  Recent experimental study on Tsai-type quasicrystalline approximant Au-Al-Gd
has revealed the presence of magnetic orders and phase transitions with
changing the Au/Al concentration. Motivated by the experiment, we theoretically
investigate whether a successive change of magnetic orders occurs in a minimal
magnetic model including the RKKY interaction only. We find that the model
induces multifarious magnetic orders depending on the Fermi wavenumber and
gives a good starting point for understanding the experimental observation. In
addition, we predict the presence of an undiscovered novel magnetic order
called cuboc order at large Fermi wavenumber region.
