Recent inelastic neutron scattering (INS) experiments on La2−xSrxCuO4 observed a magnetic coherence effect, i.e., strong frequency and momentum dependent changes of the spin susceptibility, χ ′′ , in the superconducting phase. We show that this effect is a direct consequence of changes in the damping of incommensurate antiferromagnetic spin fluctuations due to the appearance of a d-wave gap in the fermionic spectrum. Our theoretical results provide a quantitative explanation for the weak momentum dependence of the observed spin-gap. Moreover, we predict (a) a Fermi surface in La2−xSrxCuO4 which is closed around (π, π) up to optimal doping, and (b) similar changes in χ ′′ for all cuprates with an incommensurate magnetic response.PACS numbers: 74.25. Ha, 74.25.Jb, The spin excitation spectrum in La 2−x Sr x CuO 4 [1][2][3][4][5] in the normal and superconducting state has been intensively studied during the last few years in inelastic neutron scattering (INS) experiments. The normal state spectrum for compounds with x > 0.04 is characterized by peaks in χ ′′ (q, ω) at incommensurate wave-vectors [5] show striking momentum and frequency dependent changes in χ ′′ upon entering the superconducting state, which the authors called the magnetic coherence effect. For both compounds, χ ′′ (Q i ) in the superconducting state is considerably decreased from its normal state value below ω ≈ 7 meV, while it increases above this frequency. For frequencies in the vicinity of 7 meV, the incommensurate peaks sharpen in the superconducting state, while at higher frequencies the peak widths in the normal and superconducting state are approximately equal. Moreover, by employing a Kramers-Kronig transformation, the authors found that the static susceptibility, χ ′ , at Q i decreases in the superconducting state [5].In this communication, we show that the magnetic coherence effect is a direct consequence of changes in the damping of incommensurate antiferromagnetic spin fluctuations due to the appearance of a d-wave gap in the fermionic spectrum. We obtain results for the frequency and momentum dependence of χ ′′ that are in good qualitative, and to a large extent quantitative agreement with the experimental data, and also explain the weak momentum dependence of the spin-gap. We show that INS data in the superconducting state provide information on the symmetry of the order parameter and the topology of the Fermi surface (FS) and that for La 2−x Sr x CuO 4 , INS experiments suggest a FS closed around (π, π). We predict that the magnetic coherence effect is to be expected for any cuprate superconductor with an incommensurate spin spectrum, and thus in particular for YBa 2 Cu 3 O 6+x (YBCO), in which an incommensurate spin structure at low frequencies has been observed [6][7][8].The starting point for our calculations is a spin-fermion model [9] in which the damping of incommensurate spinexcitations arises from their interaction with fermionic quasi-particles. In this model, the spin propagator, χ, is given bywhere χ 0 is the bare propa...