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Unconventional superconductivity often couples to other electronic orders in a cooperative or competing fashion. Identifying external stimuli that tune between these two limits is of fundamental interest. Here, we show that strain perpendicular to the copper-oxide planes couples directly to the competing interaction between charge stripe order and superconductivity in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO). Compressive $c$-axis pressure amplifies stripe order within the superconducting state, while having no impact on the normal state. By contrast, strain dramatically diminishes the magnetic field enhancement of stripe order in the superconducting state. These results suggest that $c$-axis strain acts as tuning parameter of the competing interaction between charge stripe order and superconductivity. This interpretation implies a uniaxial pressure-induced ground state in which the competition between charge order and superconductivity is reduced.

The ability to efficiently control charge and spin in the cuprate high-temperature superconductors is crucial for fundamental research and underpins technological development. Here, we explore the tunability of magnetism, superconductivity and crystal structure in the stripe phase of the cuprate La_2-xBa_xCuO_4, with x = 0.115 and 0.135, by employing temperature-dependent (down to 400 mK) muon-spin rotation and AC susceptibility, as well as X-ray scattering experiments under compressive uniaxial stress in the CuO_2 plane. A sixfold increase of the 3-dimensional (3D) superconducting critical temperature T_c and a full recovery of the 3D phase coherence is observed in both samples with the application of extremely low uniaxial stress of 0.1 GPa. This finding demonstrates the removal of the well-known 1/8-anomaly of cuprates by uniaxial stress. On the other hand, the spin-stripe order temperature as well as the magnetic fraction at 400 mK show only a modest decrease under stress. Moreover, the onset temperatures of 3D superconductivity and spin-stripe order are very similar in the large stress regime. However, a substantial decrease of the magnetic volume fraction and a full suppression of the low-temperature tetragonal structure is found at elevated temperatures, which is a necessary condition for the development of the 3D superconducting phase with optimal T_c. Our results evidence a remarkable cooperation between the long-range static spin-stripe order and the underlying crystalline order with the three-dimensional fully coherent superconductivity. Overall, these results suggest that the stripe- and the SC order may have a common physical mechanism., Comment: 11 pages, 5 figures. This work builds on our earlier findings on LBCO, arXiv:2008.01159, and substantially expands it

Spontaneous symmetry breaking constitutes a paradigmatic classification scheme of matter. However, broken symmetry also entails domain degeneracy that often impedes identification of novel low symmetry states. In quantum matter, this is additionally complicated by competing intertwined symmetry breaking orders. A prime example is that of unconventional superconductivity and density-wave orders in doped cuprates in which their respective symmetry relation remains a key question. Using uniaxial pressure as a domain-selective stimulus in combination with x-ray diffraction, we unambiguously reveal that the fundamental symmetry of the charge order in the prototypical cuprate La$_{1.88}$Sr$_{0.12}$CuO$_4$ is characterized by uniaxial stripes. We further demonstrate the direct competition of this stripe order with unconventional superconductivity via magnetic field tuning. The stripy nature of the charge-density-wave state established by our study is a prerequisite for the existence of a superconducting pair-density-wave -- a theoretical proposal that clarifies the interrelation of intertwined quantum phases in unconventional superconductors -- and paves the way for its high-temperature realization., Comment: 6 pages, 4 figures, 9 supplementary figures

We explore the evolution of the structural phase transition of $\rm{(Sr, Ca)_3Ir_4Sn_{13}}$, a model system to study the interplay between structural quantum criticality and superconductivity, by means of high-energy x-ray diffraction measurements at high pressures and low temperatures. Our results confirm a rapid suppression of the superlattice transition temperature $T^*$ against pressure, which extrapolates to zero at a critical pressure of $\approx 1.79(4)$ GPa. The temperature evolution of the superlattice Bragg peak in $\rm{Ca_3Ir_4Sn_{13}}$ reveals a drastic decrease of the intensity and an increase of the linewidth when $T \rightarrow 0$ K and $p \rightarrow p_c$. Such anomaly is likely associated to the emergence of quantum fluctuations that disrupt the formation of long-range superlattice modulation. The revisited temperature-pressure phase diagram of $\rm{(Sr, Ca)_3Ir_4Sn_{13}}$ thus highlights the intertwined nature of the distinct order parameters present in this system and demonstrates some similarities between this family and the unconventional superconductors.

