CuGeO₃ is examined. It is shown that, if the magnitude of the exchange interaction exceeds the splitting of the energy levels of the and d _xy orbitals, then an alternate filling of the d orbitals along a chain (orbital ordering) is possible. This effect creates an antiferromagnetic interaction between Cu²⁺ pairs in 90° exchange and a doubling of the lattice period. A Jahn-Teller pseudoeffect causes singletization of the ground state of the antiferromagnetic chain of Cu²⁺ spins. Fiz. Tverd. Tela (St. Petersburg) 40, 1686–1692 (September 1998)     

Orbital dependence of the fermi liquid state in Sr2RuO4

We have used angle-resolved photoemission spectroscopy to determine the bulk electronic structure of Sr(2)RuO(4) above and below the Fermi liquid crossover near 25 K. Our measurements indicate that the properties of the system are highly orbital dependent. The quasi-2D gamma band displays Fermi liquid behavior while the remaining low energy bands show exotic properties consistent with quasi-1D behavior. In the Fermi liquid state below 25 K, the gamma band dominates the electronic properties, while at higher temperatures the quasi-1D beta and alpha bands become more important.     

Orbital ordering and magnetic field effect in MnV2O4

We studied the structural properties of an orbital-spin-coupled spinel oxide, MnV2O4, mainly by single-crystal x-ray diffraction measurement. It was found that a structural phase transition from cubic to tetragonal and ferrimagnetic ordering occur at the same temperature (Ts,TN=57 K). The structural phase transition was induced also by magnetic field above Ts. In addition, magnetic-field-induced alignment of tetragonal domains results in large magnetostriction below Ts. We also found that the structural phase transition is caused by the antiferro-type ordering of the V t2g orbitals.     

Orbital ordering in La0.5Sr1.5MnO4 studied by soft X-ray linear dichroism

We found that the conventional model of orbital-ordering of 3x(2)-r(2)/3y(2)-r(2) type in the e(g) states of La0.5Sr1.5MnO4 is incompatible with measurements of linear dichroism in the Mn 2p-edge x-ray absorption, whereas these e(g) states exhibit predominantly cross-type orbital ordering of x(2)-z(2)/y(2)-z(2). LDA+U band-structure calculations reveal that such a cross-type orbital-ordering results from a combined effect of antiferromagnetic structure, Jahn-Teller distortion, and on-site Coulomb interactions.     

Orbital ordering in charge transfer insulators

We discuss a new mechanism of orbital ordering, which in charge transfer insulators is more important than the usual exchange interactions and which can make the very type of the ground state of a charge transfer insulator, i.e., its orbital and magnetic ordering, different from that of a Mott-Hubbard insulator. This purely electronic mechanism allows us to explain why orbitals in Jahn-Teller materials typically order at higher temperatures than spins, and to understand the type of orbital ordering in a number of materials, e.g., K2CuF4, without invoking the electron-lattice interaction.     

Change of electronic structure in Ca2RuO4 induced by orbital ordering

Optical conductivity spectra sigma(omega) were used to investigate the effect of orbital ordering on the electronic structure of Ca2RuO4. Our LDA+U calculation predicts Ru 4d(xy) ferro-orbital ordering at the ground state, and well explains the present sigma(omega) as well as the reported O 1s x-ray absorption spectra. Variation of temperature (T) causes a large change of spectral weight over several eV as well as collapse of a charge gap accompanied by elongation of the c-axis Ru-O bond length. These results clearly indicate that the d(xy) orbital ordering plays a crucial role in the metal-insulator transition and the T-dependent electronic structure on a large energy scale.     

Charge ordering and polaron formation in the magnetoresistive oxide La0.7Ca0.3MnO3

Neutron scattering has been used to study the nature of the ferromagnetic transition in a single crystal of the perovskite La0. 7Ca0.3MnO3. Diffuse scattering from lattice polarons develops as the Curie temperature is approached from below, along with short range polaron correlations that are consistent with stripe formation. Both the scattering due to the polaron correlations and the anomalous quasielastic component in the magnetic fluctuation spectrum maximize very close to T(C), in a manner remarkably similar to the resistivity, indicating that they have a common origin.     

Orbital ordering and frustration of p-band Mott insulators

We investigate the general structure of orbital exchange physics in Mott-insulating states of p-orbital systems in optical lattices. Orbital orders occur in both the triangular and kagome lattices. In contrast, orbital exchange in the honeycomb lattice is frustrated as described by a novel quantum 120 degrees model. Its classical ground states are mapped into configurations of the fully packed loop model with an extra U(1) rotation degree of freedom. Quantum orbital fluctuations select a six-site plaquette ground state ordering pattern in the semiclassical limit from the "order from disorder" mechanism. This effect arises from the appearance of a zero energy flat band of orbital excitations.     

Magnetic ordering in (La,Gd) Al2 alloys

The detailed dependence of the magnetic ordering temperature θ on Gd concentration n below ～ 15 at.% Gd substitution for La is reported for the system ($\text{La}$Gd) Al₂. In this concentration range, the θ vs.n curve lies markedly below the extrapolation of the linear behavior previously observed for concentrations ? 20 at.% Gd, and apparantely goes to zero at a finite concentration. The effective moment of Gd is enhanced by 1 μ_B over the free ion value.     

