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 P6′ 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 P6′, 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) μ_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.