Orbital Order and Orbital Excitations in Degenerate Itinerant Electron Systems

We present a theory of orbital ordering in orbital-degenerate itinerant electron systems. The orbital instability in a two-orbital degenerate Hubbard model is investigated in the random phase approximation （RPA）. After demonstrating the criteria for the formation of orbital ordering or the orbital density wave ordering, we find that the orbital and the spin-orbital collective excitation spectra in the ferro-orbital ordered phase exhibit finite gaps. The possible application of the present theory in orbital-ordered 4d compounds is also discussed.     

Evidence for electronic phase separation between orbital orderings in SmVO3

We report evidence for phase coexistence of orbital orderings of different symmetry in SmVO3 by high resolution x-ray powder diffraction. The phase coexistence is triggered by an antiferromagnetic ordering of the vanadium spins near 130 K, below an initial orbital ordering near 200 K. The phase coexistence is the result of the intermediate ionic size of samarium coupled to exchange striction at the vanadium spin ordering.     

Tuning charge and orbital ordering in DyNiO3 by biaxial strain

The first-principles calculations were used to explore the tunable electronic structure in DyNiO₃ (DNO) under the effects of the biaxial compressive and tensile strains. We explored how the biaxial strain tunes the orbital hybridization and influences the charge and orbital ordering states. We found that breathing mode and Jahn-Teller distortion play a primary role in charge ordering state and orbital ordering state, respectively. Additionally, the calculated results revealed that the biaxial strain has the ability to manipulate the phase competition between the two states. A phase transition point has been found under tensile train. If the biaxial train is larger than the point, the system favors orbital ordering state. If the strain is smaller than the point, the system is in charge ordering state favorably.     

Magnetic order driven by orbital ordering in the semiconducting KFe1.5Se2

The two-orbital Hubbard model is studied numerically by using the Hartree-Fock approximation in both real space and momentum space, and the ground-state properties of the alkali metal iron selenide semiconducting KFe_1.5Se₂ are investigated. A rhombus-type Fe vacancy order with stripetype antiferromagnetic (AFM) order is found, as was observed in neutron scattering experiments [J. Zhao, et al., Phys. Rev. Lett. 109, 267003 (2012)]. Hopping parameters are obtained by fitting the experimentally observed stripe AFM phase in real space. These hopping parameters are then used to study the ground-state properties of the semiconductor in momentum space. It is found to be a strongly correlated system with a large on-site Coulomb repulsion U, similar to the AFM Mott insulator — the parent compound of copper oxide superconductors. We also find that the electronic occupation numbers and magnetizations in the d_xz and d_yz orbitals become different simultaneously when U>U_c (～3.4 eV), indicating orbital ordering. These results imply that the rotational symmetry between the two orbitals is broken by orbital ordering and thus drives the strong anisotropy of the magnetic coupling that has been observed by experiments and that the stripe-type AFM order in this compound may be caused by orbital ordering together with the observed large anisotropy.     

Orbital ordering in e(g) orbital systems: ground states and thermodynamics of the 120° model

Orbital degrees of freedom shape many of the properties of a wide class of Mott insulating, transition metal oxides with partially filled 3d shells. Here we study orbital ordering transitions in systems where a single electron occupies the e(g) orbital doublet and the spatially highly anisotropic orbital interactions can be captured by an orbital-only model, often called the 120° model. Our analysis of both the classical and quantum limits of this model in an extended parameter space shows that the 120° model is in close proximity to several T=0 phase transitions and various competing ordered phases. We characterize the orbital order of these nearby phases and their associated thermal phase transitions by extensive numerical simulations and perturbative arguments.     

Successive orbital ordering transitions in NaVO2

Physical property measurements on samples of triangular-lattice NaVO2 reveal two successive orbital ordering transitions. At 300 K, the structure is rhombohedral. At 98 K, the system undergoes a second-order transition to a monoclinic phase in which the in-plane V-V distances separate into four short and two long bonds, corresponding to orbital ordering of one electron per V3+. Below 93 K, there is a first-order transition to a second monoclinic phase with four long and two short V-V bonds, consistent with orbital ordering of two electrons per V3+. Long range magnetic ordering of 0.98(2)mu_(B) per V3+ (3d(2)) sets in at the 93 K structural transition. The orbital ordering relieves the geometric frustration and leads to a magnetically ordered ground state.     

