Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal Symmetry

TL;DR

This paper investigates the unique magnetic properties of geometrically frustrated low-dimensional systems with pentagonal symmetry, focusing on classical spins on Penrose tilings and their complex ground states.

Contribution

It introduces a recursive analytical approach and Monte Carlo simulations to study magnetic frustration in pentagon-based quasicrystal structures.

Findings

Identification of complex ground states in pentagonal frustrated systems

Development of recursion relations for infinite Penrose tiling clusters

Insights into magnetic behavior in quasicrystalline geometries

Abstract

In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a structure having pentagonal loops. Such five-fold loops can be expected to occur naturally in quasicrystals, as seen for example in a number of experimental studies of surfaces of icosahedral alloys. Our model considers classical vector spins placed on vertices of a subtiling of the two dimensional Penrose tiling, and interacting with nearest neighbors via antiferromagnetic bonds. We give a set of recursion relations for this system, which consists of an infinite set of embedded clusters with sizes that increase as a power of the golden mean. The magnetic ground states of this fractal system are studied analytically, and by Monte Carlo simulation.