Realizing corner states in artificial crystals based on topological spin textures*

The recent discovery of higher-order topological insulators (HOTIs) has significantly extended our understanding of topological phases of matter. Here, we predict that second-order corner states can emerge in the dipolar-coupled dynamics of topological spin textures in two-dimensional artificial crystals. Taking a breathing honeycomb lattice of magnetic vortices as an example, we derive the full phase diagram of collective vortex gyrations and identify three types of corner states that have not been discovered before. We show that the topological "zero-energy" corner modes are protected by a generalized chiral symmetry in the sexpartite lattice, leading to particular robustness against disorder and defects, although the conventional chiral symmetry of bipartite lattices is absent. We propose the use of the quantized Z_6 Berry phase to characterize the nontrivial topology. Full micromagnetic simulations confirm the theoretical predictions with good agreement. Our findings open up a promising route for realizing higher-order topologically protected corner states in magnetic systems and finally achieving topological spintronic memory and computing.