Revisiting the antiferromagnetic structure of Tb14Ag51: the importance of distinguishing alternative symmetries for a multidimensional order parameter

The antiferromagnetic structure of Tb14Ag51 with the propagation vector [1/3, 1/3, 0] and the parent space group P6/m is revisited using both magnetic symmetry and irreducible representation arguments. A new magnetic structure under the hexagonal Shubnikov magnetic space group P (6) over bar' which fits much better the experimental data is found. This new solution was obtained by constraining the spin arrangement to one of the three possible magnetic space groups of maximal symmetry that can be realized by a magnetic ordering transforming according to the four-dimensional physically irreducible representation that is known to be relevant in this magnetic phase. The refined model, parameterized under P (6) over bar', implicitly includes the presence of a third harmonic with the propagation vector at the gamma point [0, 0, 0], which has an important weight in the final result. The structure consists of 13 symmetry-independent Tb magnetic moments with the same size of 8.48 (2) mu(B), propagating cycloidally in the ab plane. The modulation has a substantial deviation from being purely sinusoidal due to the contribution of the mentioned third harmonic.