We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa$_2$Cu$_3$O$_{6.6}$, an underdoped high-temperature superconductor that exhibits a prominent spin-pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin-pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La$_{2-x}$Sr$_x$CuO$_{4}$ suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.
We study isotropic antiferromagnetic Heisenberg chains coupled by antiferromagnetic Ising interaction as an effective spin model for the ytterbium aluminum perovskite YbAlO$_3$. Using the density-matrix renormalization group (DMRG) method we calculate the magnetization curve, local spin, central charge, and dynamical spin structure factors in the presence of magnetic field. From the fitting of the experimental magnetization curve, the effective intrachain and interchain couplings are estimated as $J=2.3$K and $J_{\rm ic}=0.8$K, respectively. We can quantitatively explain the experimental obser…
We use inelastic neutron scattering to demonstrate that at low temperatures, the low frequency magnetic fluctuations in YBa_2Cu_3O_{6.6} ($T_c=62.7$ K) are incommensurate, being found at positions displaced by $\pmδ$ ($0.057\pm 0.006$ r.l.u.) along the $[π,π]$ direction from the wave vector $(π,π)$ associated with the antiferromagnetic order of the parent insulator, YBa_2Cu_3O_{6}. The dynamical susceptibility $χ''(q,ω)$ at the incommensurate positions increases on cooling below $T_c$, accompanied by a suppression of magnetic fluctuations at the commensurate points.
Motivated by the recent observations of incommensurate magnetic order and electric polarization in YBaCuFeO5 up to temperatures TN2 as high as 230K [1,2] we report here for the first time a model for the incommensurate magnetic structure of this material that we complement with ab-initio calculations of the magnetic exchange parameters. Using neutron powder diffraction we show that the appearance of polarization below TN2 is accompanied by the replacement of the high temperature collinear magnetic order by a circular inclined spiral with propagation vector ki=(1/2, 1/2, 1/2+-q). Moreover, we f…
Detailed neutron scattering measurements of YBa_2Cu_3O_6.95 found that the resonance peak and incommensurate magnetic scattering induced by superconductivity represent the same physical phenomenon: two dispersive branches that converge near 41 meV and the in-plane wave-vector q_af=(pi/a, pi/a) to form the resonance peak. One branch has a circular symmetry around q_af and quadratic downward dispersion from ~41 meV to the spin gap of 33+-1meV. The other, of lower intensity, disperses from ~41 meV to at least 55 meV. Our results exclude a quartet of vertical incommensurate rods in q-w space expec…
We present a neutron-scattering study of the static and dynamic spin correlations in the underdoped high-temperature superconductor YBa(2)Cu(3)O(6.45) in magnetic fields up to 15 T. The field strongly enhances static incommensurate magnetic order at low temperatures and induces a spectral-weight shift in the magnetic-excitation spectrum. A reconstruction of the Fermi surface driven by the field-enhanced magnetic superstructure may thus be responsible for the unusual Fermi surface topology revealed by recent quantum-oscillation experiments.
