Magnetic ordering in the ultra-pure site-diluted spin chain materials SrCu$_{1-x}$Ni$_x$O$_2$

Muon spin rotation technique is used to study magnetic ordering in ultra-pure samples of SrCu$_{1-x}$Ni$_x$O$_2$, an archetypical $S=1/2$ antiferromagnetic Heisenberg chain system with a small amount of $S=1$ defects. The ordered state in the parent compound is shown to be highly homogeneous, contrary to previous report [M. Matsuda et al., Phys. Rev. B \textbf{55}, R11953 (1997)]. Even minute amount of Ni impurities result in inhomogeneous order and a decrease of the transition temperature. At as little as $0.5$~\% Ni concentration, magnetic ordering is entirely suppressed. The results are compared to previous theoretical studies of weakly coupled spin chains with site-defects.