Magnetism in Rare Earth Quasicrystals: RKKY Interactions and Ordering

TL;DR

This paper investigates magnetic behavior in rare earth quasicrystals by calculating RKKY interactions on quasiperiodic tilings and analyzing Ising spin models, revealing cluster formation and long-range magnetic order.

Contribution

It introduces a two-step theoretical approach combining RKKY interaction calculations with Monte Carlo simulations to study magnetism in quasicrystals, highlighting cluster formation and phase transition phenomena.

Findings

Emergence of strongly coupled spin clusters

Weak inter-cluster coupling

Transition to long-range ordered phase

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.