Polarized and unpolarized neutron triple-axis spectrometry was used to study the dynamical magnetic susceptibility $χ^{\prime\prime}({\bf q},ω)$ as a function of energy ($\hbarω$) and wave vector (${\bf q}$) in a wide temperature range for the bilayer superconductor YBa$_2$Cu$_3$O$_{6+x}$ with oxygen concentrations, $x$, of 0.45, 0.5, 0.6, 0.7, 0.8, 0.93, and 0.95. The most prominent features in the magnetic spectra include a spin gap in the superconducting state, a pseudogap in the normal state, the much-discussed resonance, and incommensurate spin fluctuations below the resonance. We establi…
Using a spin-rotation invariant version of the slave-boson approach we investigate the relative stability and band structure of various incommensurate phases in the cuprates. Our findings obtained in the Hubbard model with next-nearest neighbor hopping $-t'/t\simeq 0.15$, as appropriate for the La$_{2-x}$Sr$_x$CuO$_4$ family, support the formation of diagonal (vertical) stripe phases in the doping regime $x=1/16$ ($x=1/8$), respectively. In contrast, based on the fact that a larger value $-t'/t=0.3$ expected for YBa$_2$Cu$_3$O$_{6+δ}$ triggers a crossover to the diagonal (1,1) spiral phase at …
A comprehensive inelastic neutron scattering study of magnetic excitations in the near-optimally doped high-temperature superconductor ${\rm YBa_{2}Cu_{3}O_{6.85}}$ is presented. The spin correlations in the normal state are commensurate with the crystal lattice, and the intensity is peaked around the wave vector characterizing the antiferromagnetic state of the insulating precursor ${\rm YBa_{2}Cu_{3}O_{6}}$. Profound modifications of the spin excitation spectrum appear abruptly below the superconducting transition temperature, $\rm T_C$, where a commensurate resonant mode and a set of weaker…
Motivated by a recent neutron scattering experiment on detwinned YBa$_2$Cu$_3$O$_{6+δ}$ superconductor, we examine the frequency and doping dependence of the anisotropy in the spin and charge fluctuation arising from the coupling between the plane and the chain. Starting from the two-dimensional $t$-$t^{'}$-$J$ model and using the random-phase approximation (RPA), we find a pronounced anisotropy of the incommensurate (IC) peaks in the spin channel, namely the peak intensity at the $(π\pmδ,π)$ direction is stronger than that at the $(π,π\pmδ)$ direction in a wide frequency range from $ω=0.2J$ t…
We have investigated the spin fluctuations at energy transfers up to ~110 meV, well above the resonance energy (33 meV) in the YBa2Cu3O6.5 ortho-II superconductor using neutron time-of-flight and triple-axis techniques. The spectrum at high energies differs from the low-energy incommensurate modulations previously reported where the incommensurate wave vector is largely independent of energy. Well above the resonance the peak of the spin response lies at wave vectors that increase with energy. Within error the excitations at all energies above the resonance are best described by a ring around …
We study the spin fluctuation dynamics of Cu-O chains in the oxygen deficient planes of YBa(2)Cu(3)O(6+x). The chains are described by a model including antiferromagnetic interactions between the spins and Kondo-like scattering of the oxygen holes by the copper spins. There are incommensurate spin fluctuations along the direction of the chains. The dynamic structure factor of this system is qualitatively different from that of a quasi one-dimensional localized antiferromagnet due to the presence of itinerant holes. We compute the dynamic structure factor that could be measured in neutron scatt…
We study the spin fluctuation of the oxygen deficient planes of YBa(2)Cu(3)O(6+x). The Cu-O chains that constitute these planes are described by a model that includes antiferromagnetic interactions between spins and Kondo-like scattering of oxygen holes. The spectrum of magnetic excitations shows the presence of incommensurate dynamic fluctuations along the direction of the chains. The presence of itinerant holes is responsible for the existence of important differences between the spin dynamics of this system and that of a quasi-one-dimensional localized antiferromagnet. We comment on the pos…
We investigate the nature of the quantum phase transition out of charge-density-wave phase in the spinless fermion model with nearest- and next-nearest-neighbor interaction at one-third filling. Using an extensive Density Matrix Renormalization Group (DMRG) simulations we show that the transition changes it nature. We show that for weak next-nearest-neighbor coupling the transition is of Kosterlitz-Thouless type in agreement with bosonisation predictions. We also provide strong numerical evidences that for large next-nearest-neighbor repulsion the transition belongs to the Pokrovsky-Talapov un…
Recent inelastic neutron scattering measurements found that the spin susceptibility of detwinned and highly ordered ortho-II YBa_2Cu_3O_{6.5} exhibits, in both the normal and superconducting states, one-dimensional incommensurate modulations at low energies which were interpreted as a signature of dynamic stripes. We propose an alternative model based on quasiparticle transitions between the arcs of a truncated Fermi surface. Such transitions are resonantly enhanced by scattering to the triplet spin resonance. We show that the anisotropy in the experimental spin response is consistent with thi…
Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa$_2$Cu$_3$O$_{6+x}$ in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface. Here we use resonant X-ray scattering to demonstrate …
It is shown that in the t-J model of Cu-O planes at low frequencies the dynamic spin structure factor is peaked at incommensurate wave vectors (1/2+-delta,1/2)$, (1/2,1/2+-delta). The incommensurability is connected with the momentum dependencies of the magnon frequency and damping near the antiferromagnetic wave vector. The behavior of the incommensurate peaks is similar to that observed in La_{2-x}(Ba,Sr)_xCuO_{4+y} and YBa_2Cu_3O_{7-y}: for hole concentrations 0.02<x<=0.12 we find that delta is nearly proportional to x, while for x>0.12 it tends to saturation. The incommensurability disappe…
We report the results a comprehensive study of charge density wave (CDW) correlations in untwinned YBCO6+x single crystals with 0.4<x<0.99 using Cu-L3 edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for 0.45<x<0.93, but not for samples with x<0.44 that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with x=0.99. This suggests the presence of two proximate zero-temperature CDW critical points at doping pc1~0.08 and pc2~0.18. The CDW reflections are observed at incommensurate in-plane wave vectors (d_a, 0) and (0, d_b). Both decrease lin…
We present a neutron triple-axis and resonant spin-echo spectroscopy study of the spin correlations in untwinned YBCO crystals with x= 0.3, 0.35, and 0.45 as a function of temperature and magnetic field. As the temperature T approaches 0, all samples exhibit static incommensurate magnetic order with propagation vector along the a-direction in the CuO2 planes. The incommensurability delta increases monotonically with hole concentration, as it does in LSCO. However, delta is generally smaller than in LSCO at the same doping level. The intensity of the incommensurate Bragg reflections increases w…
We study magnetic order induced by non-magnetic impurities in quantum paramagnets with incommensurate host spin correlations. In contrast to the well-studied commensurate case where the defect-induced magnetism is spatially disordered but non-frustrated, the present problem combines strong disorder with frustration and, consequently, leads to spin-glass order. We discuss the crossover from strong randomness in the dilute limit to more conventional glass behavior at larger doping, and numerically characterize the robust short-range order inherent to the spin-glass phase. We relate our findings …
We report a detailed Raman scattering study of the lattice dynamics in detwinned single crystals of the underdoped high temperature superconductor YBa2Cu3O6+x (x=0.75, 0.6, 0.55 and 0.45). Whereas at room temperature the phonon spectra of these compounds are similar to that of optimally doped YBa2Cu3O6.99, additional Raman-active modes appear upon cooling below ~170-200 K in underdoped crystals. The temperature dependence of these new features indicates that they are associated with the incommensurate charge density wave state recently discovered using synchrotron x-ray scattering techniques o…
Contrary to a widely accepted view the phase diagrams of La$_{2-x}$Sr$_x$CuO$_4$ and YBa$_2$Cu$_3$O$\rm_{6+y}$, in spite of similarities are remarkably different. Both the electric conduction properties and the commensurate/incommensurate spin ordering properties differ dramatically. It is argued that the role of disorder in YBCO is insignificant while the bilayer structure is crucial. On the other hand in LSCO the intrinsic disorder to a large extent drives the properties of the system. The developed approach explains the low-temperature magnetic properties of the systems. The most important …
Charge density wave (CDW) correlations have recently been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured by x-ray scattering at zero and low fields. Here we combine a pulsed magnet with an x-ray free electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields up to 28 Tesla. While the zero-field CDW order, which develops below T ~ 150 K, is essentially two-dimensional, at lower temperature and beyond 15 Tesla, another three-dimensionally ordered CDW eme…
The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t-J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at the momenta $({1/2},{1/2}\pmδ)$, $({1/2}\pmδ,{1/2})$ and at $({1/2}\pmδ,{1/2}\pmδ)$, $({1/2}\pmδ,{1/2}\mpδ)$ in the lower and upper parabolas, respectively. The upper parabola reflects the disper…
We show that a new resonant magnetic excitation at incommensurate momenta, observed recently by inelastic neutron scattering experiments on YBa$_2$Cu$_3$O$_{6.85}$ and YBa$_2$Cu$_3$O$_{6.6}$, is a {\it spin exciton}. Its location in the magnetic Brillouin zone and its frequency are determined by the momentum dependence of the particle-hole continuum. We identify several features that distinguish this novel mode from the previous resonance mode observed near ${\bf Q}=(π,π)$, such as its intensity maximum which occurs in a different part of the magnetic Brillouin zone.
