NMR and Neutron Scattering Experiments on the Cuprate Superconductors: A Critical Re-Examination

TL;DR

This paper demonstrates how NMR and neutron scattering experiments on cuprate superconductors can be reconciled using a phenomenological response function and a revised hyperfine Hamiltonian, explaining various experimental observations.

Contribution

It introduces a new transferred hyperfine coupling term and reexamines the hyperfine Hamiltonian to unify NMR and neutron scattering results in cuprates.

Findings

Quantitative agreement between neutron scattering and NMR measurements achieved.

Introduction of a new hyperfine coupling $C'$ explains relaxation rates and anisotropy.

Doping dependence of relaxation anisotropy explained by hyperfine constant adjustments.

Abstract

We show that it is possible to reconcile NMR and neutron scattering experiments on both LSCO and YBCO, by making use of the Millis-Monien-Pines mean field phenomenological expression for the dynamic spin-spin response function, and reexamining the standard Shastry-Mila-Rice hyperfine Hamiltonian for NMR experiments. The recent neutron scattering results of Aeppli et al on LSCO (x=14%) 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 $^{17}T_1$ relaxation rates with the degree of incommensuration in the spin fluctuation spectrum seen in neutron experiments is achieved by introducing a new transferred hyperfine coupling $C'$ between oxygen 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 oxygen relaxation rates of LSCO. The inclusion of the new $C'$ term also leads to a natural explanation, within the one-component model, the different temperature dependence of the anisotropic oxygen relaxation rates for different field orientations, recently observed by Martindale $et~al$. The measured significant decrease with doping of the anisotropy ratio, $R= ^{63}T_{1ab}/^{63}T_{1c}$ in LSCO system, from $R =3.9$ for ${\rm La_2CuO_4}$ to $R ~ 3.0$ for LSCO (x=15%) 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.