By means of muon spin rotation and relaxation (mu+SR) techniques, we have investigated the magnetism of quasi-one-dimensional (1D) cobalt oxides A(n+2)Co(n+1)O(3n+3) (A=Ca, Sr, and Ba; n=1, 2, 3, 5, and infinity), in which the 1D CoO3 chain is surrounded by six equally spaced chains forming a triangular lattice in the ab plane, using polycrystalline samples, from room temperature down to 1.8 K. For the compounds with n=1-5, transverse field mu+SR experiments showed the existence of a magnetic transition below similar to 100 K, although there were no clear anomalies in the susceptibility-vs-T curve. The onset temperature of the transition (T-c(on)) was found to decrease with n; from 100 K for n=1 to 60 K for n=5. A damped muon spin oscillation was observed only in the sample with n=1 (Ca3Co2O6), whereas only a fast relaxation obtained even at 1.8 K in the other three samples. Combining the fact that the paramagnetic Curie temperature ranges from -150 to -200 K for the compound with n=2 and 3, the mu+SR result indicates that a two-dimensional (2D) short-range antiferromagnetic (AF) order, which has been thought to be unlikely to exist at high T due to a relatively strong 1D ferromagnetic (F) interaction, appears below T-c(on) for all compounds with n=1-5; but quasistatic long-range AF order formed only in Ca3Co2O6, below 25 K. For BaCoO3 (n=infinity), as T decreased from 300 K, 1D F order appeared below 53 K, and a sharp 2D AF transition occurred at 15 K.
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