Anomalous temperature dependence of the magnetic field induced antiferromagnetic moment in the antiferroquadrupolar ordered state of CeB6

The magnetic field induced antiferromagnetic moment M(AF) at low magnetic fields in the antiferroquadrupolar (AFQ) ordered phase of CeB6 was investigated by elastic neutron diffraction experiments for H parallel [110]. The peak intensity at the AF magnetic reciprocal point (1 / 2,1 / 2,1 / 2) corresponding to M(2)(AF) increases with decreasing temperature below the AFQ ordering temperature T(Q), and exhibits a broad maximum at T approximately 3 K and decreases with a further decrease of temperature. This unusual behavior of M(AF) at low fields is explained as a result of the competition between the AF-octupolar and AF-exchange interactions in the O(xy) type AFQ ordered state.     

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.     

Analysis of hyperfine interactions in NMR studies of Pr skutterudites

The splitting of NMR signal, which is analyzed in terms of the invariant hyperfine coupling between the nuclear spin and the multipolar moments of magnetic ions, gives important information about the multipolar ordering. The NMR splitting of P nuclei is analyzed for the low-temperature phase of PrFe₄P₁₂, whose nature has been controversial. Two scenarios are examined: one is a modulation of the hyperfine coupling caused by the antiferro-quadrupole (AFQ) ordering; another is the hyperfine coupling due to a monopole-type ordering.     

Magnetic anisotropy of the antiferroquadrupole phase in Ce0.50La0.50B6

Magnetic phase diagrams for antiferroquadrupole (AFQ) phase II and antiferromagnetic (AFM) phase III in Ce0.50La0.50B6 with a Gamma(8) ground state have been investigated by ultrasonic measurements. The hybrid magnet (Gama) in the National Institute for Materials Science was employed for high-field measurements up to 30 T and a 3He-4He dilution refrigerator was used for low-temperature experiments down to 20 mK. The phase boundary from paramagnetic phase I to AFQ phase II under [001] magnetic fields closes at H(I-II) approximately 29 T, while the boundary is still open under fields along the [110] and [111] directions even up to 30 T. This anisotropic character of phase II in fields is consistent with the theoretical calculation based on the O(xy)-type AFQ ordering. We also found that AFM phase III reduces considerably in fields turning from the [001] to [110] and [111] directions.     

Spin exciton formation inside the hidden order phase of CeB6

The heavy fermion metal CeB(6) exhibits a hidden order of the antiferroquadrupolar (AFQ) type below T(Q)=3.2 K and a subsequent antiferromagnetic (AFM) order at T(N)=2.3 K. It was interpreted as an ordering of the quadrupole and dipole moments of a Γ(8) quartet of localized Ce 4f(1) electrons. This established picture has been profoundly shaken by recent inelastic neutron scattering (G. Friemel et al., arXiv:1111.4151) that found the evolution of a feedback spin exciton resonance within the hidden order phase at the AFQ wave vector which is stabilized by the AFM order. We develop an alternative theory based on a fourfold degenerate Anderson lattice model, including both order parameters as particle-hole condensates of itinerant heavy quasiparticles. This explains in a natural way the appearance of the spin exciton resonance and the momentum dependence of its spectral weight, in particular, around the AFQ vector and its rapid disappearance in the disordered phase. Analogies to the feedback effect in unconventional heavy fermion superconductors are pointed out.     

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.     

Direct observation of t2g orbital ordering in magnetite

Using soft-x-ray diffraction at the site-specific resonances in the Fe L2,3 edge, we find clear evidence for orbital and charge ordering in magnetite below the Verwey transition. The spectra show directly that the (001/2) diffraction peak (in cubic notation) is caused by t2g orbital ordering at octahedral Fe2+ sites and the (001) by a spatial modulation of the t2g occupation.     