The interplay of structural and electronic phases in iron-based superconductors is a central theme in the search for the superconducting pairing mechanism. While electronic nematicity, defined as the breaking of four-fold symmetry triggered by electronic degrees of freedom, is competing with superconductivity, the effect of purely structural orthorhombic order is unexplored. Here, using x-ray diffraction (XRD), we reveal a new structural orthorhombic phase with an exceptionally high onset temperature ($T_\mathrm{ort} \sim 250$ K), which coexists with superconductivity ($T_\mathrm{c} = 25$ K), in an electron-doped iron-pnictide superconductor far from the underdoped region. Furthermore, our angle-resolved photoemission spectroscopy (ARPES) measurements demonstrate the absence of electronic nematic order as the driving mechanism, in contrast to other underdoped iron pnictides where nematicity is commonly found. Our results establish a new, high temperature phase in the phase diagram of iron-pnictide superconductors and impose strong constraints for the modeling of their superconducting pairing mechanism., Comment: SI available upon request

The charge density wave in the high-temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) is now known to have two different ordering tendencies differentiated by their $c$-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDW in neighbouring CuO$_2$ bilayers. This discovery has prompted a number of fundamental questions. For example, how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use high-energy x-ray diffraction to study YBa$_2$Cu$_3$O$_{6.67}$ as a function of magnetic field and temperature. We show that regions of the sample with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a weak or fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is furthermore concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations have an important impact on superconducting and normal state properties of underdoped YBCO., Comment: 9 pages, 5 figures, and supplementary information

Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu$_2$Si$_2$ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here we present a high-resolution x-ray diffraction study of the URu$_2$Si$_2$ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold $p_c\approx3$ kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition $T_{HO}=17.5$ K. For $p>p_c$, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures $T_{OR}\sim 100$ K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem., Comment: 6 pages, 4 figures and supplemental materials

Low-dimensional electron systems, as realized naturally in graphene or created artificially at the interfaces of heterostructures, exhibit a variety of fascinating quantum phenomena with great prospects for future applications. Once electrons are confined to low dimensions, they also tend to spontaneously break the symmetry of the underlying nuclear lattice by forming so-called density waves; a state of matter that currently attracts enormous attention because of its relation to various unconventional electronic properties. In this study we reveal a remarkable and surprising feature of charge density waves (CDWs), namely their intimate relation to orbital order. For the prototypical material 1T-TaS2 we not only show that the CDW within the two-dimensional TaS2-layers involves previously unidentified orbital textures of great complexity. We also demonstrate that two metastable stackings of the orbitally ordered layers allow to manipulate salient features of the electronic structure. Indeed, these orbital effects enable to switch the properties of 1T-TaS2 nanostructures from metallic to semiconducting with technologically pertinent gaps of the order of 200 meV. This new type of orbitronics is especially relevant for the ongoing development of novel, miniaturized and ultra-fast devices based on layered transition metal dichalcogenides.

