Types Of Charge Ordering Research Articles

Two types of charge order with distinct interplay with superconductivity in the kagome material CsV3Sb5

The kagome metals of the family AV3Sb5, featuring a unique structural motif, harbor an array of intriguing phenomena such as chiral charge order and superconductivity. CsV3Sb5 is of particular interest because it displays a double superconducting dome in the region of the temperature-pressure phase diagram where charge order is still present. However, the microscopic origin of such an unusual behavior remains an unsolved issue. Here, to address it, we combine high-pressure, low-temperature muon spin relaxation/rotation with first-principles calculations. We observe a pressure-induced threefold enhancement of the superfluid density, which also displays a double-peak feature, similar to the superconducting critical temperature. This leads to three distinct regions in the phase diagram, each of which features distinct slopes of the linear relation between superfluid density and the critical temperature. These results are attributed to a possible evolution of the charge order pattern from the superimposed tri-hexagonal Star-of-David phase at low pressures (within the first dome) to the staggered tri-hexagonal phase at intermediate pressures (between the first and second domes). Our findings suggest a change in the nature of the charge-ordered state across the phase diagram of CsV3Sb5, with varying degrees of competition with superconductivity.

Charge-order on the triangular lattice: Effects of next-nearest-neighbor attraction in finite temperatures

The extended Hubbard model in the atomic limit, which is equivalent to lattice S=1/2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W1) and next-nearest-neighbor (W2) density–density intersite interactions. The variational approach treating the U term exactly and the Wl terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T>0) phase diagrams (as a function of particle concentration) for W1>0 and W2<0. Two different types of charge-order (i.e., DCO and TCO phases) within 3×3 unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W2<0 stabilizes PS states at T=0 and it extends the regions of their occurrence at T>0. The evolution of the diagrams with increasing of |W2|/W1 is investigated. It is found that some of the PS states are stable only at T>0. Two different critical values of |W2|/W1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist.

Two types of charge ordering in bismuth nickelate

Among the transition-metal oxides, bismuth nickelate is particular in that, under normal conditions, it crystallizes in a triclinic structure with charge ordering in the Bi sites. Upon increasing pressure, a phase transition takes the material to the $\mathrm{Gd}\mathrm{Fe}{\mathrm{O}}_{3}$-type orthorhombic phase commonly found in perovskite oxides; recent attention to $\mathrm{Bi}\mathrm{Ni}{\mathrm{O}}_{3}$ arises, in part, because this transition can be engineered to be accompanied by a colossal negative thermal expansion. On the other hand, the closely related rare-earth nickelates also show the orthorhombic phase, but as temperature decreases they undergo a metal-insulator transition to a monoclinic phase where charge ordering appears instead in the Ni sites. Since bismuth is similar in valence and size to some of the rare-earth atoms, it has been conjectured that a $\mathrm{Bi}\mathrm{Ni}{\mathrm{O}}_{3}$ phase with charge ordering in the Ni sites might also exist---this would make this perovskite unique in that it can harbor charge ordering in either set of cation species, while the other set contains identical nominal ionic charges. In this paper we show that such a phase indeed corresponds to a special point of the energy surface of $\mathrm{Bi}\mathrm{Ni}{\mathrm{O}}_{3}$ when studied with methods based on density-functional theory. The existence of this phase could explain the somewhat conflicting experimental reports regarding the valence state of the Ni ions in the high-pressure phase of $\mathrm{Bi}\mathrm{Ni}{\mathrm{O}}_{3}$.

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas.

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite and (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive , the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state () diagram for as well as finite temperature () phase diagrams for are presented. Two different types of charge order within unit cell can occur. At , for phase separated states are degenerated with homogeneous phases (but removes this degeneration), whereas attractive stabilizes phase separation at incommensurate fillings. For and only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.

Interface reconstruction with emerging charge ordering in hexagonal manganite.

