Interplay between magnetic and spatial order in quasicrystals

TL;DR

This paper explores how magnetic and spatial orders interact in quasicrystals, revealing complex noncollinear ground states influenced by geometric frustration and quasiperiodic structure.

Contribution

It provides a theoretical analysis of magnetisation configurations in antiferromagnets on quasiperiodic tilings, highlighting the formation of subtilings with distinct magnetic and spatial properties.

Findings

Subtilings of different energies exhibit distinct magnetic orderings.

Low-energy subtilings are magnetically ordered, high-energy ones are disordered.

Quasiperiodic order influences the symmetry and spatial arrangement of subtilings.

Abstract

The stable magnetisation configurations of antiferromagnets on quasiperiodic tilings are investigated theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the combination of geometric frustration and the quasiperiodic order of atoms leads to complicated noncollinear ground states. The structure can be divided into subtilings of different energies. The symmetry of the subtilings depends on the quasiperiodic order of magnetic moments. The subtilings are spatially ordered. However, the magnetic ordering of the subtilings in general does not correspond to their spatial arrangements. While subtilings of low energy are magnetically ordered, those of high energy can be completely disordered due to local magnetic frustration.