Neutron scattering experiments have been carried out to explore Ni-impurity effects on static spin correlations in La2-xSrxCuO4 (LSCO) in the vicinity of the superconductor-insulator boundary where both parallel and diagonal spin-density modulations (SDM) coexist at low temperature. Upon dilute Ni substitution the incommensurability decreases for both types of SDM, while the volume fraction of the diagonal (parallel) SDM increases (decreases). Subsequent Ni doping induces a bulk three-dimensional antiferromagnetic (AF) order when x ~ Ni concentration. TN of such the AF order depends on x and seems to disappear at x ~ 0.1. These effects are approximately ascribed by a reduction of mobile holes, and by a transition from the parallel to the diagonal SDM induced by Ni.

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