To explore the doping dependence of the recently discovered charge density wave (CDW) order in YBa2Cu3Oy, we present a bulk-sensitive high-energy x-ray study for several oxygen concentrations, including strongly underdoped YBa2Cu3O6.44. Combined with previous data around the so-called 1/8 doping, we show that bulk CDW order exists at least for hole concentrations (p) in the CuO2 planes of 0.078 <~ p <~ 0.132. This implies that CDW order exists in close vicinity to the quantum critical point for spin density wave (SDW) order. In contrast to the pseudogap temperature T*, the onset temperature of CDW order decreases with underdoping to T_CDW ~ 90K in YBa2Cu3O6.44. Together with a weakened order parameter this suggests a competition between CDW and SDW orders. In addition, the CDW order in YBa2Cu3O6.44 shows the same type of competition with superconductivity as a function of temperature and magnetic field as samples closer to p = 1/8. At low p the CDW incommensurability continues the previously reported linear increasing trend with underdoping. In the entire doping range the in-plane correlation length of the CDW order in b-axis direction depends only very weakly on the hole concentration, and appears independent of the type and correlation length of the oxygen-chain order. The onset temperature of the CDW order is remarkably close to a temperature T^\dagger that marks the maximum of 1/(T_1T) in planar 63^Cu NQR/NMR experiments, potentially indicating a response of the spin dynamics to the formation of the CDW. Our discussion of these findings includes a detailed comparison to the charge stripe order in La2-xBaxCuO4., Comment: 11 pages, 5 figures

We present a volume-sensitive high-energy x-ray diffraction study of the underdoped cuprate high temperature superconductor La2-xSrxCuO4 (x = 0.12, Tc=27 K) in applied magnetic field. Bulk short-range charge stripe order with propagation vector q_ch = (0.231, 0, 0.5) is demonstrated to exist below T_ch = 85(10) K and shown to compete with superconductivity. We argue that bulk charge ordering arises from fluctuating stripes that become pinned near boundaries between orthorhombic twin domains., Comment: 5 pages, 4 figures. To be submitted to Phys. Rev. Lett

Resonant and non-resonant X-ray scattering studies on HoFe3(BO3)O4 reveal competing magnetic ordering of Ho and Fe moments. Temperature and X-ray polarization dependent measurements employed at the Ho L3 edge directly reveal a spiral spin order of the induced Ho moments in the ab-plane propagating along the c-axis, a screw-type magnetic structure. At about 22.5 K the Fe spins are observed to rotate within the basal plane inducing spontaneous electric polarization, P. Components of P in the basal plane and along the c-axis can be scaled with the separated magnetic X-ray scattering intensities of the Fe and Ho magnetic sublattices, respectively., Comment: 5 pages, 4 figures

We present a state-of-the-art x-ray diffraction study of the charge density wave order in 1T-TaS2 as a function of temperature and pressure. Our results prove that the charge density wave, which we characterize in terms of wave vector, amplitude and the coherence length, indeed exists in the superconducting region of the phase diagram. The data further imply that the ordered charge density wave structure as a whole becomes superconducting at low temperatures, i. e, superconductivity and charge density wave coexist on a macroscopic scale in real space. This result is fundamentally different from a previously proposed separation of superconducting and insulating regions in real space and, instead, provides evidence that the superconducting and the charge density wave gap exist in separate regions of reciprocal space.

X-ray diffraction measurements show that the high-temperature superconductor YBa$_2$Cu$_3$O$_{6.54}$, with ortho-II oxygen order, has charge density wave order (CDW) in the absence of an applied magnetic field. The dominant wavevector of the CDW is $\mathbf{q}_{\mathrm{CDW}} = (0, 0.328(2), 0.5)$, with the in-plane component parallel to the $\mathbf{b}$-axis (chain direction). It has a similar incommensurability to that observed in ortho-VIII and ortho-III samples, which have different dopings and oxygen orderings. Our results for ortho-II contrast with recent high-field NMR measurements, which suggest a commensurate wavevector along the $\mathbf{a}$-axis. We discuss the relationship between spin and charge correlations in YBa$_2$Cu$_3$O$_{y}$, and recent high-field quantum oscillation, NMR and ultrasound experiments., Comment: Accepted for publication in Physical Review Letters. More data along the a-axis direction is included in this version 2

