  We report muon-spin rotation and neutron-scattering experiments on
non-magnetic Zn impurity effects on the static spin-stripe order and
superconductivity of the La214 cuprates. Remarkably, it was found that, for
samples with hole doping x = 1/8, the spin-stripe ordering temperature T_so
decreases linearly with Zn doping y and disappears at around y = 4\%,
demonstrating a high sensitivity of static spin-stripe order to impurities
within a CuO_2 plane. Moreover, T_so is suppressed by Zn in the same manner as
is the superconducting transition temperature T_c for samples near optimal hole
doping. This surprisingly similar sensitivity suggests that the spin-stripe
order is dependent on intertwining with superconducting correlations.
