NMR and neutron-scattering experiments on the cuprate superconductors: A critical re-examination

We show that it is possible to reconcile NMR and neutron-scattering experiments on both ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ and $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$, by making use of the Millis-Monien-Pines mean-field phenomenological expression for the dynamic spin-spin response function, and re-examining the standard Shastry-Mila-Rice hyperfine Hamiltonian for NMR experiments. The recent neutron-scattering results of Aeppli et al. on${\mathrm{La}}_{1.86}$ ${\mathrm{Sr}}_{0.14}$Cu${\mathrm{O}}_4$ are shown to agree quantitatively with the NMR measurements of ${}_{}{}^{63}{}_{}{}^{}T_1^{}{}_{}{}^{}$ and the magnetic scaling behavior proposed by Barzykin and Pines. The reconciliation of the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ relaxation rates with the degree of incommensuration in the spin-fluctuation spectrum seen in neutron experiments is achieved by introducing a transferred hyperfine coupling $C^{\prime }$ between ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ nuclei and their next-nearest-neighbor ${\mathrm{Cu}}^{2+}$ spins; this leads to a near-perfect cancellation of the influence of the incommensurate spin-fluctuation peaks on the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ relaxation rates of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. The inclusion of the $C^{\prime }$ term also leads to a natural explanation, within the one-component model, the different temperature dependence of the anisotropic ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ relaxation rates for different field orientations, recently observed by Martindale et al. The measured significant decrease with doping of the anisotropy ratio, ${}_{}{}^{63}{}_{}{}^{}R=\frac{{}_{}{}^{63}{}_{}{}^{}T_{1ab}^{}{}_{}{}^{}}{{}_{}{}^{63}{}_{}{}^{}T_{1c}^{}{}_{}{}^{}}$ in the ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ system, from ${}_{}{}^{63}{}_{}{}^{}R=3.9\mathrm{}$ for ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$ to ${}_{}{}^{63}{}_{}{}^{}R\simeq 3.0$ for ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$ is made compatible with the doping dependence of the shift in the incommensurate spin-fluctuation peaks measured in neutron experiments, by suitable choices of the direct and transferred hyperfine coupling constants $A_{\beta }$ and $B$.