Roles of Electron Hopping on Orbital Ordering for Vanadium Spinels

We investigate the orbital ordering quantitatively for the spinel systems RV₂O₄ (R=Mg, Zn, Cd) in the viewpoint of single-ion physics through the method of diagonalization. Through the quantitative calculation, it is found that the spin-orbit (SO)coupling and the Jahn-Teller (JT) effect enable the orbital ordering under the conditions of negligible electron hopping among different V³⁺ sites. For the systems RV₂O₄, the electron hopping is implied to be observable from the energy gap in conductivity, so the orbital ordering of RV₂O₄ cannot be induced by the SO coupling and JT effect at definite temperature, which is on contrary to the conclusions in [Phys. Rev. Lett. 93 (2004) 157206].     

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     

Direct observation of antiferroquadrupolar ordering: resonant X-Ray scattering study of DyB2C2

Antiferroquadrupolar (AFQ) ordering has been conjectured in several rare-earth compounds to explain their anomalous magnetic properties. No direct evidence for AFQ ordering, however, has been reported. Using the resonant x-ray scattering technique near the Dy L(III) absorption edge, we have succeeded in observing the AFQ order parameter in DyB2C2 and analyzing the energy and polarization dependence. The much weaker coupling between the orbital degrees of freedom and the lattice in 4f electron systems than in 3d compounds makes them an ideal platform to study orbital interactions originating from electronic mechanisms.     

A new approach to analyse H⊗(2h⊕g) Jahn-Teller system for C60

It is now well-known that electron (hole)-vibron coupling and hence Jahn-Teller (JT) effect is important understanding the properties of C₆₀ and related molecules. In this paper, we study H(2) coupling case to find the potential energy surfaces for the positively charged C₆₀ molecule due to distortion. The H(2) Jahn-Teller system is of particular importance as this will be the JT effect displayed by C₆₀ molecules removed with an electron. C₆₀ ⁺ is obtained by removing one electron from fivefold degenerate H_u highest occupied molecular orbital (HOMO) and a hole in HOMO interacts with the vibrational modes of C₆₀ and symmetry is broken. We apply the method of symmetry breaking mechanism to obtain expressions for the potential energy surface. Received 27 December 1999 and Received in final form 15 May 2000     

Ferroelectricity due to orbital ordering in E-type undoped rare-earth manganites

Aiming at understanding the origin of the electronic contribution to ferroelectric polarization in undoped manganites, we evaluate the Berry phase of orbital-polarizable Bloch electrons as an orbital ordering (OO) establishes in the background of an antiferromagnetic E-type configuration. The onset of OO is tuned by the Jahn-Teller (JT) interaction in a tight-binding model for interacting electrons moving along zigzag chains. A finite polarization is found as soon as the JT coupling is strong enough to induce OO, supporting the large electronic contribution predicted from first principles.     

T1u×hg Jahn-Teller系统：D3d势阱中的频率分解与能级分裂

在C60分子中，未被填充的最低电子态具有T1u对称性，因此，对中性的C60而言，不论是通过分子内部激发，或是外部掺杂，都易被一个电子占据而形成Jahn-Teller（JT）活跃电子态.此态与五重简并的hg声子态耦合，构成所谓的T1u-hg -JT系统.在这一JT系统中，当只考虑电声的线性耦合时，其绝热势能面是一个槽形.但在实际的系统中，二阶电声耦合是存在的，理论研究表明，原来的势槽将被这二阶非线性耦合弯曲成D3d或D5d对称性的势阱.声子振动态在阱中将显示各向异性效应，使得声子沿不同的方向有不同的振动频率，进而影响势阱中的能级分布、势阱间的重叠积分，以及整个系统的隧道能级分裂等.对D3d势阱中各向异性效应进行了研究，利用幺正平移、?pik Pryce和标度变换等方法计算了系统势阱中的能级，以及阱中的振动频率，研究了势阱中的能级间隔以及微绕修正能量的变化，并由此导出了这些物理量在仅有线性耦合的势槽中变化的情形. 关键词： C60 Jahn-Teller效应 各向异性 电声耦合     

Orbital correlations in the pseudocubic O and rhombohedral R phases of LaMnO3

The local and intermediate structure of stoichiometric LaMnO3 has been studied in the pseudocubic and rhombohedral phases at high temperatures (300-1150 K). Neutron powder diffraction data were collected and a combined Rietveld and high real space resolution atomic pair distribution function analysis was carried out. The nature of the Jahn-Teller (JT) transition around 750 K is confirmed to be orbital order to disorder. In the high-temperature orthorhombic (O) and rhombohedral (R) phases, the MnO6 octahedra are still fully distorted locally. More importantly, the intermediate structure suggests the presence of local ordered clusters of diameter approximately 16 A ( approximately 4 MnO6 octahedra) implying strong nearest-neighbor JT antiferrodistortive coupling. These clusters persist well above the JT transition temperature even into the high-temperature R phase.     