Correlations induced orbital ordering and cooperative Jahn–Teller distortion in the paramagnetic insulator KCrF<Subscript>3</Subscript>

We investigate the origin of the orbital ordering in the paramagnetic phase of KCrF₃. All previous studies described structural parameters of the paramagnetic phase using a magnetic ordering in the compound. Our simulations of real paramagnetic KCrF₃ were performed within an approach combining density functional theory and dynamical mean field theory (DFT+DMFT). As a result, it was found that the experimentally observed cooperative Jahn–Teller effect is successfully described in a lattice relaxation calculation for structure without any long-range magnetic ordering. It is established that the existence of the orbital ordering even in undistorted perovskite structure clearly confirms the electronic origin of the orbital ordering in KCrF₃.     

Microstrain sensitivity of orbital and electronic phase separation in SrCrO3

An orbital ordering transition and electronic phase coexistence have been discovered in SrCrO3. This cubic, orbitally-degenerate perovskite transforms to a tetragonal phase with partial orbital order. The tetragonal phase is antiferromagnetic below 35-40 K, whereas the cubic phase remains paramagnetic at low temperatures. The orbital ordering temperature (35-70 K) and coexistence of the two electronic phases are very sensitive to lattice strain. X-ray measurements show a preferential conversion of the most strained regions in the cubic phase. This reveals that small fluctuations in microstrain are sufficient to drive long range separation of competing electronic phases even in undoped cubic oxides.     

Effect of short-range order on electronic and magnetic properties of disordered Co-based alloys

We here study electronic structure and magnetic properties of disordered CoPd and CoPt alloys using augmented space recursion technique coupled with the tight-binding linearized muffin tin orbital (TB-LMTO) method. Effect of short-range ordering present in disordered phase of alloys on electronic and magnetic properties has been discussed. We present results for magnetic moments, Curie temperatures and electronic band energies with varying degrees of short-range order for different concentrations of Co and try to understand and compare the magnetic properties and ordering phenomena in these systems.     

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.     

Direct observation of orbital ordering in La0.5Sr1.5MnO4 using soft x-ray diffraction

We report the first direct resonant soft x-ray scattering observations of orbital ordering. We have studied the low temperature phase of La0.5Sr1.5MnO4, a compound that displays charge and orbital ordering. Previous claims of orbital ordering in such materials have relied on observations at the manganese K edge. These claims have been questioned in several theoretical studies. Instead we have employed resonant soft x-ray scattering at the manganese L(III) and L(II) edges which probes the orbital ordering directly. Energy scans at constant wave vector are compared to theoretical predictions and suggest that at all temperatures there are two separate contributions to the scattering: direct orbital ordering and strong cooperative Jahn-Teller distortions of the Mn3+ ions.     

Spin, charge, and orbital orderings in iron-based superconductors

In this article, we briefly review spin, charge, and orbital orderings in iron-based superconductors, as well as the multi-orbital models. The interplay of spin, charge, and orbital orderings is a key to understand the high temperature superconductivity. As an illustration, we use the two-orbital model to show the spin and charge orderings in iron-based superconductors based on the mean-field approximation in real space. The typical spin and charge orderings are shown by choosing appropriate parameters, which are in good agreement with experiments. We also show the effect of Fe vacancies, which can introduce the nematic phase and interesting magnetic ground states. The orbital ordering is also discussed in iron-based superconductors. It is found that disorder may play a role to produce the superconductivity.     

On the possible mechanism of structural transition in cuprates

A possible mechanism of tetragonal to orthorhombic transition in high-T_c cuprates based on the removal of orbital degeneracy of p states in the CuO₂ cell by electron lattice interaction is proposed. Spontaneous distortion creates a finite energy gap or a pseudogap in the density of states depending on the relative strength of the next-near and nearest neighbour hopping strengths. The gap is a function of electron density and vanishes beyond the structural transition temperature. The growth of the gap leads to a metal semiconductor transition as temperature decreases with attendant stripe and orbital ordering. The phase diagram for the distorted phase is examined in detail in the parameter space.     

Dilution effects in two-dimensional quantum orbital systems

Interacting orbital degrees of freedom in a Mott insulator are essentially directional and frustrated. In this Letter, the effect of dilution in a quantum-orbital system with this kind of interaction is studied by analyzing a minimal orbital model which we call the two-dimensional quantum compass model. We find that the decrease of the ordering temperature due to dilution is stronger than that in spin models, but it is also much weaker than that of the classical model. The difference between the classical and the quantum-orbital systems arises from the enhancement of the effective dimensionality due to quantum fluctuations.     

