Homotopy-Theoretic Study &Atomic-Scale Observation of Vortex Domains in Hexagonal Manganites.

Jun Li,Chao Ma,Ming-Wen Chu,Fu-Kuo Chiang,Jianqi Li,Huaixin Yang,Huanfang Tian,Cheng-Hsuan Chen,Zhen Chen

doi:10.1038/srep28047

Abstract

Essential structural properties of the non-trivial “string-wall-bounded” topological defects in hexagonal manganites are studied through homotopy group theory and spherical aberration-corrected scanning transmission electron microscopy. The appearance of a “string-wall-bounded” configuration in RMnO3 is shown to be strongly linked with the transformation of the degeneracy space. The defect core regions (~50 Å) mainly adopt the continuous U(1) symmetry of the high-temperature phase, which is essential for the formation and proliferation of vortices. Direct visualization of vortex strings at atomic scale provides insight into the mechanisms and macro-behavior of topological defects in crystalline materials.

Highlights

Essential structural properties of the non-trivial “string-wall-bounded” topological defects in hexagonal manganites are studied through homotopy group theory and spherical aberration-corrected scanning transmission electron microscopy
Topological defects are classified by the elements of homotopy groups associated with the symmetry of the order parameter space
When temperature approaches Ts, the degeneracy space expands to R2, which is isomorphic to a unit circle S1

Summary

Introduction

Essential structural properties of the non-trivial “string-wall-bounded” topological defects in hexagonal manganites are studied through homotopy group theory and spherical aberration-corrected scanning transmission electron microscopy. In. YMnO3, the crystal adopts centrosymmetric P63/mmc (D6h, Z = 2) structure at temperature above the structural phase transition (Ts ≈ 1270 K), and symmetry decreases to P63cm (C6v, Z = 6) below Ts, a transformation induced mainly by the condensation of the K3 non-polar mode. YMnO3, the crystal adopts centrosymmetric P63/mmc (D6h, Z = 2) structure at temperature above the structural phase transition (Ts ≈ 1270 K), and symmetry decreases to P63cm (C6v, Z = 6) below Ts, a transformation induced mainly by the condensation of the K3 non-polar mode This transition leads to a trimerized tilting of the. The observed structural properties are quite interesting, and there is ongoing debate about the best structural model for the domain walls, and for the vortex core as well[27,28,29,30,31,32]

Methods

Results

Conclusion