Recent acoustic and electrical-circuit experiments have reported the third-order (or octupole) topological insulating phase, while its counterpart in classical magnetic systems has 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.

• Received 4 March 2021
• Accepted 11 June 2021

DOI:https://doi.org/10.1103/PhysRevB.103.214442