Recent discovery of various magnetism in Tsai-type quasicrystal approximants, in whose alloys rare-earth ions located on icosahedral vertices are coupled with each other via the Ruderman-Kittel-Kasuya-Yosida interaction, indicates an avenue to find novel magnetism originating from the icosahedral symmetry. Here we investigate classical and quantum magnetic states on an icosahedral cluster within the Heisenberg interactions of all bonds. Simulated annealing and numerical diagonalization are performed to obtain the classical and quantum ground states. We obtain qualitative correspondence of classical and quantum phase diagrams. Our study gives a good starting point to understand the various magnetism in not only quasicrystal approximants but also quasicrystals.
- Ground-state phase diagram
- Icosahedral cluster