Classical and Quantum Magnetic Ground States on an Icosahedral Cluster

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.

arXiv comment8 pages, 6 figures

References in corpus (7)

• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Whirling spin order in the quasicrystal approximant Au${}_{72}$Al${}_{14}$Tb${}_{14}$
• Noncoplanar ferrimagnetism and local crystalline-electric-field anisotropy in the quasicrystal approximant Au${}_{70}$Si${}_{17}$Tb${}_{13}$
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Cited by in corpus (8)

• Topological magnetic textures and long-range orders in Tb-based quasicrystal and approximant
• Magnetism and topology in Tb-based icosahedral quasicrystal
• Revisit of magnetic orders in 1/1 approximant crystals of Tsai-type quasicrystal from theoretical points of view
• Monte Carlo study on critical exponents of the classical Heisenberg model in ferromagnetic icosahedral quasicrystal
• Identification of Two Distinct Antiferromagnetic Phases in the Au-Al-Gd Quasicrystal Approximant
• Non-Collinear and Non-Coplanar Magnetic Orders in 1/1 Periodic Approximant to the Icosahedral Quasicrystal
• Predicted versatile topological nodal magnons in Tb-based icosahedral quasicrystal 1/1 approximants
• Magnetism and topological property in icosahedral quasicrystal