Effects of disorder on the competition between antiferromagnetism and superconductivity

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.