We predict the emergence of second-order topological insulators in the dynamics of spin-texture-based metamaterials. We propose that the quantized Chern number and the ${\mathbb{Z}}_6$ Berry phase can completely characterize the nontrivial topology. By studying the collective gyration of magnetic vortices in a breathing honeycomb lattice, we derive the full phase diagram and show that the topological “zero-energy” corner mode is protected by a generalized chiral symmetry in the sexpartite lattice, leading to particular robustness against disorder and defects. Interestingly, we observe corner states at either obtuse-angled or acute-angled corners, depending on whether the lattice boundary has an armchair or a zigzag shape. Full micromagnetic simulations confirm the theoretical predictions with good agreement. Our findings open up a promising route to realizing higher-order symmetry-protected corner states in magnetic systems and to finally achieving topological spintronic memories, imaging, and computing.

• Received 9 October 2019
• Revised 8 December 2019
• Accepted 20 May 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.064058