Fig. 4

Spin-wave dispersion for \(d_L = 30\) nm. In (a), the case with \(N_L = 30\) is illustrated, while in (b), the number of layers is \(N_L = 31\). Bulk modes are shown on a color scale from black to red, and the surface modes are highlighted in blue and green. Note that some of the surface modes can acquire bulk properties depending on the parity of \(N_L\) and the sign of the wave vector. The insets in (a) and (b) provide a magnified view of the modes within a small wave vector range, where the peculiar behavior of the surface modes can be appreciated. Circles, squares, and stars highlight the dynamic states evaluated at \(\vert k\vert =30\) rad/\(\mu\)m, which are discussed in Fig. 5.