Magnetism in Rare Earth Quasicrystals: RKKY Interactions and Ordering

Abstract

We study magnetism in simple models for rare earth quasicrystals by means of a two-step theoretical approach. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on a two-dimensional quasiperiodic tiling. Second, we examine the statistical mechanics of Ising spins coupled via these interactions using Monte Carlo simulations. We find the emergence of strongly coupled spin clusters with significantly weaker inter-cluster coupling, and a transition to a low-temperature phase that has long-range order evidenced by a finite domain wall tension.

arXiv commentrestructuring of paper and update of numerical results, 5 pages, 4 figures

References in corpus (12)

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Cited by in corpus (12)

• Long-range Magnetic Order in Models for Rare Earth Quasicrystals
• Magnetic orders induced by RKKY interaction in Tsai-type quasicrystalline approximant Au-Al-Gd
• Classical Dimers on Penrose Tilings
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Monte Carlo study on critical exponents of the classical Heisenberg model in ferromagnetic icosahedral quasicrystal
• Competition between spin-glass and antiferromagnetic states in Tsai-type 1/1 and 2/1 quasicrystal approximants
• Hidden hyperspace geometry and long-distance quantum coupling
• Atomic structure of the unique antiferromagnetic 2/1 quasicrystal approximant
• Fragile magnetic order in metallic quasicrystals
• Predicted versatile topological nodal magnons in Tb-based icosahedral quasicrystal 1/1 approximants
• Site-selective correlations in interacting "flat-band" quasicrystals
• Ground states of a family of frustrated spin models for quasicrystals and their approximants