Superconductivity often emerges in the proximity of, or in competition with, symmetry breaking ground states such as antiferromagnetism or charge density waves (CDW)1-5. A number of materials in the cuprate family, which includes the high-transition-temperature (high-Tc) superconductors, show spin and charge density wave order5-7. Thus a fundamental question is to what extent these ordered states exist for compositions close to optimal for superconductivity. Here we use high-energy x-ray diffraction to show that a CDW develops at zero field in the normal state of superconducting YBa2Cu3O6.67 (Tc = 67 K). Below Tc, the application of a magnetic field suppresses superconductivity and enhances the CDW. Hence, the CDW and superconductivity are competing orders in this typical high-Tc superconductor, and high-Tc superconductivity can form from a pre-existing CDW state. Our results explain observations of small Fermi surface pockets8, negative Hall and Seebeck effect9,10 and the "Tc plateau"11 in this material when underdoped., Comment: Supplementary Information is available on request

We present angle-resolved photoemission studies of (La1-zPrz)2-2xSr1+2xMn2O7 with x=0.4 and z=0.1,0.2 and 0.4 along with density functional theory calculations and x-ray scattering data. Our results show that the bilayer splitting in the ferromagnetic metallic phase of these materials is small, if not completely absent. The charge carriers are therefore confined to a single MnO2-layer, which in turn results in a strongly nested Fermi surface. In addition to this, the spectral function also displays clear signatures of an electronic ordering instability well below the Fermi level. The increase of the corresponding interaction strength with z and its magnitude of ~400 meV make the coupling to a bare phonon highly unlikely. Instead we conclude that fluctuating order, involving electronic and lattice degrees of freedom, cause the observed renormalisation of the spectral features., Comment: 4 pages, 3 figures, if not displayed correctly try Adobe Reader

The correlations between stripe order, superconductivity, and crystal structure in La(2-x)Ba(x)CuO(4) single crystals have been studied by means of x-ray and neutron diffraction as well as static magnetization measurements. The derived phase diagram shows that charge stripe order (CO) coexists with bulk superconductivity in a broad range of doping around x=1/8, although the CO order parameter falls off quickly for x<>1/8. Except for x=0.155, the onset of CO always coincides with the transition between the orthorhombic and the tetragonal low temperature structures. The CO transition evolves from a sharp drop at low x to a more gradual transition at higher x, eventually falling below the structural phase boundary for optimum doping. With respect to the interlayer CO correlations, we find no qualitative change of the stripe stacking order as a function of doping, and in-plane and out-of-plane correlations disappear simultaneously at the transition. Similarly to the CO, the spin stripe order (SO) is also most pronounced at x=1/8. Truly static SO sets in below the CO and coincides with the first appearance of in-plane superconducting correlations at temperatures significantly above the bulk transition to superconductivity (SC). Indications that bulk SC causes a reduction of the spin or charge stripe order could not be identified. We argue that CO is the dominant order that is compatible with SC pairing but competes with SC phase coherence. Comparing our results with data from the literature, we find good agreement if all results are plotted as a function of x' instead of the nominal x, where x' represents an estimate of the actual Ba content, extracted from the doping dependence of the structural transition between the orthorhombic phase and the tetragonal high-temperature phase., Comment: 16 pages, 16 figures

Hard x-ray scattering (HXS) experiments with a photon energy of 100keV were performed as a function of temperature and applied magnetic field on selected compounds of the RFe$_3$(BO$_3$)$_4$ family. The results show the presence of several unexpected diffraction features, in particular non-resonant magnetic reflections in the magnetically ordered phase, and structural reflections that violate the diffraction conditions for the low temperature phase $P3_121$ of the rare-earth iron borates. The temperature and field dependence of the magnetic superlattice reflections corroborate the magnetic structures of the borate compounds obtained by neutron diffraction. The detailed analysis of the intensity and scattering cross section of the magnetic reflection reveals details of the magnetic structure of these materials such as the spin domain structure of NdFe$_3$(BO$_3$)$_4$ and GdFe$_3$(BO$_3$)$_4$. Furthermore we find that the correlation length of the magnetic domains is around 100 \AA{} for all the compounds and that the Fe moments are rotated $53^\circ\pm3^\circ$ off from the hexagonal basal plane in GdFe$_3$(BO$_3$)$_4$, Comment: 13 figure, 12 pages

