Fig. 5

In-plane dynamic magnetization component \(m_z\) as a function of the normal coordinate y. Calculations are realized for the bulk and surface modes highlighted by markers (circles, squares, and stars) in Fig. 4. In (a), a schematic representation of the magnetization oscillations is depicted. In (b–h), the case with \(N_L=30\), \(d_L=30\), and \(k=-30\) rad/\(\mu\)m is shown, where the bulk (b–d) and surface (e–h) modes are plotted as a function of the multilayer thickness. In (i–l), the system with \(N_L=31\) and \(d_L=30\) is considered. Panels (i) and (l) show the bulk modes, evaluated at \(k=-30\) rad/\(\mu\)m, against the thickness of the structure. In (j) and (k), the low-frequency surface waves are depicted for \(k=-30\) rad/\(\mu\)m and \(k=+30\) rad/\(\mu\)m, respectively.