Motivated by the observation of unusual magnetism in CexCu2Si2 (x similar t
o 1), we study the effect of disorder, such as Ce vacancy. on the competiti
on between superconductivity (SC) and antiferromagnetism (AF) on the basis
of the phenomenological Ginzburg-Landau theory. Assuming that the AF-SC tra
nsition is of first order in a clean system, we show that a single impurity
in the SC slate can induce staggered magnetization by suppressing the SC a
round it. For finite concentration of impurities, the first-order AF-SC bou
ndary in the clean case is replaced by a finite region where the SC and the
induced AF moments coexist microscopically with spatially varying order pa
rameters. We argue that the spin excitation spectrum in the coexistent stat
e has a dual structure of the SC gapped mode and the low-energy spin-wave m
ode. In accordance with the: emergence of AF out of SC ground state, the sp
ectral weight will be transferred from the former mode to the latter one, w
hile keeping the structure of both modes basically unchanged.