  Motivated by the observation of unusual magnetism in Ce_xCu_2Si_2 ($x\sim
1$), we study the effect of disorder, such as Ce vacancy, on the competition
between superconductivity (SC) and antiferromagnetism (AF) on the basis of the
phenomenological Ginzburg-Landau theory. Assuming that the AF-SC transition is
of first order in clean system, we show that a single impurity in the SC state
can induce staggered magnetization by suppressing the SC around it. For finite
concentration of impurities, the first-order AF-SC boundary in the clean case
is replaced by a finite region where the SC and the induced AF moments coexist
microscopically with spatially varying order parameters. We argue that spin
excitation spectrum in the coexistent state has a dual structure of SC gapped
mode and the low-energy spin-wave mode. In accordance with the emergence of AF
out of SC ground state, the spectral weight will be transferred from the former
mode to the latter, keeping the structure of both modes basically unchanged.
