We have measured the thermal conductivity along the c-axis parallel to the spin-chains, kappa_c, of the one-dimensional antiferromagnetic spin system SrCuO_2, using as-grown and O_2-annealed single-crystals grown from raw materials with 99.9% (3N) and 99.99% (4N) purity. The value of kappa_c around 50K, where large contribution of the thermal conductivity due to spinons, kappa_spinon, is observed, is markedly enhanced by both the increase of the purity of raw materials and the O_2-annealing. Therefore, the increase of kappa_c implies that kappa_spinon is enhanced due to the decrease of spin defects caused by impurities in raw materials and by oxygen defects. The mean free path of spinons is as large as about 24000 angstrom at low temperatures in the O_2-annealed single-crystal grown from raw materials with 4N purity.
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