Neutron powder diffraction investigation on the crystal and magnetic structure of (Ho(0.50+x)Ca(0.50-x))(Mn(1-x)Cr(x))O3

The crystal and magnetic structure of (Ho(0.50+x)Ca(0.50-x))(Mn(1-x)Cr(x))O(3) (x = 0.00, 0.01, 0.02, 0.03) has been investigated between 5 and 300 K by means of neutron powder diffraction followed by Rietveld refinement and dc magnetic measurements. During cooling an orthorhombic to monoclinic phase transition occurs on account of the charge and orbital ordering taking place in the Mn sub-lattice; at low temperature phase separation takes place and the main monoclinic phase coexists with a secondary orthorhombic phase, whose amount slightly increases with the increase of Cr content. Cr(3+) is not involved in orbital ordering or superexchange interactions. The charge and magnetic ordering are decoupled: the Mn moments order according to a CE-type structure in all samples.     

轨道序对半掺杂锰氧化物光学性质的影响

在两轨道双交换模型基础上，讨论了电子关联作用对半掺杂锰氧化物轨道序的影响，推导出能计算各个相的光电导公式.结果显示，光吸收与轨道序之间存在关联现象.对于铁磁相，当格点库仑相互作用(U)从无到有逐渐增加时，铁磁相会从无轨道序过渡到有轨道序，相变前 后非相干光吸收有一个从无能隙到有能隙的明显变化.对于层状反铁磁的A相，U的增加会使 轨道序更明显，非相干光吸收部分的能隙随之也增大. 关键词： 轨道序 光电导 锰氧化物 库仑相互作用     

Surface Verwey transition in magnetite

We report density functional studies of the (001) surface of magnetite that account for local Coulomb interactions. Iron cations in the surface layers exhibit charge and t2g orbital ordering that is coupled with the lattice strains. Orbital ordering is present for various surface stoichiometries and causes opening of the band gap Eg approximately 0.3 eV at the surface, such that the (001) surface of Fe3O4 remains insulating also in the high temperature cubic phase. The (radical 2 x radical 2)R45 degrees surface reconstruction is related to orbital ordering.     

Novel orbital ordering induced by anisotropic stress in a manganite thin film

A novel structure of orbital ordering is found in a Nd0.5Sr0.5MnO3 thin film, which exhibits a clear first-order transition, by synchrotron x-ray diffraction measurements. Lattice parameters vary drastically at the metal-insulator transition at 170 K (= T(MI)), and superlattice reflections appear below 140 K (= T(CO)). The electronic structure between T(MI) and T(CO) is identified as A-type antiferromagnetic with a d(x2-y2) ferro-orbital ordering. The new type of antiferro-orbital ordering characterized by the wave vector (1/4 1/4 1/2) in cubic notation emerges below T(CO). The accommodation of the large lattice distortion at the first-order phase transition and the appearance of the novel orbital ordering are brought about by the anisotropy in the substrate, a new parameter for the phase control.     

Study of the ferrodistorsive orbital ordering in NaNiO2 by neutron diffraction and submillimeter wave ESR

NaNiO₂ has been studied by neutron-powder diffraction, magnetic susceptibility and submillimeter wave ESR. The monoclinic structure at room temperature is characterised by a ferrodistorsive orbital ordering due to the Jahn-Teller (JT) effect of the Ni³⁺ ions in the low spin state. NaNiO₂ undergoes a structural transition at around 480 K, above which the orbital ordering disappears. The high temperature phase is rhombohedral with the layered -NaFeO₂ structure ( space group). The magnetic susceptibility exhibits hysteresis and we observe a change of the Curie-Weiss law parameters above the JT transition. The anisotropy of the g-factor at 200 K can be attributed to the JT effect which favours the orbital occupation. Finally, the interplay between the magnetic and structural properties of NaNiO₂ and Li_1-xNi_1+xO₂ is discussed. Received 29 May 2000     

A model for phase separation in systems with orbital ordering

The possibility of phase separation in the substances with orbital ordering is analyzed. The additional charge carriers introduced due to doping favor the formation of nanosize inhomogeneities with the orbital structure different from that in the undoped material. The shapes and sizes of such inhomogeneities are determined.