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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 report inelastic neutron scattering measurements at excitation energies h cu -41 meV in YBa2Cu307. We separate magnetic and phonon contributions to the scattering cross section by a detailed analysis of the momentum dependence of the scattered intensity. The previously reported broad peak around q = (7r/a, 7r/a) in the normal state can be entirely accounted for by a phonon which primarily involves vibrations of the in-plane oxygen. Magnetic scattering centered around 41 meV and q = (m/a,~/a) appears in the superconducting state only Th.eoretical implications of these findings are discussed. PACS numbers: 74.25.Jb, 74.25.Kc, 74.72.Bk An important experimental constraint on microscopic models of the normal and superconducting states of the copper oxide superconductors is the generalized magnetic susceptibility whose imaginary part y"(q, co) is measurable by neutron scattering.Below the superconducting transition temperature of fully oxygenated YBa2Cu 306+(

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.

We report an extensive study of magnetic excitations in fully oxygenated YBa 2 Cu 3 O 7 , using neutron scattering with and without spin polarization analysis. By calibrating the measured magnetic intensity against calculated structure factors of optical phonons and against antiferromagnetic spin waves measured in the same crystal after deoxygenation to YBa 2 Cu 3 O 6.2 , we establish an absolute intensity scale for the dynamical spin susceptibility, Љ͑q,͒. The integrated spectral weight of the sharp magnetic resonance at បϭ40 meV and q ʈ ϭ(/a,/a) in the superconducting state is ͐d(ប) res Љ (q,)ϭ(0.52Ϯ0.1) at low temperatures. The energy and spectral weight of the resonance are measured up to Tϭ0.8T c . The resonance disappears in the normal state, and a conservative upper limit of 30 states/eV is established for the normal state dynamical susceptibility at q ʈ ϭ(/a,/a) and 10 meVрបр40 meV. Our results are compared to previous neutronscattering data on YBa 2 Cu 3 O 7 , theoretical interpretations of NMR data and current models of the 40 meV resonance.

Polarized and unpolarized neutron scattering has been used to determine the effect of superconductivity on the magnetic excitation spectra of YBa 2 Cu 3 O 6.5 (T c = 52K) and YBa 2 Cu 3 O 6.7 (T c = 67K). Pronounced enhancements of the spectral weight centered around 25 meV and 33 meV, respectively, are observed below T c in both crystals, compensated predominantly by a loss of spectral weight at higher energies. The data provide important clues to the origin of the 40 meV magnetic resonance peak in YBa 2 Cu 3 O 7 .

Inelastic neutron scattering has been used to obtain a comprehensive description of the absolute dynamical spin susceptibility Љ(q,) of the underdoped superconducting cuprate YBa 2 Cu 3 O 6.5 (T c ϭ52 K͒ over a wide range of energies and temperatures ͑2 meV рបр 120 meV and 5 KрTр200 K͒. Spin excitations of two distinct symmetries ͑even and odd under the exchange of two adjacent CuO 2 layers͒ are observed which exhibit two different gaplike features ͑rather than a single ''spin pseudogap''͒. The excitations show dispersive behavior at high energies.

We have used high-energy inelastic neutron scattering to detect optical magnons directly in antiferromagnetic YBa 2 Cu 3 O 6.2 . The optical magnon gap is 67Ϯ5 meV. This implies an intrabilayer superexchange constant perpendicular to the CuO 2 layers of J Ќ ϭ0.08J ʈ where J ʈ is the in-plane nearest-neighbor superexchange constant.