Optical evidence of quantum rotor orbital excitations in orthorhombic manganites

In magnetic compounds with Jahn–Teller (JT) ions (such as Mn³⁺ or Cu²⁺), the ordering of the electron or hole orbitals is associated with cooperative lattice distortions. There the role of JT effect, although widely recognized, is still elusive in the ground state properties. Here we discovered that, in these materials, there exist excitations whose energy spectrum is described in terms of the total angular momentum eigenstates and is quantized as in quantum rotors found in JT centers. We observed features originating from these excitations in the optical spectra of a model compound LaMnO₃ using ellipsometry technique. They appear clearly as narrow sidebands accompanying the electron transition between the JT split orbitals at neighboring Mn³⁺ ions, displaying anomalous temperature behavior around the Néel temperature T_N ≈ 140 K. We present these results together with new experimental data on photoluminescence found in LaMnO₃, which lend additional support to the ellipsometry implying the electronic-vibrational origin of the quantum rotor orbital excitations. We note that the discovered orbital excitations of quantum rotors may play an important role in many unusual properties observed in these materials upon doping, such as high-temperature superconductivity and colossal magnetoresistance.     

Orbital order in ZnV(2)O(4)

In view of recent controversy regarding the orbital order in the frustrated spinel ZnV(2)O(4), we analyze the orbital and magnetic ground state of this system within an ab initio density functional theory approach. While local density approximation+Hubbard U calculations in the presence of a cooperative Jahn-Teller distortion stabilize an A-type staggered orbital order, the consideration of relativistic spin-orbit (SO) effects unquenches the orbital moment and leads to a uniform orbital order with a net magnetic moment close to the experimental one. Our results show that ab initio calculations are able to resolve the existing discrepancies in previous theories and that it is the SO coupling along with electronic correlations which play a significant role in determining the orbital structure in these materials.     

Magnetic,transport, thermal properties and orbital state for spinel MnTi2O4

We systematically investigated the various properties of MnTi₂O₄. The compounds are found to be conducted by small polarons with different activation energies across the temperature T₁ and deviate from the Curie–Weiss law for the magnetic susceptibility at T₁. Also at T₁ do the specific heat undergo a crossover. As indicated by the X-ray diffraction peaks, the series of phenomena near the characteristic temperature T₁ are attributed to the happening of the micro-structural distortion, and the distortion implies the short-range orbital ordering state below T₁. This short-range oribtal ordering state is supported by the little upturn of the thermal conductance at T₁. As the temperature decreases, the systems enter a long-ranged collinear ferrimagnetic state at a lower temperature T_N. Moreover, the compounds decreases in thermal-electric power with the decrease of temperature and undergoes a p-type to n-type transition at the temperature T_pn. Through the quantitative theoretical analysis, both the decrease of the thermal power and the p-type to n-type transition are cooperatively induced by spin–orbit (SO) coupling and the Jahn–Teller (JT) effect.     

Vibronic coupling effects in the C60 molecule

Many recent experiments have established that the Jahn-Teller (JT) effect plays a very important role in determining the properties of the C₆₀ molecule. A review of the underlying theory developed by the Nottingham group is presented for cases in which distinct minima in the potential energy surface occur. This relates directly to the C₆₀ molecule through the consideration of the T ⊗ h and H ⊗ h JT systems. When only linear coupling terms exist in the T ⊗ h system, the minima form a continuous trough of SO(3) symmetry and new methods must be used. Some details of these results are presented.     

Orbital-driven electronic structure changes and the resulting optical anisotropy of the quasi-two-dimensional spin gap compound La4Ru2O10

We investigated the electronic response of the quasi-two-dimensional spin gap compound La4Ru2O10 using optical spectroscopy. We observed the drastic changes in the optical spectra as the temperature decreased, resulting in anisotropy in the electronic structure of the spin-singlet ground state. Using the orbital-dependent hopping analysis, we found that orbital ordering plays a crucial role in forming the spin gap state in the non-one-dimensional material.     

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.     

