Neutron-scattering study of the dynamical spin susceptibility in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.6}$

We report a detailed neutron-scattering study of the dynamical spin susceptibility in a single crystal of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$, with x=0.6 and ${\mathit{T}}_{\mathit{c}}$=53 K. The measurements cover the energy range from 5 to 50 meV, and temperatures from 10 to 100 K. It is shown that antiferromagnetic correlations between nearest-neighbor ${\mathrm{CuO}}_2$ layers are quite strong. As a result, only in-phase bilayer spin fluctuations are observed at low energies, with the out-of-phase fluctuations making a weak appearance at 40 meV. Within the two-dimensional (2D) Brillouin zone corresponding to a single layer, the imginary part of the dynamical susceptibility χ’’(Q,ω) exhibits a broad peak about the point corresponding to antiferromagnetic order ${\mathbf{Q}}_{\mathrm{AF}}$ with a width that is mildly energy dependent. At 10 K, χ’’(${\mathbf{Q}}_{\mathrm{AF}}$,ω) has a rather sharp peak near 27 meV; integrating χ’’ over the 2D magnetic Brillouin zone makes the peak in energy much broader. (We have verified that the falloff at high energies also occurs in a previously studied crystal with x=0.5, ${\mathit{T}}_{\mathit{c}}$=50 K.) Although the amplitude at 5 meV and 10 K is near zero, considerable spectral weight is observed at energies well below the weak-coupling limit for 2Δ, where Δ is the superconducting gap. The temperature dependence of the 2D Q-integrated χ’’ is well described by a simple function containing a temperature-independent energy gap of 9 meV. A study of the Q dependence of χ’’ at ħω=15 meV indicates that the signal falls off rather abruptly on moving away from ${\mathbf{Q}}_{\mathrm{AF}}$ (compared to a simple Gaussian distribution). Measurements along two different directions in the 2D zone suggest that the width of the distribution about ${\mathbf{Q}}_{\mathrm{AF}}$ is anisotropic. These results are discussed in the context of current theoretical models.