The magnetic properties of the Zn-substituted overdoped high-T_c superconductor La_2-xSr_xCu_1-yZn_yO_4 have been studied by magnetization measurements and neutron scattering. Magnetization measurements reveal that for Zn-free samples with x ≥ 0.22 a Curie term is induced in the temperature dependence of the magnetic susceptibility implying the existence of local paramagnetic moments. The induced Curie constant corresponds to a moment of 0.5 μ_B per additional Sr^2+ ion that exceeds x=0.22.

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... ubstitution in the overdoped also induces a Curie term that corresponds to 1.2 μ_B per Zn^2+ ion, simultaneously suppressing T_c. The relationship between T_c and the magnitude of the Curie term for Zn-free with x ≥ 0.22 and for Zn-substituted with x = 0.22 are closely similar. This signifies a general competitive relationship between the superconductivity and the induced paramagnetic moment. Neutron scattering measurements show that Zn-substitution in overdoped anomalously enhances the inelastic magnetic scattering spectra around the (π, π) position, peaking at ω∼ 7 meV. These facts are discussed on the basis of a "swiss-cheese" model of Zn-substituted systems as well as a microscopic phase separation scenario in the overdoped region indicated by muon-spin-relaxation measurements.