Realizing Corner States in Artificial Crystals Based on Topological Spin Textures

TL;DR

This paper predicts and confirms the existence of higher-order topological corner states in artificial magnetic crystals, specifically in topological spin textures, using theoretical modeling and micromagnetic simulations, with potential for spintronic applications.

Contribution

It introduces a new class of topological corner states in magnetic vortex lattices, characterized by a quantized Berry phase and protected by generalized chiral symmetry, expanding topological spintronics.

Findings

Identification of three types of corner states in a breathing honeycomb lattice.

Protection of zero-energy corner modes by generalized chiral symmetry.

Confirmation of theoretical predictions through micromagnetic simulations.

Abstract

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 $\mathbb{Z}_{6}$ Berry phase to characterize the nontrivial topology. Interestingly, we observe corner states at either obtuse-angled or acute-angled corners, depending on whether the lattice boundary has an armchair or zigzag shape. Full micromagnetic simulations confirm the theoretical predictions with good agreement. Experimentally, we suggest using the recently developed ultrafast Lorentz microscopy technique [M\"{o}ller \emph{et al}.,{arXiv:1907.04608}] to detect the topological corner states by tracking the nanometer-scale vortex orbits in a time-resolved manner. 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.