For ThCr2Si2 structure (space group I4/mmm) sample, e.g. CaCo2As2, Co atoms occupy the 4d site - site position (0, 0.5, 0.25). Assume that the propagation vector as (0,0,0) and that a antiferromagnetic structure occurs along the c-axis. According to irreducible representation analysis using BasIreps in FullProf, there is only one possible model as shown in Fig1. However, one journal paper presented another kind of antiferromagnetic structure as shown in Fig2 which is not included in the model from irreducible representation.

http://journals.aps.org/prb/pdf/10.1103/PhysRevB.88.174420

So my question is that a magnetic structure model must agree with a model from irreducible representation theory?