Neutron diffraction is used to probe the (H,T) phase diagram of magneto-electric (ME) LiNiPO4 for magnetic fields along the c-axis. At zero field the Ni spins order in two antiferromagnetic phases. One has commensurate (C) structures and general ordering vectors (0,0,0), the other one is incommensurate (IC) with ordering vector (0,q,0). At low temperatures the C order collapses above 12 Tesla and adopts an IC structure with modulation vector parallel to (0,q,0). We show that C order is required for the ME effect and establish how electric polarization results from a field-induced reduction of the total magneto-elastic energy., Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. B

We present new x-ray and neutron scattering measurements of stripe order in La(1.875)Ba(0.125)CuO(4), along with low-field susceptibility, thermal conductivity, and specific heat data. We compare these with previously reported results for resistivity and thermopower. Temperature-dependent features indicating transitions (or crossovers) are correlated among the various experimental quantities. Taking into account recent spectroscopic studies, we argue that the most likely interpretation of the complete collection of results is that an unusual form of two-dimensional superconducting correlations appears together with the onset of spin-stripe order. Recent theoretical proposals for a sinusoidally-modulated superconducting state compatible with stripe order provide an intriguing explanation of our results and motivate further experimental tests. We also discuss evidence for one-dimensional pairing correlations that appear together with the charge order. With regard to the overall phenomenology, we consider the degree to which similar behavior may have been observed in other cuprates, and describe possible connections to various puzzling phenomena in cuprate superconductors., Comment: 14 pages, 6 figures; several references added, accepted in Phys. Rev. B

Multiferroicity in LiCu2O2 single crystals is studied using resonant soft x-ray magnetic scattering, hard x-ray diffraction, heat capacity, magnetic susceptibility, and electrical polarization. Two magnetic transitions are found at 24.6 K (T1) and 23.2 K (T2). Our data are consistent with a sinusoidal spin structure at T2

Multiferroic TbMnO3 is investigated using x-ray diffraction in high magnetic fields. Measurements on first and second harmonic structural reflections due to modulations induced by the Mn and Tb magnetic order are presented as function of temperature and field oriented along the a and b-directions of the crystal. The relation to changes in ordering of the rare earth moments in applied field is discussed. Observations below T_N(Tb) without and with applied magnetic field point to a strong interaction of the rare earth order, the Mn moments and the lattice. Also, the incommensurate to commensurate transition of the wave vector at the critical fields is discussed with respect to the Tb and Mn magnetic order and a phase diagram on basis of these observations for magnetic fields H||a and H||b is presented. The observations point to a complicated and delicate magneto-elastic interaction as function of temperature and field., Comment: 12 pages, 15 figures, 2 references added

Ferroelectric spiral magnets DyMnO3 and TbMnO3 show similar behavior of electric polarization in applied magnetic fields. Studies of the field dependence of lattice modulations on the contrary show a completely different picture. Whereas in TbMnO3 the polarization flop from P||c to P||a is accompanied by a sudden change from incommensurate to commensurate wave vector modulation, in DyMnO3 the wave vector varies continuously through the flop transition. This smooth behavior may be related to the giant magnetocapacitive effect observed in DyMnO3.

The influence of high electric fields on the charge stripe order in Nd1.67Sr0.33NiO4 was studied by means of simultaneous hard x-ray diffraction and electrical transport experiments. Direct measurements of the charge stripe satellite peaks in zero and high electric fields provide no evidence for a deformation or a sliding of the stripe lattice, which contradicts previous indications from non-linear conductance effects. By using the order parameter of a structural phase transition for instant sample temperature measurements, non-linear transport effects can be attributed to resistive heating. Implications for the pinning of stripes in the nickelates are discussed., Comment: 4 pages, 4 figures

