Spin dynamics of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathrm{x}}$ as revealed by NMR

We show that Knight-shift and relaxation-rate data at Cu and Y sites provide strong evidence in favor of the single-quantum-spin-fluid picture of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathrm{x}}$. We also argue that this picture is not inconsistent with different temperature behaviors at Cu, O, and Y sites because of the strong antiferromagnetic correlations. We show explicitly that different power laws can be obtained at high temperature within the framework of a spin-wave approximation and comment on a possible gap in the spin excitation spectrum of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathrm{x}}$ larger the $T_c$. However, this simple model does not allow a detailed account of the observed temperature dependences.