Cooperative jahn-teller coupling in the manganites

The cooperative Jahn-Teller coupling between the Mn e(g) electrons and the oxygen octahedral distortions in LaMnO3 is studied using ab initio density-functional calculations and tight-binding models. The linear and quadratic vibronic coupling parameters are calculated using density-functional methods. It is shown that the cooperative Jahn-Teller coupling, primarily due to the interoctahedral electron hopping (band structure term), leads to the ordering of the octahedral distortion and simultaneously to orbital ordering. The coupling results in a two-minima adiabatic potential surface in the solid, instead of the three-minima "Mexican-hat" surface for the isolated octahedron.     

A new interpretation of the CO state in half-doped manganites: new results from neutron diffraction and synchrotron radiation experiments

In the R_1−xD_xMnO₃ (x0.5) manganites, the structural phase transition at T_CO is commonly interpreted as a concomitant charge and orbital ordering (CO/OO) process driven by a co-operative Jahn–Teller effect and Coulomb repulsion forces. The low-temperature phase is supposed to contain well-separated and ordered Mn³⁺ and Mn⁴⁺ ionic species in an NaCl-like pattern. Structure refinement, from a neutron diffraction experiment below T_CO on a Pr_0.6Ca_0.4MnO₃ single crystal, gives us a model for the displacement of atoms with respect to the high-temperature phase that invalidates the standard model based in the CO/OO picture. Our result is a non-centrosymmetric crystal structure with two non-equivalent MnO₆ octahedra, both being slightly elongated but displaying very similar average Mn–O distances (1.96 and 1.95 Å, respectively) and having off-centered Mn atoms. We argue that this is a proof of the absence of charge ordering in half-doped manganites in the sense of formation of separated Mn³⁺ and Mn⁴⁺ ionic species. A new qualitative interpretation of the CE-type spin ordering (SO) is proposed. The so-called CO transition is, in fact, a structural transition induced by the change in the mean free path of electrons that continue to be thermally activated below T_CO by forming ferromagnetic Mn–Mn pairs stabilized by a local double-exchange process. The CE SO pattern results from the ordering of these pairs formed at T_CO. High-resolution synchrotron powder diffraction shows a complex anisotropic/asymmetric strains appearing at the transition that can be phenomenologically fitted by additional phases. Complementary electron diffraction and microscopy have shown no trace of macroscopic phase separation.     

Electrofluorescence polarity in a molecular diode

The kinetic equations describing the transmission of an electron in the molecular compound “electrode 1–molecule–electrode 2” (1M2 system) are derived using the method of a nonequilibrium density matrix. The steady-state transmission regime is considered, for which detailed analysis of the kinetics of electrofluorescence formation in systems with symmetric and asymmetric couplings between the molecule and the electrodes is carried out. It is shown that the optically active state of the molecule is formed as a result of electron hops between the molecule and each of the electrodes, as well as due to inelastic interelectrode tunneling of the electron. The electrofluorescence power for a molecular diode (asymmetric 1M2 system) depends on the polarity of the voltage bias applied to the electrodes. The polarity is explained using a model in which the optically active part of the molecule (chromophore group) is represented by the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Two mechanisms of the emergence of polarity are revealed. One mechanism is associated with nonidentical Stark shifts of the HOMO and LUMO levels relative to the Fermi levels of the electrodes. The second mechanism is associated with the fact that the rates of an electron hopping between HOMO (LUMO) and one of the electrodes are much higher than the rates of such a hopping with the other electrode. The conditions in which each mechanism can be implemented experimentally are indicated.     

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.     

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.     

Cooperative Jahn-Teller phase transition in LaMnO3 studied by X-ray absorption spectroscopy

The local structure of LaMnO3 across the Jahn-Teller (JT) transition at T(JT)=750 K was studied by means of x-ray absorption near edge structure and extended x-ray absorption fine structure at the Mn K-edge. Our results indicate a similar electronic local structure for Mn atoms above and below T(JT) and a dynamical tetragonal JT distortion of MnO6 octahedra above T(JT). The structural transition is originated by the ordering of tetragonally distorted octahedra. The entropy content of the transition is analyzed within the framework of the three-state Potts model with nearest neighbor antiferrodistortive coupling.     

Polar antiferromagnets produced with orbital order

Polar states are realized in pseudocubic manganite films fabricated on high-index substrates, in which a Jahn-Teller (JT) distortion remains an active variable. Several types of orbital orders (OOs) were found to develop large optical second harmonics, signaling broken-inversion symmetry distinct from their bulk forms and films on (100) substrates. The observed symmetry lifting and first-principles calculation both indicate that the modified JT q2 mode drives Mn-site off centering, which can be controlled by a magnetic-field-induced phase transition via a coupling of OO and spin orders.