Magnetic Coherence as a Universal Feature of Cuprate Superconductors

Recent inelastic neutron scattering (INS) experiments on La$_{2-x}$Sr$_x$CuO$_4$ have established the existence of a {\it magnetic coherence effect}, i.e., strong frequency and momentum dependent changes of the spin susceptibility, $\chi''$, in the superconducting phase. We show, using the spin-fermion model for incommensurate antiferromagnetic spin fluctuations, that the magnetic coherence effect establishes the ability of INS experiments to probe the electronic spectrum of the cuprates, in that the effect arises from the interplay of an incommensurate magnetic response, the form of the underlying Fermi surface, and the opening of the d-wave gap in the fermionic spectrum. In particular, we find that the magnetic coherence effect observed in INS experiments on La$_{2-x}$Sr$_x$CuO$_4$ requires that the Fermi surface be closed around $(\pi,\pi)$ up to optimal doping. We present several predictions for the form of the magnetic coherence effect in YBa$_2$Cu$_3$O$_{6+x}$ in which an incommensurate magnetic response has been observed in the superconducting state.