[Show abstract][Hide abstract] ABSTRACT: Na(10)Co(4)O(10) was investigated by neutron powder diffraction at 230, 70, and 4 K. The crystal structure, determined previously by X-ray diffraction on single crystals, was confirmed. Na(10)Co(4)O(10) orders magnetically below 37 K. All observed magnetic reflections could be indexed by integers (hkl) with respect to the chemical unit cell and the magnetic propagation vector q=0. The refinement was performed in the Shubnikov space group C2/c and indicated a collinear antiferromagnetic spin structure. The determined spin arrangement is consistent with the magnetic intratetramer interactions suggested previously from the analysis of magnetic susceptibility data: the magnetic moments of the central Co(III) ions of the Co(4)O(10) tetramer lie parallel to each other and couple in an antiparallel fashion to the terminal Co(II) moments. The Rietveld analysis shows that the net moments of 0.64 mu(B) per tetramer form ferromagnetic layers parallel to the ab plane. Adjacent layers are coupled antiferromagnetically along c. The spins are aligned in the ac plane along the line connecting adjacent Co(II) and Co(III) ions of the tetramer. We have determined unusually low values for the ordered magnetic moments of 2.43(5) mu(B) and 2.11(6) mu(B) for Co(III) and Co(II), respectively. The occurrence of spontaneous magnetization below 37 K indicates a slight canting of 2.2 degrees of the antiferromagnetic structure. A representation analysis shows that a weak ferromagnetic component along b is compatible with the determined antiferromagnetic structure.