Coupled Dipolar Spin Waves of Magnetic Multilayer Systems With Cylindrical Geometries

A theory is developed for the dipolar spin waves in cylindrical multilayer systems consisting of a core surrounded by any arbitrary number of concentric layers (or tubes). Each layer may be magnetic (either ferromagnetic or antiferromagnetic) or a nonmagnetic spacer. The long-range dipolar fields provide coupling between magnetic layers across the spacer regions, resulting in a coupling between the dipolar modes of the system. A transfer matrix approach is employed to calculate the dispersion relations for the mode frequencies in terms of a longitudinal wave number. Numerical applications are made to multilayer systems that include several layers of the ferromagnet Ni, or the uniaxial antiferromagnet GdAlO₃, or both. Particular attention is given to the localized interface modes, which are shown to be strongly modified (for example, in their frequency and wave number cutoff) by the multilayer structure, compared to the behavior found in single magnetic wires and tubes.