Orbital ordering and Jahn-Teller distortion in Perovskite ruthenate SrRuO3

Local density approximation plus on-site Coulomb interaction U band structure calculations reveal that SrRuO3 exhibits a half-metallic ground state with an integer spin moment of 2.0 microB/SrRuO3. An associated tilting 4dt2g orbital ordering on a Ru sublattice is observed under the on-site Coulomb interaction U in the presence of lattice distortion. This finding unravels the on-site Coulomb correlation as the driving force of the 4d orbital ordering and Jahn-Teller distortion as well as of the half-metallic ground state.     

Orbital ordering and fluctuations in a kagome superconductor CsV3Sb5

Recently,competing electronic instabilities,including superconductivity and density-wave-like order,have been discovered in vanadium-based kagome metals AV₃Sb₅(A=K,Rb,Cs)with a nontrivial band topology.This finding stimulates considerable interest to study the interplay of these competing electronic orders and possible exotic excitations in the superconducting state.Here,we performed51V and133Cs nuclear magnetic resonance(NMR)measurements on a CsV₃Sb₅single crystal to clarify the nature of density-wave-like transition in these kagome superconductors.A first-order structural transition is unambiguously revealed below T_s~94 K by observing the sudden splitting of Knight shift in⁵¹V NMR spectrum.Moreover,combined with¹³³Cs NMR spectrum,the present result confirms a three-dimensional structural modulation.By further analyzing the anisotropy of Knight shift and 1/T₁T at⁵¹V nuclei,we proposed that the orbital order is the primary electronic order induced by the firstorder structural transition,which is supported by further analysis on electric field gradient at⁵¹V nuclei.In addition,the evidence for possible orbital fluctuations is also revealed above T_s.The present work sheds light on a rich orbital physics in kagome superconductors AV₃Sb₅.     

Magnetic ordering in Fe-doped Gd2BaCuO5

The structural and magnetic properties of iron-doped Gd₂BaCuO₅ have been studied by X-ray diffractometry, Mössbauer spectroscopy and susceptibility measurements. Mössbauer data on Gd₂BaCu_0.8Fe_0.2O₅ show that at room temperature Fe is not magnetically ordered, displaying hyperfine parameters similar to those generally assigned to Fe at Cu(2) sites in the GdBa₂(Cu_1–x Fe _x )₃O₇ superconductor. Susceptibility measurements demonstrate that Gd₂BaCu_1–x Fe _x O₅ behaves like a three-dimensional antiferromagnet withT _N=11.9±0.1 K, independent ofx. The effective magnetic moment calculated within a mean field approximation is consistent with an ordering of the Gd sublattice.     

Weak ferromagnetism and oxygen ordering in La2CuO4+x single crystals

The changes produced in the magnetic properties and structure of La₂CuO_4+x (0< x<0.015) single crystals by doping with oxygen are investigated by differential magnetic susceptibility and x-ray diffraction methods. It is found that the appearance of a weak ferromagnetism in weak fields H<50 Oe is accompanied by a lowering of lattice symmetry as a result of the oxygen ordering. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 159–162 (10 August 1997)     

Orbital ordering in frustrated Jahn-Teller systems with 90 degrees exchange

We show that superexchange interactions in frustrated Jahn-Teller systems with transition metal ions connected by the 90 degrees metal-oxygen-metal bonds (e.g., NaNiO2, LiNiO2, and ZnMn2O4) are much different from those in materials with the 180 degrees bonds. In the 90 degrees -exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Though the mean-field orbital ground state is strongly degenerate, quantum orbital fluctuations select particular ferro-orbital states. We explain the orbital and magnetic ordering observed in NaNiO2 and show that LiNiO2 is not a spin-orbital liquid.     

Orbital ordering in LaMnO3 : electron-electron versus electron-lattice interactions

The relative importance of electron-lattice (e-l) and electron-electron (e-e) interactions in ordering orbitals in LaMnO3 is systematically examined within the local-density approximation + Hubbard U approximation of density functional theory. A realistic effective Hamiltonian is derived from novel Wannier state analysis of the electronic structure. Surprisingly, e-l interaction (approximately or = 0.9 eV) alone is found insufficient to stabilize the orbital ordered state. On the other hand, e-e interaction (approximately or = 1.7 eV) not only induces orbital ordering, but also greatly facilitates the Jahn-Teller distortion via enhanced localization. Further experimental means to quantify the competition between these two mechanisms are proposed.     

Orbital ordering in LaMnO3 investigated by resonance Raman spectroscopy

Orbital ordering leads to an unconventional excitation spectrum that we investigate by resonance Raman scattering using incident photon energies between 1.7 and 5.0 eV. We use spectral ellipsometry to determine the corresponding dielectric function. Our results show resonant behavior of the phonon Raman cross section when the laser frequency is close to the orbiton-excitation energy of 2 eV in LaMnO3. We show an excellent agreement between theoretical calculations based on the Franck-Condon mechanism activating multiphonon Raman scattering in first order of the electron-phonon coupling and the experimental data of phonons with different symmetries.