Effect of Superconductivity on the Incommensurate Magnetic Response of Cuprate Superconductors

We explain the effects of superconductivity on the incommensurate magnetic response ${\chi }^{\mathrm{\prime }\mathrm{\prime }}(q,\omega )$ 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 ${\chi }^{\mathrm{\prime }\mathrm{\prime }}$ 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 $(\pi ,\pi )$.