  We study magnetic excitations in a bilayer of an antiferromagnetic (AF)
insulator and a correlated metal, in which double occupancy is forbidden. The
effective action of the AF spin wave in the AF insulator is derived by using
the path integral formula within the second order of interplane coupling. The
electron correlation in the correlated metal is treated by the Gutzwiller
approximation, which renormalizes the hopping integrals by g_t as proportional
to the hole density. The linewidth of the AF spin wave excitations originates
from particle-hole excitations in the correlated metal. By increasing the
correlation effect, i.e., by decreasing g_t, it is found that the linewidth at
low energies increases inversely proportional to g_t. The present results will
also be useful for bilayers of a metal and ferrimagnet.
