Spin excitation in d-wave superconductors: A Fermi liquid picture

A detailed study of the inelastic neutron scattering (INS) spectra of the high-T_c cuprates based on the Fermi liquid (FL) picture is given. We focus on the issue of the transformation between the commensurate and incommensurate (IC) excitation driven by frequency or temperature. For La_2-xSr_xCuO₄ (LSCO), the condition of small Δ(0)/v_F can simultaneously reproduce the always existing IC peaks in the superconducting (SC) and normal states, and the always fixed location at temperature or frequency change. For YBa₂Cu₃O_6+x (YBCO), a moderate Δ(0)/v_F and proximity of the van Hove singularity (vHS) at M=(0,π) to the Fermi level can reproduce the frequency- and temperature-driven shifting IC peaks in the SC state, and the vanishing of the IC peak in the normal state. We address the conditional peak shifting behavior to a refined consideration on the nesting effect which is previously overlook. As a result, both the well documented data on LSCO and the recent data on YBCO (on YBa₂Cu₃O_6.7 by [Phys. Rev. Lett 83 (1999) 608] and YBa₂Cu₃O_6.85 by [Science 288 (2000) 1234]) can be reasonably reconciled within a FL picture. We also point out that the one-dimensional-like data by [Condmat/9811100; Nature 404 (2000) 729] on a detwinned and more underdoped sample YBa₂Cu₃O_6.6 could be due to a gap anisotropy effect originally discussed by [Phys. Rev. B 53 (1996) 5889], and we proceed to suggest a way of clarifying it.