The concept that superconductivity competes with other orders in cuprate superconductors has become increasingly apparent, but obtaining direct evidence with bulk-sensitive probes is challenging. We have used resonant soft x-ray scattering to identify two-dimensional charge fluctuations with an incommensurate periodicity of similar to 3.2 lattice units in the copper-oxide planes of the superconductors (Y,Nd)Ba2Cu3O6+x, with hole concentrations of 0.09 to 0.13 per planar Cu ion. The intensity and correlation length of the fluctuation signal increase strongly upon cooling down to the superconducting transition temperature (T-c); further cooling below T-c abruptly reverses the divergence of the charge correlations. In combination with earlier observations of a large gap in the spin excitation spectrum, these data indicate an incipient charge density wave instability that competes with superconductivity

Intense paramagnon excitations in a large family of high-temperature superconductor

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.

We probe the collective magnetic modes of La2CuO4 and underdoped La2-xSrxCuO4 (LSCO) by momentum resolved resonant inelastic x-ray scattering (RIXS) at the Cu L3 edge. For the undoped antiferromagnetic sample, we show that the single magnon dispersion measured with RIXS coincides with the one determined by inelastic neutron scattering, thus demonstrating that x rays are an alternative to neutrons in this field. In the spin dynamics of LSCO, we find a branch dispersing up to approximately 400 meV coexisting with one at lower energy. The high-energy branch has never been seen before. It indicates that underdoped LSCO is in a dynamic inhomogeneous spin state.

Heisenberg interactions are ubiquitous in magnetic materials and have been prevailing in modeling and designing quantum magnets. Bonddirectional interactions 1-3 offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model 4 , which has a quantum spin liquid (QSL) as its exact ground state. Honeycomb iridates, A 2 IrO 3 (A=Na,Li), offer potential realizations of the Kitaev model, and their reported magnetic behaviors may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bonddirectional interactions remains indirect or conjectural. Here, we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na 2 IrO 3 and show that they lead to strong magnetic frustration. Diffuse magnetic xray scattering reveals broken spin-rotational symmetry even above T N , with the three spin components exhibiting nano-scale correlations along distinct crystallographic directions. This spinspace and real-space entanglement directly manifests the bond-directional interactions, provides the missing link to Kitaev physics in honeycomb iridates, and establishes a new design strategy toward frustrated magnetism.Iridium (IV) ions with pseudospin-1/2 moments form in Na 2 IrO 3 a quasi-two-dimensional (2D) honeycomb network, which is sandwiched between two layers of oxygen ions that frame edge-shared octahedra around the magnetic ions and mediate superexchange interactions between neighboring pseudospins (Fig. 1a). Owing to the particular spin-orbital structure of the pseudospin 5,6 , the isotropic part of the magnetic interaction is strongly suppressed in the 90• bonding geometry of the edgeshared octahedra 2,3 , thereby allowing otherwise subdominant bond-dependent anisotropic interactions to play the main role and manifest themselves at the forefront of magnetism. This bonding geometry, common to many transition-metal oxides, in combination with the pseudospin that arises from strong spin-orbit coupling gives rise to an entirely new class of magnetism beyond the traditional paradigm of Heisenberg magnets. On a honeycomb lattice, for instance, the leading anisotropic interactions take the form of the Kitaev model 3 , which is a rare example of exactly solvable models with nontrivial properties such as Majorana fermions and non-abelian statistics, and with potential links to quantum computing 4 . Realization of the Kitaev model is now being intensively sought out in a growing number of materials 7-13 , including 3D extensions of the honeycomb Li 2 IrO 3 , dubbed "hyper-honeycomb" 7 and "harmonichoneycomb" 8 , and 4d transition-metal analogs such as RuCl 3 12 and Li 2 RhO 3 13 . Although most of these are known to magnetically order at low temperature, they exhibit a rich array of magnetic structures including zigzag 14-16 , spiral 17 , and other more complex non-coplanar structures 18,19 that are predicted to occur in the vicinity of the Kitaev QSL phase [20][21][22][23] , which hosts man...

We measured the momentum dependence of magnetic excitations in the model spin-1=2 2D antiferromagnetic insulator Sr 2 CuO 2 Cl 2 (SCOC). We identify a single-spin-wave feature and a multimagnon continuum, with different polarization dependences. The spin waves display a large (70 meV) dispersion between the zone-boundary points (, 0) and (=2, =2). Employing an extended t-t 0 -t 00 -U one-band Hubbard model, we find significant electronic hopping beyond nearest-neighbor Cu ions, indicative of extended magnetic interactions. The spectral line shape at (, 0) indicates sizable quantum effects in SCOC and probably more generally in the cuprates. DOI: 10.1103/PhysRevLett.105.157006 PACS numbers: 74.72.Cj, 75.30.Ds, 78.70.Ck Magnetism in low-dimensional cuprates remains of considerable interest, in relation both to the fundamental quest to understand strong electron correlation and quantum spin effects in Mott insulators, and to the search for the mechanism of high-T c superconductivity. To lowest order, the undoped cuprate superconductors can be described by the spin 1=2 two-dimensional (2D) square-lattice nearestneighbor (NN) Heisenberg antiferromagnet, which is among the simplest and most studied models in magnetism [1]. The ground state displays classical order, reduced by quantum fluctuations at zero temperature and destroyed by thermal fluctuations at finite temperature. A possible crossover between renormalized classical [2] and quantum critical [3] scaling was tested experimentally in the undoped cuprates Sr 2 CuO 2 Cl 2 (SCOC) [4] and La 2 CuO 4 (LCO) [5], and in the organometallic salt CuðDCOOÞ 2 Á 4D 2 O (CFTD) [6]. However, while the latter shows only nearest-neighbor coupling, high-energy inelastic neutron scattering (INS) data on LCO [7] suggest that further-neighbor magnetic interactions influence the scaling measurements. Frustrated further-neighbor interactions could also bring the undoped cuprates closer to the valence bond liquid proposed as mechanism for superconductivity [8].It is therefore timely to investigate the excitation spectrum of SCOC, as an important model system. Inelastic neutron scattering (INS) measurements of SCOC have been limited to low energies and small momenta around the ordering wave vector [4]. In this Letter we report the full magnetic excitation spectrum measured by resonant inelastic x-ray scattering (RIXS). We discover a surprisingly large dispersion along the magnetic Brillouin zone boundary (ZB). An analysis of the data in terms of an extended Hubbard model yields a quantitative estimation of sizable further-neighbor electronic hopping. The resulting series of longer-ranged magnetic interactions enhance quantum fluctuations, in agreement with the reduced ordered moment. The importance of quantum fluctuations is further revealed by differences in the spectral line shapes at the (À, 0) and (À=2, =2) ZB points.SCOC is an insulating single-layer parent compound of the high-T c superconducting (SC) materials. It is isostructural to the high-temperature tetragonal phase of...