We report a comprehensive Cu L$_3$-edge resonant x-ray scattering study of two- and three-dimensional (2D and 3D) incommensurate charge correlations in single crystals of the underdoped high-temperature superconductor YBa$_2$Cu$_3$O$_{6.67}$ under uniaxial compression up to 1% along the two inequivalent Cu-O-Cu bond directions (a and b) in the CuO$_2$ planes. The pressure response of the 2D charge correlations is symmetric: pressure along a enhances correlations along b, and vice versa. Our results imply that the underlying order parameter is uniaxial. In contrast, 3D long-range charge order i…
Motivated by recent progress on field-induced phase transitions in quasi-one-dimensional quantum antiferromagnets, we study the phase diagram of $S=1/2$ antiferromagnetic Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations. The interchain interactions is shown to enhance longitudinal spin correlations to stabilize an incommensurate longitudinal spin density wave order at low temperatures. With increasing field the ground state changes to a canted antiferromagnetic order until the magnetization fully s…
Recent experiments have revealed incommensurate charge density wave (CDW) in the pseudogap regime in underdoped cuprates, e.g. YBa$_2$Cu$_3$O$_{6+δ}$ and HgBa$_2$CuO$_{4+δ}$. However, its relationship with the pseudogap is still controversial. In this work, we take a phenomenological synthesis of the doped resonating valence bond (RVB) state and the CDW order. Starting from the Yang-Rice-Zhang Green's function ansatz for the doped RVB state [Phys. Rev. B {\bf 73}, 174501 (2006)], in which the Fermi surface is partially truncated into four nodal hole-like Fermi pockets by the antinodal RVB gap,…
While charge density wave (CDW) instabilities are ubiquitous to superconducting cuprates, the different ordering wavevectors in various cuprate families have hampered a unified description of the CDW formation mechanism. Here we investigate the temperature dependence of the low energy phonons in the canonical CDW ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$. We discover that the phonon softening wavevector associated with CDW correlations becomes temperature dependent in the high-temperature precursor phase and changes from a wavevector of 0.238 reciprocal space units (r.l.u.) below the o…
When sufficient numbers of holes are introduced into the two-dimensional CuO2 square lattice, dynamic magnetic correlations become incommensurate with underlying lattice in all previously investigated La_{2-x}A_xCu_{1-z}B_zO_{4+y} (A=Sr or Nd, B=Zn) including high T_C superconductors and insulators, and in bilayered superconducting YBa_2Cu_3O_{6.6} and Bi_2Sr_2CaCu_2O_8. Magnetic correlations also become incommensurate in structurally related La_2NiO_4 when doped with Sr or O. We report an exception to this so-far well established experimental "rule" in La_2Cu_{1-z}Li_{z}O_4 in which magnetic …
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 refl…
Recent inelastic neutron scattering (INS) experiments on La$_{2-x}$Sr$_x$CuO$_4$ have established the existence of a {\it magnetic coherence effect}, i.e., strong frequency and momentum dependent changes of the spin susceptibility, $χ''$, in the superconducting phase. We show, using the spin-fermion model for incommensurate antiferromagnetic spin fluctuations, that the magnetic coherence effect establishes the ability of INS experiments to probe the electronic spectrum of the cuprates, in that the effect arises from the interplay of an incommensurate magnetic response, the form of the underlyi…
We study the magnetic behaviors of a spin-1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the field-induced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Isi…
We have measured the spin fluctuations in the YBa2Cu3O6.5 (YBCO6.5, Tc=59 K) superconductor at high-energy transfers above ~ 100 meV. Within experimental error, the momentum dependence is isotropic at high-energies, similar to that measured in the insulator for two dimensional spin waves, and the dispersion extrapolates back to the incommensurate wave vector at the elastic position. This result contrasts with previous expectations based on measurements around 50 meV which were suggestive of a softening of the spin-wave velocity with increased hole doping. Unlike the insulator, we observe a sig…
Motivated by recent inelastic neutron scattering experiments up to a high-energy region for La-based cuprates, we compute (q,omega) maps of the imaginary part of the dynamical magnetic susceptibility chi(q,omega) in the slave-boson mean-field approximation to the two-dimensional t-J model. While the strong spectral weight appears at incommensurate positions, namely at q neq Q =(pi,pi), for low energy, the incommensurate signals disperse with increasing omega and finally merge into a commensurate signal at a particular energy omega=omega_Q. These features are seen in both the d-wave pairing sta…