Multiferroic materials, which simultaneously have multiple orderings, hold promise for use in the next generation of memory devices. We report a novel self-assembled MnO double layer forming at the interface between a multiferroic YMnO3 film and a c-Al2O3 substrate. The crystal structures and the valence states of this MnO double layer were studied by atomically resolved scanning transmission electron microscopy and spectroscopy, as well as density functional theory (DFT) calculations. A new type of charge ordering has been identified within this MnO layer, which also contributes to a polarization along the [001] direction. DFT calculations further establish the occurrence of multiple couplings between charge and lattice in this novel double layer, in addition to the polarization in nearby YMnO3 single layer. The interface reconstruction reported here creates a new playground for emergent physics, such as giant ferroelectricity and strong magnetoelectric coupling, in manganite systems.

Neutron, electron, and x-ray scattering investigation ofCr1−xVxnear quantum criticality

The weakness of electron-electron correlations in the itinerant antiferromagnet Cr doped with V has long been considered the reason that neither new collective electronic states or even non Fermi liquid behaviour are observed when antiferromagnetism in Cr$_{1-x}$V$_{x}$ is suppressed to zero temperature. We present the results of neutron and electron diffraction measurements of several lightly doped single crystals of Cr$_{1-x}$V$_{x}$ in which the archtypal spin density wave instability is progressively suppressed as the V content increases, freeing the nesting-prone Fermi surface for a new striped charge instability that occurs at x$_{c}$=0.037. This novel nesting driven instability relieves the entropy accumulation associated with the suppression of the spin density wave and avoids the formation of a quantum critical point by stabilising a new type of charge order at temperatures in excess of 400 K. Restructuring of the Fermi surface near quantum critical points is a feature found in materials as diverse as heavy fermions, high temperature copper oxide superconductors and now even elemental metals such as Cr.

X-ray natural dichroism and chiral order in underdoped cuprates

The origin of the Kerr rotation observed in the pseudogap phase of cuprates has been the subject of much speculation. Recently, it has been proposed that this rotation might be due to chiral charge order. Here, I investigate whether such order can be observed by x-ray natural circular dichroism (XNCD). Several types of charge order were considered, and they can give rise to an XNCD signal depending on the stacking of the order along the c-axis.

Charge Orderings and Phase Separations in Itinerant Fermion Systems at Half Filling

We analyse the ground state phase diagrams of the charge orderings in narrow band materials using two e ective models: (1) the spinless fermion model (t−W ) with repulsive intersite interaction (Wij > 0) and (2) the molecular crystal model with the coupling of electrons to intramolecular (crystal eld) vibrations. We present results for the case of half lled bands for d = 2 square lattice. The calculations are performed within the (broken symmetry) Hartree-Fock approximation. The study takes into consideration the e ects of frustrating next-nearest-neighbour hopping (t2) on the charge ordered states in these systems. We focus on the two cases: (i) homogeneous phases and phase separations involving checkerboard charge ordering with the nesting vector Q = (π, π) only and (ii) homogeneous phases and phase separations involving two types of charge ordering: (a) checkerboard charge ordering with the nesting vector Q = (π, π), and (b) collinear (CL) charge ordering with Q = (0, π) or Q = (π, 0).

Formation of charge and spin ordering in strongly correlated electron systems

In this review we present results of our theoretical study of charge and spin ordering in strongly correlated electron systems obtained within various generalizations of the Falicov-Kimball model. The primary goal of this study was to identify crucial interactions that lead to the stabilization of various types of charge ordering in these systems, like the axial striped ordering, diagonal striped ordering, phase-separated ordering, phase-segregated ordering, etc. Among the major interactions that come into account, we have examined the effect of local Coulomb interaction between localized and itinerant electrons, long-range and correlated hopping of itinerant electrons, long-range Coulomb interaction between localized and itinerant electrons, local Coulomb interaction between itinerant electrons, local Coulomb interaction between localized electrons, spin-dependent interaction between localized and itinerant electrons, both for zero and nonzero temperatures, as well as for doped and undoped systems. Finally, the relevance of resultant solutions for a description of rare-earth and transition-metal compounds is discussed.