Using resonant inelastic x-ray scattering (RIXS) at the Cu L-absorption edge, we have observed intense, dispersive spin excitations in highly overdoped Tl2Ba2CuO 6+δ (superconducting Tc = 6 K), a compound whose normal-state charge transport and thermodynamic properties have been studied extensively and shown to exhibit canonical Fermi-liquid behavior. Complementary RIXS experiments on slightly overdoped Tl2Ba2CuO 6+δ (Tc = 89 K) and on Y1−xCaxBa2Cu3O 6+δ compounds spanning a wide range of doping levels indicate that these excitations exhibit energies and energy-integrated spectral weights closely similar to those of antiferromagnetic magnons in undoped cuprates. The surprising coexistence of Fermi-liquid-like charge excitations and high-energy spin excitations reminiscent of antiferromagnetic insulators in highly overdoped compounds poses a challenge to current theoretical models of the cuprates.High temperature superconductivity arises when the CuO 2 planes of layered copper-oxide compounds are doped with mobile charge carriers. When the number of mobile carriers per Cu atom, p, vanishes, the CuO 2 planes are antiferromagnetically ordered and exhibit conventional spin wave excitations with a total bandwidth of ∼ 300 meV. For hole doping p 0.05, the antiferromagnetic long-range order disappears, and the low-temperature ground state becomes superconducting. Inelastic neutron scattering (INS) experiments have demonstrated that dispersive spin excitations akin to antiferromagnetic spin waves persist in the superconducting state, although their low-energy spectral weight is progressively reduced with increasing p. According to current theories, these "paramagnon" excitations act as a key driving force for Cooper pairing [1]. Up to now, however, the INS studies have been largely limited to underdoped (0.05 p 0.15) [2-4] and lightly overdoped (0.15 p 0.2) cuprates, [5-7] where the spectral features attributable to paramagnons remain relatively sharp and intense. In the highly overdoped regime (p > 0.2), where the superconducting transition temperature, T c , and the superconducting energy gap are sharply reduced and eventually vanish, [8-10] INS experiments have thus far only been reported for a single cuprate family, La 2−x Sr x CuO 4 (La-214). [11, 12] They show progressive weakening of the spin excitations with energies E100 meV, continuing the trend already identified in the underdoped regime, but also indicate that excitations at higher E are less affected by doping. Since La-214 exhibits incommensurate magnetic order ("stripes") near optimal doping, and its T c is limited to ∼ 40 K, it is unclear whether these findings are generic for the cuprate superconductors. Recent resonant inelastic xray scattering (RIXS) experiments [13,14] allowed the detection of dispersive high-energy (E 100 meV) spin excitations in optimally doped cuprates with maximal T c ∼ 90 K, as well as in iron-based superconductors [15]. Although these high-energy paramagnons are strongly broadened by scattering from mobile carriers and thus diff...

We show that, contrary to common lore, in resonant inelastic x-ray scattering (RIXS) at the copper L-and M-edge direct spin-flip scattering is in principle allowed. We demonstrate how this possibility can be exploited to probe the momentum dependent magnetic properties of cuprates such as the high Tc superconductors and compute in detail the relevant local and momentum dependent magnetic scattering amplitudes, which we compare to the elastic and dd-excitation scattering intensities. For cuprates these results put RIXS as a technique on the same footing as neutron scattering.Introduction. In recent years the experimental technique of resonant inelastic x-ray scattering (RIXS) has made tremendous progress in terms of energy and momentum resolution [1,2,3,4,5,6,7,8,9,10,11]. RIXS is particularly apt to probe the properties of strongly correlated electrons, for instance the ones of the transition metal oxides [1,2]. With an incoming x-ray of energy ω in first an electron is resonantly excited from a core level into the valence shell. Subsequently one measures the energy ω out of the outgoing x-ray resulting from the recombination of the core hole with a valence electron. Depending on the resonance that the experiment is performed at, ω in corresponds to the transition metal K-edge (1s → 4p), L-edge (2p → 3d) or M-edge (3p → 3d). Compared to the many other photon scattering techniques, RIXS has the advantage that there is no core hole present in the final state, so that the energy lost by the scattered photon at a transition metal L-or M-edge is directly related to electronic excitations within the strongly correlated 3d valence bands. The chemical selectivity and bulk sensitivity of RIXS allows the study of the electronic and magnetic properties of, for example, complex and nanostructured materials that might be inaccessible with non-resonant techniques.