  Zero-field muon-spin-relaxation (muSR) and magnetic-susceptibility
measurements have been carried out in La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ with x =
0.10, 0.115 and 0.13 changing the Zn-concentration y finely up to 0.10, with
the aim to clarify effects of the nonmagnetic impurity Zn on the Cu-spin
dynamics and superconductivity. The muSR measurements have revealed that, in
each x, a magnetic order of Cu spins is observed at y ~ 0.0075, while it
disappears and Cu spins turn into a fast fluctuating state for y > 0.03. From
the magnetic-susceptibility measurements, on the other hand, it has been found
that the volume fraction of the superconducting state rapidly decreases through
the slight doping of Zn and that its y dependence corresponds to the y
dependence of the volume fraction of the fast fluctuating region of Cu spins
estimated from the muSR results. Both the rapid decrease of the volume fraction
of the superconducting state and the formation of the magnetic order through
the slight doping of Zn can be interpreted in terms of the development of the
so-called "Swiss cheese" model. That is, it is concluded that Cu spins in a
non-superconducting region around Zn exhibit slowing-down of the fluctuations
or form an incoherent or coherent static magnetic order. Moreover, the
formation of a non-superconducting region around Zn is considered to be due to
the pinning of the dynamical spin correlation or dynamical stripe correlations.