Electronic structure analysis of the quasi-one-dimensional oxide Sr6Co5O15 within the LDA+U method

The quasi-one-dimensional cobalt oxide Sr6Co5O15 is studied using first-principles electronic-structure calculations and Boltzmann transport theory. We have been able to describe the electronic structure, characterized by the structural one-dimensionality and a particular type of charge ordering, with unexpected electronic structure of the different Co atoms. The origin of the large unquenched misaligned orbital angular momenta comes out naturally from a correct description of the different crystal-field environments. The evolution with the on-site Coulomb repulsion (U) of the electronic structure and the transport properties is discussed, with a best agreement with experiment found for the smallest value of U that allows to converge the correct in-chain ferrimagnetic ground state.

Extended Hubbard model in the presence of a magnetic field

Within the Green's function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site $U$ and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional space (U, n, h) - n is the filling - with relative phase transitions, as well as different types of charge ordering. The magnetic field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in the magnetization curves, and a change from a single to a double-peak structure in the specific heat. According to the value of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed study of several thermodynamic quantities is also presented at finite temperature.

One-dimensional extended Hubbard model in the atomic limit

We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.

Experimental confirmation of Zener-polaron-type charge and orbital ordering inPr1−xCaxMnO3

Pr{sub 1-x}Ca{sub x}MnO{sub 3} in the doping range between 0.3<x<0.5 represent an extremely interesting manganite system for the study of the interplay of different kinds of ordering (charge, orbital, lattice, and spin). While there is consensus that a charge- and orbital-ordered state develops below a transition temperature T{sub co}{approx_equal}230 K, recent controversial structural refinements resulting from neutron and x-ray diffraction studies challenged our understanding of the particular type of charge ordering (CO) and orbital ordering (OO), and consequently, the underlying mechanism of the colossal resistance effects. Here, we present a detailed high-resolution transmission electron microscopy and electron-diffraction study that, based on extinction rules, resolves the current controversy and confirms the existence of the Zener-polaron (ZP)-type CO and/or OO in Pr{sub 1-x}Ca{sub x}MnO{sub 3}. The ZP-type ordering is further verified by atomic-column-resolved electron energy-loss spectroscopy revealing strong charge ordering of the in-plane oxygen-Mn bonds, while valence disproportionation at the Mn sites is less than expected. Over wide doping and temperature ranges, we observed structural phase coexistence between the ZP-CO/OO P2{sub 1}nm and the disordered Pbnm structure.

Band structure of charge-ordered doped antiferromagnets

We study the distribution of electronic spectral weight in a doped antiferromagnet with various types of charge order and compare to angle resolved photoemission experiments on lightly doped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and electron doped Nd$_{2-x}$Ce$_x$CuO$_{4\pm\delta}$. Calculations on in-phase stripe and bubble phases for the electron doped system are both in good agreement with experiment including in particular the existence of in-gap spectral weight. In addition we find that for in-phase stripes, in contrast to anti-phase stripes, the chemical potential is likely to move with doping. For the hole doped system we find that ``staircase'' stripes which are globally diagonal but locally vertical or horizontal can reproduce the photoemission data whereas pure diagonal stripes cannot. We also calculate the magnetic structure factors of such staircase stripes and find that as the stripe separation is decreased with increased doping these evolve from diagonal to vertical separated by a coexistence region. The results suggest that the transition from horizontal to diagonal stripes seen in neutron scattering on underdoped LSCO may be a crossover between a regime where the typical length of straight stripe segments is longer than the inter-stripe spacing to one where it is shorter and that locally the stripes are always aligned with the Cu-O bonds.

Formula omitted]-NMR studies of charge ordering in organic conductors

Experimental evidences of the charge ordering with the use of 13 C -NMR techniques in various organic conductors are reviewed. In the insulating states of two-dimensional BEDT-TTF salts, α-I 3 and θ-RbZn(SCN) 4, the formation of charge stripes perpendicular to molecular stacks are confirmed. Charge disproportionation is estimated as 0.8:0.2 in the latter and more in the former. New type of charge ordering in a TTM-TTP salt with one-dimensional half-filled band is suggested.

