  Magnetic excitations in the energy range up to 100 meV are studied for
over-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.25$ and 0.30, using
time-of-flight neutron spectroscopy. Comparison of spectra integrated over the
width of an antiferromagnetic Brillouin zone demonstrates that the magnetic
scattering at intermediate energies, $20 \lesssim \omega \lesssim 100$ meV,
progressively decreases with over-doping. This strongly suggests that the
magnetism is not related to Fermi surface nesting, but rather is associated
with a decreasing volume fraction of (probably fluctuating) antiferromagnetic
bubbles.
