Third-order topological insulator in three-dimensional lattice of magnetic vortices

TL;DR

This paper predicts and verifies a third-order topological insulator phase in a 3D lattice of magnetic vortices, demonstrating stable corner states protected by topology through simulations.

Contribution

It introduces a new magnetic system supporting higher-order topological phases with stable corner states, expanding topological insulator realizations to classical magnetic systems.

Findings

Magnetic vortex lattices can host zero-dimensional corner states.

Topological protection ensures corner state stability against external frustrations.

Micromagnetic simulations confirm theoretical predictions.

Abstract

Recent acoustic and electrical-circuit experiments have reported the third-order (or octupole) topological insulating phase, while its counterpart in classical magnetic systems is yet to be realized. Here we explore the collective dynamics of magnetic vortices in three-dimensional breathing cuboids, and find that the vortex lattice can support zero-dimensional corner states, one-dimensional hinge states, two-dimensional surface states, and three-dimensional bulk states, when the ratio of alternating intralayer and interlayer bond lengths goes beyond a critical value. We show that only the corner states are stable against external frustrations because of the topological protection. Full micromagnetic simulations verify our theoretical predictions with good agreement.