Edge and corner skin effects of chirally coupled magnons characterized by a topological winding tuple

We investigate a long-ranged coupled and non-Hermitian two-dimensional array of nanomagnets, fabricated on a thin magnetic substrate and subjected to an in-plane magnetic field. We predict topology-driven edge and corner skin effects of magnetic eigenmodes with the localization position at boundaries precisely characterized by a topological winding tuple $({\mathcal{W}}_1,{\mathcal{W}}_2)$. By varying the direction of the in-plane field, all magnon states pile up either at different edges of the array with $({\mathcal{W}}_1=\pm 1,{\mathcal{W}}_2=0)$ or $({\mathcal{W}}_1=0,{\mathcal{W}}_2=\pm 1)$, or at different corners characterized by $({\mathcal{W}}_1=\pm 1,{\mathcal{W}}_2=\pm 1)$. Exploiting the non-Hermitian topology is potentially helpful for designing useful magnonic metasurface in the future.