Charge and Spin Order in RNiO3(R=Nd, Y) by LSDA+U Method

Electronic structures of NdNiO 3 and YNiO 3 are calculated by using the LSDA+U method with rotational invariance. No orbital order on Ni sites is observed in the calculations for the two systems. Different types of charge ordering are found in the two systems. In a small distorted system NdNiO 3 , all nickel ions are trivalent, while oxygen sites show charge ordering and spin density polarization in the energy range of Ni e g σ * band. In a large distorted system YNiO 3 , charge disproportionation occurs. Therefore, the charge ordering stabilizes the asymmetry of the arrangement of Ni magnetic moments in both systems.

Double “Mn3+” Stripes in Bi1‐xSrxMnO3: New Type of Charge Ordering at Room Temperature.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Double “Mn3+” Stripes in Bi1-xSrxMnO3: New Type of Charge Ordering at Room Temperature

The electron microscopy study of the manganites Bi1-xSrxMnO3, especially for x = 1/2 and x = 2/3, has allowed a new type of modulated structure, correlated to charge ordering (CO) phenomena, to be evidenced. The Bi1-xSrxMnO3 manganites are characterized by a modulated structure, the modulation vector being qa* (q ≈ 1 − x), and the I-type symmetry of the perovskite subcell. A model is proposed: the structure can be described by double Mn3+ stripes alternating with double (x = 1/2) or with quadruple (x = 2/3) Mn4+ stripes. This type of ordering, observed at room temperature (RT), is compared to that observed in the manganites Ln1-xCaxMnO3 at low temperature and in Bi1-xCaxMnO3 at RT. The absence of magnetoresistance up to 7T suggests that the CO state of Bi0.5Sr0.5MnO3 is exceptionally stable, with a very high TCO close to 500 K. The electron diffraction study carried out versus T shows that the superstructure disappears at 500 K and that the phenomenon is reversible.

Two types of charge ordering in DCNQI-metal complexes studied by 13C-NMR

The π electron charge ordering in (DI-DCNQI) 2Ag with a 1/4-filled l-d band and the d electron charge ordering in deuterated (DMe-DCNQI) 2Cu with the π-d hybridization have been characterized by 13C NMR. The profile of the ordering is quite different between the two systems, reflecting the different driving force. The intersite Coulomb interaction between the π-electrons is considered to be crucial in the former case while the perfect charge ordering found in the latter salt seems to invoke cooperative mechanism including the π electron-lattice (Peierls) instability, dry level-lattice instability and strong correlation in the Cu site.

Percolative phase separation underlies colossal magnetoresistance in mixed-valent manganites

Colossal magnetoresistance1—an unusually large change of resistivity observed in certain materials following application of magnetic field—has been extensively researched in ferromagnetic perovskite manganites. But it remains unclear why the magnetoresistive response increases dramatically when the Curie temperature (T C) is reduced. In these materials, T C varies sensitively with changing chemical pressure; this can be achieved by introducing trivalent rare-earth ions of differing size into the perovskite structure2,3,4, without affecting the valency of the Mn ions. The chemical pressure modifies local structural parameters such as the Mn–O bond distance and Mn–O–Mn bond angle, which directly influence the case of electron hopping between Mn ions (that is, the electronic bandwidth). But these effects cannot satisfactorily explain the dependence of magnetoresistance on T C. Here we demonstrate, using electron microscopy data, that the prototypical (La,Pr,Ca)MnO3 system is electronically phase-separated into a sub-micrometre-scale mixture of insulating regions (with a particular type of charge-ordering) and metallic, ferromagnetic domains. We find that the colossal magnetoresistive effect in low-T C systems can be explained by percolative transport through the ferromagnetic domains; this depends sensitively on the relative spin orientation of adjacent ferromagnetic domains which can be controlled by applied magnetic fields.