Direct relation between the low-energy spin excitations and superconductivity of overdoped high-Tc superconductors.

The dynamic spin susceptibility, chi(")(omega), has been measured over the energy range of 2</=omega</=10 meV for overdoped La2-xSrxCuO4. Incommensurate (IC) spin excitations are observed at 8 K for all superconducting samples for 0.25</=x</=0.28 with chi(") peaking at approximately 6 meV. The IC peaks at 6 meV become smaller in intensity with increasing x and, finally, become unobservable for a sample with x=0.30 which has no bulk superconductivity. The maximum chi(") decreases linearly with T(c)(onset) in the overdoped region, implying a direct cooperative relation between the spin fluctuations and the superconductivity.