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 La_2-xSrₓCuO₄ and YBa₂Cu₃O₆₊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. onLa1.86{Sr}0.14$Cu${O}₄$ are shown to agree quantitatively with the NMR measurements of $⁶³T₁$ and the magnetic scaling behavior proposed by Barzykin and Pines. The reconciliation of the $¹⁷O$ relaxation rates with the degree of incommensuration in the spin-fluctuation spectrum seen in neutron experiments is achieved by introducing a transferred hyperfine coupling ${C}^{{'}}$ between $¹⁷O$ nuclei and their next-nearest-neighbor ${Cu}²⁺$ spins; this leads to a near-perfect cancellation of the influence of the incommensurate spin-fluctuation peaks on the $¹⁷O$ relaxation rates of ${La}_{2{-}x}{Sr}ₓCu{O}₄$. The inclusion of the ${C}^{{'}}$ term also leads to a natural explanation, within the one-component model, the different temperature dependence of the anisotropic $¹⁷O$ relaxation rates for different field orientations, recently observed by Martindale et al. The measured significant decrease with doping of the anisotropy ratio, $⁶³R={⁶³T1ab}{⁶³T1c}$ in the ${La}_{2{-}x}{Sr}ₓCu{O}₄$ system, from $⁶³R=3.9$ for ${La}₂$Cu${O}₄$ to $⁶³R{}3.0$ for ${La}1.85Sr0.15CuO₄ 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_β and B.