Combining inelastic neutron scattering and numerical simulations, we study the quasi-one dimensional Ising anisotropic quantum antiferromagnet \bacovo\ in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinl…
Neutron scattering can provide detailed information about the energy and momentum dependence of the magnetic dynamics of materials provided sufficiently large single crystals are available. This requirement has limited the number of rare earth high temperature superconducting materials that have been studied in any detail. However, improvements in crystal growth in recent years has resulted in considerable progress in our understanding of the behaviour of the magnetism of the CuO planes in both the superconducting and normal state. This review will focus primarily on the spin fluctuations in L…
We study spin and charge susceptibilities in the d-wave superconducting state whose underlying electronic dispersion is anisotropic due to the formation of the electronic nematic order. We show that the amplitude of the incommensurate peaks in the spin susceptibility near (π,π) reveals a pronounced anisotropy in the momentum space. The relevance of our findings to the magnetic scattering pattern observed in a recent neutron scattering measurement on untwinned YBa_2Cu_3O_{6+x} is discussed. In the charge channel, we identify a well-defined collective mode at small momentum transfer with strong …
In this communication we consider the doping dependence of the strong antiferromagnetic spin fluctuations in the cuprate superconductors. We investigate the effect of an incommensurate magnetic response, as recently observed in inelastic neutron scattering (INS) experiments on several YBa_2Cu_3O_{6+x} compounds, on the spin-lattice and spin-echo relaxation rates measured in nuclear magnetic resonance (NMR) experiments. We conclude that a consistent theoretical description of INS and NMR can be reached if one assumes spatially inhomogeneous but locally commensurate spin correlations and that NM…
We measure the magnetic susceptibility nearby Li spinless impurities in the superconducting phase of the high Tc cuprate YBaCuO. The induced moment which was found to exist above Tc persists below Tc. In the underdoped regime, it retains its Curie law below Tc. In contrast, near optimal doping, the large Kondo screening observed above Tc (T_K=135 K) is strongly reduced below Tc as expected theoretically when the superconducting gap develops. This moment still extends essentially on its 4 near neighbour Cu, showing the persistence of AF correlations in the superconducting state. A direct compar…
Electronic phases with symmetry properties matching those of conventional liquid crystals have recently been discovered in transport experiments on semiconductor heterostructures and metal oxides at milli-Kelvin temperatures. We report the spontaneous onset of a onedimensional, incommensurate modulation of the spin system in the high-temperature superconductor YBa2Cu3O6.45 upon cooling below ~150 K, while static magnetic order is absent above 2 K. The evolution of this modulation with temperature and doping parallels that of the in-plane anisotropy of the resistivity, indicating an electronic …
Inelastic neutron scattering experiments have been performed on lightly-doped La$_{1.96}$Sr$_{0.04}$CuO$_{4}$, which shows diagonal incommensurate spin correlations at low temperatures. We previously reported that this crystal, with a single orthorhombic domain, exhibits the "hourglass" dispersion at low energies [Phys. Rev. Lett. 101, 197001 (2008)]. In this paper, we investigate in detail the energy evolution of the magnetic excitations up to 65 meV. It is found that the anisotropic excitations at low energies, dispersing only along the spin modulation direction, crossover to an isotropic, c…
As additional neutron scattering experiments are performed on a variety of high temperature superconducting compounds it appears that magnetic incommensuration is a phenomenon common to all of the samples studied. The newest experimental results indicate that incommensurate peaks exist at momentum ${\bf q}=π(1,1\pmδ)$ and $π(1\pmδ,1)$ in $La_{2-x}Sr_xCuO_4}$ (LSCO) and ${\rm YBa_2Cu_3O_{7-δ}}$ (YBCO). The dependence of $δ$ with hole doping appears to be similar in both materials. In addition, new ARPES data for LSCO as a function of doping show that its Fermi surface is qualitatively similar t…
Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard lattice with nearest and next-to-nearest neighbor interactions. We calculate the phase diagram at half filling, which presents, in particular, an interaction-induced quantum anomalous Hall phase. We study the system at incommensurate fillings using an unrestricted Hartree-Fock ansatz and report a rich zoo of solutions such as self-trapped polarons and domain …
