We report a detailed inelastic neutron scattering study of the collective magnetic excitations of overdoped superconducting La1.78Sr0.22CuO4 for the energy range 0-160 meV. Our measurements show that overdoping suppresses the strong response present
for optimally doped La2-xSrxCuO4 which is peaked near 50 meV. The remaining response is peaked at incommensurate wavevectors for all energies investigated. We observe a strong high-frequency magnetic response for E >= 80 meV suggesting that significant antiferromagnetic exchange couplings persist well into the overdoped part of the cuprate phase diagram.
