Entropic crystallization of geometrically frustrated magnets on 1/1 approximant Tsai-type quasicrystal

TL;DR

This study uses Monte Carlo simulations to explore entropic crystallization and magnetic ordering in a geometrically frustrated Ising model on a quasicrystal-like lattice, revealing a second-order phase transition with residual entropy.

Contribution

It demonstrates that residual entropy influences magnetic order formation, introducing the concept of entropic crystallization in frustrated magnetic systems.

Findings

Second-order phase transition with ${ m Z}_3 imes { m Z}_2$ symmetry breaking.

Presence of finite residual entropy (~0.1767 per spin) at low temperatures.

Residual entropy suppresses domain wall formation, leading to entropic crystallization.

Abstract

We have studied the antiferromagnetic Ising model on the icosahedral bcc lattice, as a model system of 1/1 approximant Tsai-type quasicrystals. We addressed thermal equilibrium properties of this system with Markov-chain Monte Carlo simulation supplemented with the parallel tempering technique to accelerate the relaxation dynamics. As a result, we found a second-order phase transition takes place to the magnetic ordered phase with ${\mathbb Z_3}\times {\mathbb Z_2}$ symmetry breaking. Despite the ordering, the low-temperature phase keeps macroscopic degeneracy as identified by finite residual entropy, $\mathcal{S}\sim0.1767/{\rm spin}$. Remarkably, the existence of residual entropy turns out to play a major role in the formation of magnetic order. Generation of domain wall is suppressed, as it reduces the residual entropy locally stored in icosahedra, beyond the gain of configurational entropy due to domain wall patterns. Magnetic order arises out of this competition as entropic crystallization, which manifest universal mechanism of strongly frustrated systems with large geometrical units.