The interplay between crystal symmetry and charge stripe order in Pr1.67Sr0.33NiO4 and Nd1.67Sr0.33NiO4 has been studied by means of single crystal x-ray diffraction. In contrast to tetragonal La1.67Sr0.33NiO4, these crystals are orthorhombic. The corresponding distortion of the NiO2 planes is found to dictate the direction of the charge stripes, similar to the case of diagonal spin stripes in the insulating phase of La2-xSrxCuO4. In particular, diagonal stripes seem to always run along the short a-axis, which is the direction of the octahedral tilt axis. In contrast, no influence of the crystal symmetry on the charge stripe ordering temperature itself was observed, with T_CO 240K for La, Pr, and Nd. The coupling between lattice and stripe degrees of freedom allows one to produce macroscopic samples with unidirectional stripe order. In samples with stoichiometric oxygen content and a hole concentration of exactly 1/3, charge stripes exhibit a staggered stacking order with a period of three NiO2 layers, previously only observed with electron microscopy in domains of mesoscopic dimensions. Remarkably, this stacking order starts to melt about 40K below T_CO. The melting process can be described by mixing the ground state, which has a 3-layer stacking period, with an increasing volume fraction with a 2-layer stacking period., Comment: 13 pages, 13 figures

We report on a detailed single crystal x-ray diffraction study of the unconventional spin-Peierls compound TiOCl. The intermediate phase of TiOCl is characterized by an incommensurate modulation which is virtually identical to that recently found in the homologue compound TiOBr. The first order phase transition between the spin-Peierls ground state and the incommensurate phase reveals the same kind of thermal hysteresis in both, its crystal structure and magnetic susceptibility. A weak, but significant magnetic field effect is found for this phase transition with a field induced shift of the transition temperature of Delta Tc1= -0.13 K for an applied field of B=10 T along the chain direction. The field induced changes of the incommensurate crystal structure are compatible with a scenario of competing intra- and inter-chain interactions., Comment: 4 pages, 3 figures

We unambiguously demonstrate, based on high-energy x-ray diffraction data and LDA calculations, that sodium-density stripes are formed in Na0.75CoO2 at low temperatures and rule out the previously proposed Na-ordering models. The LDA calculations prove, that the sodium-density stripes lead to a sizeable dip in the density of the Co-states at the Fermi level, pointing to band structure effects as a driving force for the stripe formation. This indicates that the sodium ordering is connected to stripe-like charge correlations within the CoO2 layers, leading to an astonishing similarity between the doped cuprates and the NaxCoO2 compounds.

We have used in-field neutron and X-ray single crystal diffraction to measure the incommensurability δ of the crystal and magnetic structure of multiferroic TbMnO3 . We show that the flop in the electric polarization at the critical field HC, for field H along the a− and b−axis coincides with a 1st order transition to a commensurate phase with propagation vector κ = (0, 1/4, 0). In-field X-ray diffraction measurements show that the quadratic magneto-elastic coupling breaks down with applied field as shown by the observation of the 1st harmonic lattice reflections above and below HC . This indicates that magnetic field induces a linear magneto-elastic coupling. We argue that the commensurate phase can be described by an ordering of Mn-O-Mn bond angles., Comment: 6 pages, 4 figures

We present synchrotron x-ray diffraction studies revealing that the lattice of thulium borocarbide is distorted below T_Q = 13.5 K at zero field. T_Q increases and the amplitude of the displacements is drastically enhanced, by a factor of 10 at 60 kOe, when a magnetic field is applied along [100]. The distortion occurs at the same wave vector as the antiferromagnetic ordering induced by the a-axis field. A model is presented that accounts for the properties of the quadrupolar phase and explains the peculiar behavior of the antiferromagnetic ordering previously observed in this compound., Comment: submitted to PRL

Structural properties of the spin chain and ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ have been studied using diffraction with hard x-rays. Strong incommensurate modulation reflections are observed due to the lattice mismatch of the chain and ladder structure, respectively. While modulation reflections of low orders display only a weak temperature independence, higher orders dramatically increase in intensity when cooling the sample to 10 K. All observed modulation reflections are indexed within the super space group symmetry and no structural phase transition could be identified between 10 K and room temperature. We argue that these modulation reflections are not caused by a five-fold periodicity of the chain lattice, as claimed by Fukuda et al. Phys. Rev. B 66, 012104 (2002), but that holes localize in the potential given by the lattice modulation, which in turn gives rise to a further deformation of the lattice., Comment: 7 pages, 6 figures

