Antiferromagnetic correlations and nuclear magnetic relaxation in high-Tcsuperconductors: A critical reexamination

We analyze in more detail a previously proposed phenomenological model for nuclear spin relaxation in high-${\mathit{T}}_{\mathit{c}}$ materials. We show that the anisotropy of the oxygen Knight shift implies that the oxygen nuclei are coupled to electronic spin degrees of freedom on the Cu site more strongly than they are to electronic spin degrees of freedom on the O site. We introduce a method of data analysis in which estimates of the uncertainty in the phenomenological parameters are easily obtained, and we show that these uncertainties are large for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ but smaller for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.63}$. We show that NMR measurements in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.63}$ imply the existence of a spin gap. We extend the model to the superconducting state to the case of incommensurate spin fluctuations, and also to finite frequencies, giving expressions that may be compared with neutron-scattering data. We show that the crucial tests of whether an ansatz for the electronic spin susceptibility explains the NMR data are that it reproduces the magnitude and temperature dependence of the ratio of copper-to-oxygen and oxygen-to-yttrium relaxation rates. Susceptibilities deduced from present neutron measurements are not consistent with the interpretation of the NMR data presented here.