Microscopic Fermi liquid theory of NMR relaxation and neutron scattering in the metallic copper oxides

Abstract

We calculate the NMR relaxation rates for the Cu and O sites, the temperature dependent magnetic susceptibility and the inelastic neutron scattering cross section using the dynamical RPA susceptibility derived previously. This approach is a Fermi liquid based scheme in which the Cu d electrons are (on the basis of considerable experimental evidence) assumed to be quasi-localized. These narrow band effects lead to low energy scales, T coh below which the Cu d electrons are fully coherent and a “one component” picture is applicable. Above this characteristic temperature the d electrons begin to lose their coherence, although they are still strongly coupled to the p orbitals. This coherence energy scale, along with the exchange interactions J H completely determine the characteristic temperatures and frequencies which appear in NMR and neutron data. Our calculations of 1/ T 1 on the Cu sites suggest that the cuprates are not as close to a magnetic instability as has been assumed elsewhere. This is because the coherence energy scale (which appears in the “bare” Lindhard function for the renormalized band structure) already provides an intrinsic “soft” frequency. Consequently, we find that antiferromagnetic interactions are playing a less dominant (but not insignificant) role in magnetic measurements. Analysis of the oxygen relaxation suggests that the sharp antiferromagnetic peaks invoked elsewhere to yield form factor cancellation effects may not be sufficiently robust to explain the data. Indeed, careful numerical calculations yield some degree of non-Korringa behavior on the oxygen sites due to imperfect cancellations of the transfer-hyperfine-coupling induced relaxation. Finally, our calculations of the neutron cross section show incommensurate peaks in the diagonal ( q, q) and off-diagonal ( q, π) directions, which are found to reflect the detailed Fermi surface geometry of the LaSrCuO system. These peaks become increasingly more incommensurate as the hole concentration increases. These predictions and their comparison with future experiments may help to determine the applicability of Fermi liquid based approaches to the cuprates.