Robust edge states in magnetic-texture based metamaterials

Topological phases in magnetic materials are of great current interest in spintronics because of their fundamental significance and practical utility for robust information processing. A particularly interesting system is magnetic-texture-based metamaterials, since they can offer flexible controllability that can benefit from modern spintronic techniques. The collective motion of magnetic texture or soliton is described by Thiele's equation, which results in a wavelike equation in the artificial crystal, and the equation differs from the wave equations of its electronic, photonic, and acoustic counterparts in the following respects: (i) The nonvanishing topological charge induces a gyration term that is analogous to an effective magnetic field acting on a quasiparticle, thus breaking time-reversal symmetry. (ii) The inertial effect is taken into account by a mass term. A non-Newtonian gyration term is included to capture the high-frequency behavior of the magnetic texture and to determine the interaction parameters with high accuracy. (iii) The particle-particle coupling is strongly anisotropic.
Through analytical and numerical calculations, we predict (higher-order) topological insulator states in magnetic-texture (e.g., skyrmion and vortex) based metamaterials, which manifests robust edge and/or corner states at device boundaries and is characterized by the quantized Chern number and the Z_N Berry phase. Note that both fabricating the spin-texture metamaterials of interest and detecting the spatially localized edge modes are already within the reach of current technology. Our findings open up a promising route to realizing (higher-order) topological insulators in magnetic systems and to achieving robust spintronic memories, imaging, and computing.

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