Topological insulators and semimetals in classical magnetic systems

TL;DR

This paper reviews recent advances in topological phases within classical magnetic systems, focusing on magnons and solitons, their topological properties, potential applications, and experimental realizations.

Contribution

It provides a comprehensive overview of topological phenomena in structured classical magnetism, including models, properties, and experimental approaches, highlighting new insights and future directions.

Findings

Topological magnon insulators and semimetals have been identified in magnetic crystals.

Magnetic solitons exhibit topological phases, including higher-order states.

Experimental detection of edge states in magnonic and solitonic crystals has been discussed.

Abstract

Pursuing topological phases in natural and artificial materials is one of the central topics in modern physical science and engineering. In classical magnetic systems, spin waves (or magnons) and magnetic solitons (such as domain wall, vortex, skyrmion, etc) represent two important excitations. Recently, the topological insulator and semimetal states in magnon- and soliton-based crystals (or metamaterials) have attracted growing attention owing to their interesting dynamics and promising applications for designing robust spintronic devices. Here, we give an overview of current progress of topological phases in structured classical magnetism. We first provide a brief introduction to spin wave, and discuss its topological properties including magnon Hall effects, topological magnon insulators, and Dirac (Weyl) magnon semimetals. Appealing proposal of topological magnonic devices is also highlighted. We then review the collective-coordinate approach for describing the dynamics of magnetic soliton lattice. Pedagogical topological models such as the Su-Schrieffer-Heeger model and the Haldane model and their manifestation in magnetic soliton crystals are elaborated. Then we focus on the topological properties of magnetic solitons, by theoretically analyzing the first-order topological insulating phases in low dimensional systems and higher-order topological states in breathing crystals. Finally, we discuss the experimental realization and detection of the edge states in both the magnonic and solitonic crystals. We remark the challenges and future prospects before concluding this article.