Effect of Superconductivity on the Incommensurate Magnetic Response of Cuprate Superconductors

We explain the effects of superconductivity on the incommensurate magnetic response $\chi''(q,\omega)$ observed in inelastic neutron scattering measurements on La$_{2-x}$Sr$_x$CuO$_4$. We show that a spin-fermion model correctly describes the frequency and momentum dependent changes of $\chi''$ in the superconducting phase. We find these changes are generic features of an incommensurate spin structure and the d-wave symmetry of the superconducting gap and are thus expected for all cuprates with an incommensurate magnetic response. Our analysis of INS experiments in La$_{2-x}$Sr$_x$CuO$_4$ up to optimal doping suggests a Fermi surface which is closed around $(\pi,\pi)$.