Short-range lattice superstructures have been studied with high-energy x-ray diffuse scattering in underdoped, optimally doped, and overdoped $\rm (Y,Ca)Ba_2 Cu_3 O_{6+x}$. A new four-unit-cell superstructure was observed in compounds with $x\sim 0.95$. Its temperature, doping, and material dependence was used to attribute its origin to short-range oxygen vacancy ordering, rather than electronic instabilities in the $\rm CuO_2$ layers. No significant diffuse scattering is observed in YBa$_2$Cu$_4$O$_{8}$. The oxygen superstructures must be taken into account when interpreting spectral anomalies in $\rm (Y,Ca)Ba_2 Cu_3 O_{6+x}$.

We report a x-ray resonant diffraction study of the perovskite Pr0.6Ca0.4MnO3. At the Mn K-edge, this technique is sensitive to details of the electronic structure of the Mn atoms. We discuss the resonant x-ray spectra measured above and below the charge and orbital ordering phase transition temperature (TCOO = 232 K), and present a detailed analysis of the energy and polarization dependence of the resonant scattering. The analysis confirms that the structural transition is a transition to an orbitally ordered phase in which inequivalent Mn atoms are ordered in a CE-type pattern. The Mn atoms differ mostly by their 3d orbital occupation. We find that the charge disproportionation is incomplete, 3d^{3.5-\delta} and 3d^{3.5+\delta} with \delta\ll0.5 . A revised CE-type model is considered in which there are two Mn sublattices, each with partial e_{g} occupancy. One sublattice consists of Mn atoms with the 3x^{2}-r^{2} or 3y^{2}-r^{2} orbitals partially occupied, the other sublattice with the x^{2}-y^{2} orbital partially occupied., Comment: 15 pages, 15 figures

We review our recent x-ray scattering studies of charge and orbital order in doped manganites, with specific emphasis on the role of orbital correlations in Pr_1-xCa_xMnO_3. For x=0.25, we find an orbital structure indistinguishable from the undoped structure with long range orbital order at low temperatures. For dopings 0.3

We report an x-ray scattering study of octahedral tilt ordering in the manganite series Pr$_{1-x}$Ca$_x$MnO$_3$ with x=0.4 and 0.25 and in LaMnO$_3$. The sensitivity to tilt ordering is achieved by tuning the incident x-ray energy to the L$_I$, L$_{II}$ and L$_{III}$ absorption edges of Pr and La, respectively. The resulting energy-dependent profiles are characterized by a dipole-resonant peak and higher energy fine structure. The polarization dependence is predominantly $\sigma$-to-$\pi$ and the azimuthal dependence follows a sin-squared behavior. These results are similar to those obtained in recent x-ray scattering studies of orbital ordering carried out in these same materials at the Mn K edge. They lead to a description of the cross-section in terms of Templeton scattering in which the tilt ordering breaks the symmetry at the rare earth site. The most interesting result of the present work is our observation that octahedral tilt ordering persists above the orbital ordering transition temperatures in all three samples. Indeed, we identify separate structural transitions which may be associated with the onset of orbital and tilt ordering, respectively, and characterize the loss of tilt ordering versus temperature in LaMnO$_3$., Comment: 24 pages, 8 figures

