Results are presented of new theoretical investigations in which spin waves in multilayered structures are calculated, properly including both magnetic interface anisotropies and exchange.1 The work is an extension of a recently introduced theory for the calculation of single‐layer spin‐wave frequencies by Rado and Hicken, including interface anisotropies and exchange.2 The calculations were carried out for two different types of multilayered structures, i.e., for multilayers consisting of alternating magnetic and nonmagnetic multilayers, and for all‐magnetic multilayers. In both cases all layers were of the same thickness. The solutions were obtained by solving for
the Maxwell equations and the Landau–Lifshitz torque equation. The boundary conditions consist of the Maxwell boundary conditions, and the Rado–Weertman boundary condition3 in the case of magnetic/nonmagnetic multilayers. In the case of all‐magnetic multilayers, modified Rado–Weertman boundary conditions were used.4,5 In the case of magnetic/nonmagnetic multilayers, both dipolar‐type (Damon–Eshbach‐type) modes and exchange‐dominated modes are obtained. The dipolar modes are frequency split as a result of the dipolar coupling of single‐layer spin waves across the nonmagnetic spacer layers. The
exchange modes show no frequency splitting apart from the crossing regimes with the dipolar modes. In the regime of small layer thicknesses, where the dipolar modes are well frequency separated from the exchange modes, the calculations reproduce results obtained by neglecting exchange contributions.6 In the limit of very small layer thicknesses (<40 Å), the influence of interface anisotropies manifests itself for the dipolar modes in a frequency increase, as well as in a reduced coupling across the nonmagnetic layers. In the crossing regimes of dipolar modes and exchange modes, the modes exchange their mode characteristics, leading to a pronounced frequency gap. The width of the gap is
mostly determined by the amount of interface anisotropy. The calculation of an all‐magnetic multilayered structure, consisting of three Fe layers with interleaving Ni layers, was carried in the limit of maximum exchange coupling across the interfaces.1 The results show frequency splittings both for dipolar modes and for exchange modes. In the limit of an infinite number of layers, the exchange modes will eventually form a band of exchange‐dominated collective spin waves reminiscent of the band of collective dipolar spin waves in magnetic/nonmagnetic multilayers. The crossing regimes of dipolar modes with the
exchange modes show frequency gaps close to those observed for magnetic/nonmagnetic multilayers.