Theory of nuclear spin-spin coupling in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

The indirect nuclear spin-spin coupling between Cu nuclei in the ${\mathrm{CuO}}_2$ planes of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, deduced from ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ transverse relaxation, is shown to yield information about the wave-vector dependence of the real part of the planar Cu static electron-spin susceptibility. The coupling is evaluated with no adjustable parameters using the antiferromagnetic Fermi-liquid theory of Millis, Monien, and Pines, providing a new test of that model. At 100 K, the theoretical relaxation time is 190±75 μsec versus the experimental 130±10 μsec.