Fig. 2. Propagation character of spin excitations on skyrmion strings.

a–c The spectra of mutual inductance ΔL₂₁ and ΔL₁₂, which represent the propagation character of spin excitation with the wave vector  +k^SW and  −k^SW, respectively. The data were measured in the SkX state under the configuration shown in d at 25 K with μ₀H = +25 mT. a, b, and c represent the CCW, B, and CW modes, respectively. e–h The corresponding data measured with μ₀H = −25 mT. i–k Dispersion relation for various spin excitations on skyrmion strings, theoretically calculated for the k^SW∥H configuration with H = 0.4H_c. Here, h, g, μ₀, μ_B, H_c, and q₀ are Planck constant, g-factor, vacuum magnetic permeability, Bohr magneton, critical field value to induce FM state, and magnetic modulation pitch, respectively. In j and k, the solid and dashed lines represent the dispersion relation for a finite sample in the magnetostatic limit and an infinitely extended sample in the bulk limit, respectively.