Incommensurate magnetic order and dynamics induced by spinless impurities in YBa(2)Cu(3)O(6.6)

Charge ordering in superconducting copper oxides

Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.

High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin-charge locking

Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La_1.875Ba_0.125CuO₄ across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.

Suppression of Superfluid Density and the Pseudogap State in the Cuprates by Impurities

We use scanning tunneling microscopy (STM) to study magnetic Fe impurities intentionally doped into the high-temperature superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Our spectroscopic measurements reveal that Fe impurities introduce low-lying resonances in the density of states at Ω_{1}≈4  meV and Ω_{2}≈15  meV, allowing us to determine that, despite having a large magnetic moment, potential scattering of quasiparticles by Fe impurities dominates magnetic scattering. In addition, using high-resolution spatial characterizations of the local density of states near and away from Fe impurities, we detail the spatial extent of impurity-affected regions as well as provide a local view of impurity-induced effects on the superconducting and pseudogap states. Our studies of Fe impurities, when combined with a reinterpretation of earlier STM work in the context of a two-gap scenario, allow us to present a unified view of the atomic-scale effects of elemental impurities on the pseudogap and superconducting states in hole-doped cuprates; this may help resolve a previously assumed dichotomy between the effects of magnetic and nonmagnetic impurities in these materials.

Momentum-dependent charge correlations in YBa2Cu3O6+δ superconductors probed by resonant X-ray scattering: evidence for three competing phases

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in YBa(2)Cu(3) O(6.55) samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a YBa(2)Cu(3)O(6.6) crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped YBa(2)Cu(3)O(6+δ).

Effect of electron correlations on magnetic excitations in the isovalently doped iron-based superconductor Ba(Fe(1-x)Ru(x))(2)As(2)

Magnetic correlations in isovalently doped Ba(Fe(1-x)Ru(x))(2)As(2) (x = 0.25, T(c) = 14.5 K; x = 0.35, T(c) = 20 K) are studied by elastic and inelastic neutron scattering techniques. A relatively large superconducting spin gap accompanied by a weak resonance mode is observed in the superconducting state in both samples. In the normal state, the magnetic excitation intensity is dramatically reduced with increasing Ru doping toward the optimally doped regime. Our results favor that the weakening of the electron-electron correlations by Ru doping is responsible for the dampening of the resonance mode, as well as the suppression of the normal state antiferromagnetic correlations near the optimally doped regime in this system.

Distinct charge orders in the planes and chains of ortho-III-ordered YBa2Cu3O(6+δ) superconductors identified by resonant elastic x-ray scattering

Recently, charge density wave (CDW) order in the CuO(2) planes of underdoped YBa(2)Cu(3)O(6+δ) was detected using resonant soft x-ray scattering. An important question remains: is the chain layer responsible for this charge ordering? Here, we explore the energy and polarization dependence of the resonant scattering intensity in a detwinned sample of YBa(2)Cu(3)O(6.75) with ortho-III oxygen ordering in the chain layer. We show that the ortho-III CDW order in the chains is distinct from the CDW order in the planes. The ortho-III structure gives rise to a commensurate superlattice reflection at Q=[0.33 0 L] whose energy and polarization dependence agrees with expectations for oxygen ordering and a spatial modulation of the Cu valence in the chains. Incommensurate peaks at [0.30 0 L] and [0 0.30 L] from the CDW order in the planes are shown to be distinct in Q as well as their temperature, energy, and polarization dependence, and are thus unrelated to the structure of the chain layer. Moreover, the energy dependence of the CDW order in the planes is shown to result from a spatial modulation of energies of the Cu 2p to 3d(x(2)-y(2)) transition, similar to stripe-ordered 214 cuprates.

Magnetic proximity effect in YBa2Cu3O7/La(2/3)Ca(1/3)MnO3 and YBa2Cu3O7/LaMnO(3+δ) superlattices

Using neutron reflectometry and resonant x-ray techniques we studied the magnetic proximity effect (MPE) in superlattices composed of superconducting YBa2Cu3O7 and ferromagnetic-metallic La0.67Ca0.33MnO3 or ferromagnetic-insulating LaMnO(3+δ). We find that the MPE strongly depends on the electronic state of the manganite layers, being pronounced for the ferromagnetic-metallic La0.67Ca0.33MnO3 and almost absent for ferromagnetic-insulating LaMnO(3+δ). We also detail the change of the magnetic depth profile due to the MPE and provide evidence for its intrinsic nature.

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang et al (2006 Phys. Rev. B 73 174501). This ansatz has had success in describing a range of experiments. The motivation underlying this ansatz is described and the comparisons with experiment are reviewed. Implications for a more microscopic theory are discussed together with the relation to theories that start directly from microscopic strongly coupled Hamiltonians.

Hidden itinerant-spin phase in heavily overdoped La(2-x)Sr(x)CuO4 superconductors revealed by dilute Fe doping: a combined neutron scattering and angle-resolved photoemission study

We demonstrated experimentally a direct way to probe a hidden propensity to the formation of a spin-density wave in a nonmagnetic metal with strong Fermi surface nesting. Substituting Fe for a tiny amount of Cu (1%) induced an incommensurate magnetic order below 20 K in heavily overdoped La(2-x)Sr(x)CuO(4). Elastic neutron scattering suggested that this order cannot be ascribed to the localized spins on Cu or doped Fe. Angle-resolved photoemission revealed a strong Fermi surface nesting inherent in the pristine La(2-x)Sr(x)CuO(4) that likely drives this order. Our finding presents the first example of the long-sought "itinerant-spin extreme" of cuprates, where the spins of itinerant doped holes define the magnetic ordering ground state; it complements the current picture of cuprate spin physics that highlights the predominant role of localized spins at lower dopings.

Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.

Disorder-induced freezing of dynamical spin fluctuations in underdoped cuprate superconductors

We study the dynamical spin susceptibility of a correlated d-wave superconductor (dSC) in the presence of nonmagnetic disorder, using an unrestricted Hartree-Fock approach. This model provides a concrete realization of the notion that disorder slows down spin fluctuations, which eventually "freeze out." The evolution of disorder-induced spectral weight transfer agrees qualitatively with experimental observations on underdoped cuprate superconductors. For sufficiently large disorder concentrations, static spin density wave (SDW) order is created when droplets of magnetism nucleated by impurities overlap. We also study the disordered stripe state coexisting with a dSC and compare its magnetic fluctuation spectrum to that of the disorder-generated SDW phase.