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We report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the YBa2Cu3O6+x high temperature superconductor: YBa2Cu3O6.5 (Tc = 52 K), YBa2Cu3O6.7 (Tc = 67 K), and YBa2Cu3O6.85 (Tc = 87 K). The spin susceptibility is determined in absolute units at excitation energies between 1 and 140 meV and temperatures between 1.5 and 300 K. Polarization analysis is used extensively at low energies. Transitional matrix elements, including those between spin states, in a bilayer system such as YBa2Cu3O6+x can be generally classified into even and odd, according to the sign change under a symmetry operation that exchanges the layers, and both even and odd excitations are detected in YBa2Cu3O6.5 and YBa2Cu3O6.7. While the even spin excitations show a true gap which depends on doping, the odd spectrum is characterized by a weakly dopingdependent pseudogap. Both even and odd components are substantially enhanced upon lowering the temperature from 300 K. The even excitations evolve smoothly through the superconducting transition temperature Tc, but the odd excitations develop a true gap below Tc. At the same time, the odd spin susceptibility is sharply enhanced below Tc around an energy that increases with doping. This anomaly in the magnetic spectrum is closely related to the magnetic resonance peak that appears at 40 meV in the superconducting state of the optimally doped compound (Tc = 93 K). From these data we extract the energy and the energy-integrated spectral weight of the resonance peak in absolute units as a function of doping level. Theoretical implications of these measurements are discussed, and a critique of recent attempts to relate the spin excitations to the thermodynamics of high temperature superconductors is given.

We present a neutron scattering study of stripe correlations measured on a single crystal of La1.875Ba0.125CuO4. Within the low-temperature-tetragonal (LTT) phase, superlattice peaks indicative of spin and charge stripe order are observed below 50 K. For excitation energieshω ≤ 12 meV, we have characterized the magnetic excitations that emerge from the incommensurate magnetic superlattice peaks. In the ordered state, these excitations are similar to spin waves. Following these excitations as a function of temperature, we find that there is relatively little change in the Q-integrated dynamical spin susceptibility forhω ∼ 10 meV as stripe order disappears and then as the structure transforms from LTT to the low-temperature-orthorhombic (LTO) phase. The Qintegrated signal at lower energies changes more dramatically through these transitions, as it must in a transformation from an ordered to a disordered state. We argue that the continuous evolution through the transitions provides direct evidence that the incommensurate spin excitations in the disordered state are an indicator of dynamical charge stripes. An interesting feature of the thermal evolution is a variation in the incommensurability of the magnetic scattering. Similar behavior is observed in measurements on a single crystal of La1.875Ba0.075Sr0.050CuO4; maps of the scattered intensity in a region centered on the antiferromagnetic wave vector and measured athω = 4 meV are well reproduced by a model of disordered stripes with a temperature-dependent mixture of stripe spacings. We discuss the relevance of our results to understanding the magnetic excitations in cuprate superconductors.

A comprehensive inelastic neutron scattering study of magnetic excitations in the near optimally doped high-temperature superconductor 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, YBa 2 Cu 3 O 6 . Profound modifications of the spin excitation spectrum appear abruptly below the superconducting transition temperature T c , where a commensurate resonant mode and a set of weaker incommensurate peaks develop. The data are consistent with models that are based on an underlying two-dimensional Fermi surface, predicting a continuous, downward dispersion relation connecting the resonant mode and the incommensurate excitations. The magnetic incommensurability in the YBa 2 Cu 3 O 6+ x system is thus not simply related to that of another high-temperature superconductor, La 2– x Sr x CuO 4 , where incommensurate peaks persist well above T c . The temperature-dependent incommensurability is difficult to reconcile with interpretations based on charge stripe formation in YBa 2 Cu 3 O 6+ x near optimum doping.

An inelastic neutron scattering study of overdoped Bi(2)Sr(2)CaCu(2)O(8+delta) ( T(c) = 83 K) has revealed a resonant spin excitation in the superconducting state. The mode energy is E(res) = 38.0 meV, significantly lower than in optimally doped Bi(2)Sr(2)CaCu(2)O(8+delta) ( T(c) = 91 K, E(res) = 42.4 meV). This observation, which indicates a constant ratio E(res)/k(B)T(c) approximately 5.4, helps resolve a long-standing controversy about the origin of the resonant spin excitation in high temperature superconductors.

A detailed inelastic neutron scattering study of the high temperature superconductor YBa2Cu3O6.85 provides evidence of new resonant magnetic features, in addition to the well-known resonant mode at 41 meV: (i) a commensurate magnetic resonance peak at 53 meV with an even symmetry under exchange of two adjacent CuO2 layers, and (ii) high-energy incommensurate resonant spin excitations whose spectral weight is around 54 meV. The locus and the spectral weight of these modes provides unrevealed insight about the momentum shape of the electron-hole spin-flip continuum of d-wave superconductors.

Inelastic-neutron-scattering experiments have been performed to study the spin-excitation spectrum in the overdoped regime of the high-T c superconducting system YBa 2 Cu 3 O 6ϩx , xϭ0.97. All the observed magnetic fluctuations are peaked at the antiferromagnetic wave vector. In the superconducting state, the magnetic response is restricted over a limited energy range ͑បϭ33-46 meV͒. The imaginary part of the magnetic susceptibility is characterized by two contributions defined by different q widths and different temperature dependences. A resonant contribution, which displays a narrower q width, appears to be connected with superconductivity. The two contributions can be accounted for in the framework of the t-tЈ-J model in the presence of superconductivity. The main new feature in the overdoped regime is the partial disappearance of magnetic correlations for temperatures above the superconducting temperature.