We investigate the Néel temperature of ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ as a function of the site dilution at the $\mathrm{Cu}$ $\left(S=1∕2\right)$ sites with $\mathrm{Pd}$ $\left(S=0\right)$, utilizing the muon spin relaxation $\left(\mu \mathrm{SR}\right)$ technique. The Néel temperature, which is $T_N=5.4\mathrm{K}$ for the undoped system, becomes significantly reduced for less than one percent of doping $\mathrm{Pd}$, giving a support for the previous proposal for the good one-dimensionality. The $\mathrm{Pd}$ concentration dependence of the Néel temperature is compared with a recent theoretical study [S. Eggert, I. Affleck, and M. D. P. Horton, Phys. Rev. Lett. 89, 47 202 (2002)] of weakly coupled one-dimensional antiferromagnetic chains of $S=1∕2$ spins, and a quantitative agreement is found. The inhomogeneity of the ordered moment sizes is characterized by the $\mu$SR time spectra. We propose a model that the ordered moment size recovers away from the dopant $S=0$ sites with a recovery length of $\xi \approx 150-200$ sites. The origin of the finite recovery length $\xi$ for the gapless $S=1∕2$ antiferromagnetic chain is compared to the estimate based on the effective staggered magnetic field from the neighboring chains.

• Received 6 March 2004

DOI:https://doi.org/10.1103/PhysRevB.70.094402