Point-gap topology of damped magnon excitations in skyrmion strings
We theoretically study the non-Hermitian topology of magnons with finite lifetimes due to Gilbert damping. By incorporating the spin-wave theory and perturbation theory for the Landau-Lifshitz-Gilbert equation including nonlocal damping terms, we analytically evaluate the spectral winding number for point gaps, which indicates the existence of the non-Hermitian skin effect (NHSE). We find that the NHSE can occur even in the absence of nonlocal damping. In the presence of nonlocal damping along one direction, we show that the winding number for an energy band with a unique minimum is determined from the sign of the wave number at the band minimum. We demonstrate these results using a model that hosts a skyrmion-string lattice as a steady state. We further investigate spin-wave propagation dynamics excited by a magnetic-field pulse and show that the propagation direction changes drastically from band to band depending on the presence of local and nonlocal damping, consistent with the nontrivial winding numbers.