We report x-ray scattering studies of broad peaks located at a (0.5 0 0)/(0 0.5 0)-type wavevector in the paramagnetic insulating phases of La_{0.7}Ca_{0.3}MnO_{3} and Pr_{0.7}Ca_{0.3}MnO_{3}. We interpret the scattering in terms of correlated polarons and measure isotropic correlation lengths of 1-2 lattice constants in both samples. Based on the wavevector and correlation lengths, the correlated polarons are found to be consistent with CE-type bipolarons. Differences in behavior between the samples arise as they are cooled through their respective transition temperatures and become ferromagnetic metallic (La_{0.7}Ca_{0.3}MnO_{3}) or charge and orbitally ordered insulating (Pr_{0.7}Ca_{0.3}MnO_{3}). Since the primary difference between the two samples is the trivalent cation size, these results illustrate the robust nature of the correlated polarons to variations in the relative strength of the electron-phonon coupling, and the sensitivity of the low-temperature ground state to such variations., Comment: 13 pages, 6 figures

We present the results of a systematic x-ray scattering study of the charge and orbital ordering in the manganite series Pr$_{1-x}$Ca$_x$MnO$_3$ with $x$=0.25, 0.4 and 0.5. The temperature dependence of the scattering at the charge and orbital wavevectors, and of the lattice constants, was characterized throughout the ordered phase of each sample. It was found that the charge and orbital order wavevectors are commensurate with the lattice, in striking contrast to the results of earlier electron diffraction studies of samples with $x$=0.5. High momentum-transfer resolution studies of the x=0.4 and 0.5 samples further revealed that while long-range charge order is present, long-range orbital order is never established. Above the charge/orbital ordering temperature T$_o$, the charge order fluctuations are more highly correlated than the orbital fluctuations. This suggests that charge order drives orbital order in these samples. In addition, a longitudinal modulation of the lattice with the same periodicity as the charge and orbital ordering was discovered in the x=0.4 and 0.5 samples. For x=0.25, only long-range orbital order was observed with no indication of charge ordering, nor of an additional lattice modulation. We also report the results of a preliminary investigation of the loss of charge and orbital ordering in the x=0.4 sample by application of a magnetic field. Finally, the polarization and azimuthal dependence of the charge and orbital ordering in these compounds is characterized both in the resonant and nonresonant limits, and compared with the predictions of current theories. The results are qualitatively consistent with both cluster and LDA+U calculations of the electronic structure., Comment: 37 pages, 22 figures

Charge ordering of V4+ and V5+ in NaV2O5 has been studied by an X-ray diffraction technique using anomalous scattering near a vanadium K-absorption edge to critically enhance a contrast between the two ions. A dramatic energy dependence of the superlattice intensities is observed below Tc=35 K. Consequently, the charge ordering pattern is the zigzag-type ladders with the unit cell 2a*2b*4c, but not the chain-type originally proposed for the spin-Peierls state. Charge disproportionation suggested in our model as the average valence V^{4.5+-delta_c/2} is observed below T_C, showing continuous variation of delta_c as a function of temperature., Comment: 4 pages, 4 figures

A neutron scattering study of the Mott-Hubbard insulator LaTiO$_{3}$ (T$_{{\rm N}}=132$ K) reveals a spin wave spectrum that is well described by a nearest-neighbor superexchange constant $J=15.5$ meV and a small Dzyaloshinskii-Moriya interaction ($D=1.1$ meV). The nearly isotropic spin wave spectrum is surprising in view of the absence of a static Jahn-Teller distortion that could quench the orbital angular momentum, and it may indicate strong orbital fluctuations. A resonant x-ray scattering study has uncovered no evidence of orbital order in LaTiO$_{3}$., Comment: final version, Phys. Rev. Lett. 85, 3946 (2000)

We report resonant x-ray scattering studies of charge and orbital order in Pr_{1-x}Ca_{x}MnO_3 with x=0.4 and 0.5. Below the ordering temperature, T_O=245 K, the charge and orbital order intensities follow the same temperature dependence, including an increase at the antiferromagnetic ordering temperature, T_N. High resolution measurements reveal, however, that long range orbital order is never achieved. Rather, an orbital domain state is formed. Above T_O, the charge order fluctuations are more highly correlated than the orbital fluctuations. Similar phenomenology is observed in a magnetic field. We conclude that the charge order drives the orbital order at the transition., Comment: 4 pages, 5 figures