Polarized and unpolarized neutron triple-axis spectrometry was used to study the dynamical magnetic susceptibility Χ″(q, ω) as a function of energy (ℏ ω) and wave vector (q) in a wide temperature range for the bilayer superconductor YBa2Cu3O6+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 establish the doping dependence of the spin gap in the superconducting state, the resonance energy, and the incommensurability of the spin fluctuations. The magnitude of the spin gap (Esg) up to the optimal doping is proportional to the superconducting transition temperature Tc with Esg/kBTc = 3.8. The resonance, which exists exclusively below Tc for highly doped YBa2Cu3O6+x with x = 0.93 and 0.95, appears above Tc for underdoped compounds with x≤0.8. The resonance energy (Er) also scales with kBTc, but saturates at Er≈40 meV for x close to 0.93. The incommensurate spin fluctuations at energies below the resonance have structures similar to that of the single-layer superconducting La2-xSrxCuO4. However, there are also important differences. While the incommensurability (δ) of the spin fluctuations in La2-xSrxCuO4 is proportional to Tc for the entire hole-doping range up to the optimal value, the incommensurability in YBa2Cu3O6+x increases with Tc for low-oxygen doping and saturates to δ = 0.1 for x≥0.6. In addition, the incommensurability decreases with increasing energy close to the resonance. Finally, the incommensurate spin fluctuations appear above Tc in underdoped compounds with x≤0.6 but for highly doped materials they are only observed below Tc. We discuss in detail the procedure used for separating the magnetic scattering from phonon and other spurious effects. In the comparison of our experimental results with various microscopic theoretical models, particular emphasis was made to address the similarities and differences in the spin fluctuations of the two most studied superconductors. Finally, we briefly mention recent magnetic-field-dependent studies of the spin fluctuations and discuss their relevance in understanding the microscopic origin of the resonance.


Materials Science and Engineering

Keywords and Phrases

barium derivative; copper complex; oxygen derivative; yttrium; conductor; dynamics; energy; magnetic field; mathematical model; nuclear magnetic resonance; polarization; spectroscopy; temperature dependence

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2001 American Physical Society (APS), All rights reserved.

Full Text Link