Classical and Quantum Magnetic Ground States on an Icosahedral Cluster

TL;DR

This paper explores classical and quantum magnetic ground states on an icosahedral cluster, revealing insights into magnetism in quasicrystalline structures through simulations and numerical methods.

Contribution

It introduces a combined classical and quantum analysis of magnetic states on an icosahedral cluster, advancing understanding of magnetism in quasicrystals.

Findings

Qualitative correspondence between classical and quantum phase diagrams

Identification of various magnetic ground states

Provides a foundation for studying magnetism in quasicrystals

Abstract

Recent discovery of various magnetism in Tsai-type quasicrystalline approximants, in whose alloys rare-earth ions located on icosahedral apices are coupled with each other via the Ruderman--Kittel--Kasuya--Yosida interaction, opens 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 quasicrystalline approximants but also quasicrystals.