Nonmagnetic ground states and phase transitions in the caged compounds PrT2Zn20 (T = Ru, Rh and Ir)

We performed electrical resistivity ρ, magnetic susceptibility χ, specific heat C and electron diffraction measurements on single-crystalline samples of PrT2Zn20 (T = Ru, Rh and Ir). The three compounds show the Van Vleck paramagnetic behavior, indicating the nonmagnetic crystalline electric field (CEF) ground states. A Schottky-type peak appears at around 14 K, irrespective of the T element, which can be moderately reproduced by a doublet–triplet model. For T = Ru, a structural transition occurs at Ts = 138 K, below which no phase transition appears down to 0.04 K. On the other hand, for T = Ir, antiferroquadrupole (AFQ) ordering arising from the nonmagnetic Γ3 doublet takes place at TQ = 0.11 K. For T = Rh, despite a structural transition between 170 and 470 K, the CEF ground state is still the non-Kramers Γ3 doublet. However, no phase transition due to the Γ3 doublet was observed even down to 0.1 K.     

Orbital ordering and spin-ladder formation in La2RuO5

The semiconductor-semiconductor transition of La2RuO5 is studied by means of augmented spherical wave electronic structure calculations as based on density-functional theory and the local density approximation. This transition has lately been reported to lead to orbital ordering and a quenching of the local spin magnetic moment. Our results hint towards an orbital ordering scenario which, markedly different from the previously proposed scheme, preserves the local S=1 moment at the Ru sites in the low-temperature phase. The unusual magnetic behavior is interpreted by the formation of spin ladders, which result from the structural changes occurring at the transition and are characterized by antiferromagnetic coupling along the rungs.     

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.     

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.     

Investigation of outer valence orbital of CF2Cl2 by a new type of electron momentum spectrometer

Electronic states of CF2Cl2 （dichlorodifluoromethane, Freon 12） have been studied using a new type of electron momentum spectrometer with a very high efficiency at an impact energy of 1200 eV plus binding energy. The experimental electron momentum profiles are compared with the density functional theory （DFT） and Hartree-Fock （HF） calculations. The relationship between orbital assignments in different coordinate systems is discussed. A new method of difference analysis based on the new type of electron momentum spectrometer is used to clarify the ambiguities regarding the orbital ordering.     

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     

Orbital ordering in Mott-insulators La2O3Fe2Se2 and La2O3Co2Se2

The electronic structure and magnetic properties of new layered oxyselenide compounds La₂O₃Fe₂Se₂ and La₂O₃Co₂Se₂ are studied by first-principles calculations. Our results indicate that both compounds are Mott-insulators with orbital ordering. The ground states of both compounds are the checkerboard antiferromagnetic states, which are different from the iron pnictide superconductors, although their structures are similar to those of the Fe-As-based superconductors.     

Orbital order in NaTiO2: A first principles study

The debate over the orbital order in the layered triangular lattice system NaTiO₂ has been rekindled by the recent experiments of McQueen et al. [Phys. Rev. Lett. 101 (2008) 166402] on NaVO₂. In view of this, the nature of orbital ordering, in both high and low temperature phases, is studied using an ab-initio electronic structure calculation. The orbital order observed in our calculations in the low temperature structure of NaTiO₂ is consistent with the predictions of McQueen et al. An LDA plus dynamical mean-field calculation shows considerable transfer of spectral weight from the Fermi level but no metal–insulator transition, confirming the poor metallic behavior observed in transport measurements.     

Ground state of BaCoS2 as a set of energy-degenerate orbital-ordered configurations of Co2+ ions

The linear muffin-tin orbital method in the local density approximation (LDA + U) explicitly considering Coulomb correlations has been applied to calculate the electronic structure, magnetic moments, and parameters of the Heisenberg exchange interaction for cobalt ions in BaCoS₂. Five solutions close in total energy with various orbital ordering of Co²⁺ ions and almost identical spin magnetic moments μ = 2.32μ_B of the Co²⁺ ion 3d-shell have been found. The BaCoS₂ ground state can be considered as a set of energy-degenerate orbital-ordered configurations of Co²⁺ ions in the high-spin state.     

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.     

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.     

Low to high spin-state transition induced by charge ordering in antiferromagnetic YBaCo2O5

The oxygen-deficient double perovskite YBaCo2O5, containing corner-linked CoO5 square pyramids as principal building units, undergoes a paramagnetic to antiferromagnetic spin ordering at 330 K. This is accompanied by a tetragonal to orthorhombic distortion. Below 220 K orbital ordering and long-range Co(2+)/Co(3+) charge ordering occur as well as a change in the Co2+ spin state from low to high spin. This transition is shown to be very sensitive to the oxygen content of the sample. To our knowledge this is the first observation of a spin-state transition induced by long-range orbital and charge ordering.