Magnetism and topology in Tb-based icosahedral quasicrystal

Shinji Watanabe

doi:10.1038/s41598-021-97024-w

Abstract

Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals. The electric property is far from complete understanding and it has been a long-standing issue whether the magnetic long-range order is realized in the QC. The main difficulty was lack of microscopic theory to analyze the effect of the crystalline electric field (CEF) at the rare-earth atom in QCs. Here we show the full microscopic analysis of the CEF in Tb-based QCs. We find that magnetic anisotropy arising from the CEF plays a key role in realizing unique magnetic textures on the icosahedron whose vertices Tb atoms are located at. Our analysis of the minimal model based on the magnetic anisotropy suggests that the long-range order of the hedgehog characterized by the topological charge of one is stabilized in the Tb-based QC. We also find that the whirling-moment state is characterized by unusually large topological charge of three. The magnetic textures as well as the topological states are shown to be switched by controlling compositions of the non-rare-earth elements in the ternary compounds. Our model is useful to understand the magnetism as well as the topological property in the rare-earth-based QCs and approximant crystals.

Highlights

Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals
Quasicrystal (QC), which was discovered in 1 9841, has a unique lattice structure with the rotational symmetry forbidden in conventional c rystals[2,3]
Theoretical studies to date have been performed as the model calculations mostly by the spin model and by the Hubbard model in a small cluster or low-dimensional s ystems[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29], where the effect of the crystalline electric field (CEF) crucial for the rare-earth system was not taken into account microscopically

Summary

Introduction

Quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in conventional crystals. In the rare-earth based approximant crystal (AC) retaining the periodicity as well as the local atomic configuration common to the QC, the magnetic long-range orders have been observed in Cd6 R (R = Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm)[5,6,7,8] and Au–SM–R (SM = Si, Ge, Sn, and Al, and R = Gd, Tb, Dy, and Ho)[9,10] Most of these measurements were performed by using the bulk probe such as susceptibility and the detailed magnetic structures remain unresolved. We propose the minimal model to clarify the magnetic structures in the QCs and ACs. Our analysis suggests that the long-range order of the hedgehog characterized by the topological charge is realized in the Tb-based QC. Distinct from the topological spin textures intensively studied so far in the periodic

Methods

Results

Conclusion