  We study classical spin models on the 1/1 Tsai-type approximant lattice using
Monte Carlo and mean-field methods. Our aim is to understand whether the phase
diagram differences between Gd- and Tb-based approximants can be attributed to
anisotropy induced by the crystal-electric field. To address this question, we
treat Gd ions as Heisenberg spins and Tb ions as Ising spins. Additionally, we
consider the presence of the RKKY interaction to replicate the experimentally
observed correlation between magnetic properties and electron concentration.
Surprisingly, our findings show that the transition between ferromagnetic and
antiferromagnetic order remains unaltered by the anisotropy, even when
accounting for the dipole interaction. We conclude that a more comprehensive
model, extending beyond the free-electron gas RKKY interaction, is likely
required to fully understand the distinctions between Gd- and Tb-based
approximants. Our work represents a systematic exploration of the impact of
anisotropy on the ground-state properties of classical spin models in
quasicrystal approximants.
