Motivated by the recent discovery of canted ferromagnetism in the Tsai-type approximants Au-Si-REs (RE = Tb, Dy, and Ho), we propose a phenomenological magnetic model reproducing their magnetic structure and thermodynamic quantities. In the model, the cubic symmetry (m (3) over bar) of the approximately regular icosahedra plays a key role in the peculiar magnetic structure determined by a neutron diffraction experiment. Our magnetic model does not only explain magnetic behaviors in the quasicrystal approximants, but also provides a good starting point for the possibility of the coexistence between the magnetic long-range order and the aperiodicity in quasicrystals.
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