Ferromagnetic and transmission resonance in magnetic metal superlattices

We have developed a mathematical formulation by which surface-impedance calculations of magnetic layered structures are significantly simplified and, hence, calculable. A transfer-function matrix is introduced in order to relate the electric and magnetic fields at one surface of a magnetic metal layer to fields at the other surface. The surface impedance of a layered structure is then expressed in terms of the four transfer-function matrix elements corresponding to surface fields of the layered structure instead of internal microwave fields corresponding to all the layers within the layered structure. The ferromagnetic resonance fields and line shapes are calculated for layered structures containing alternating dielectric and iron magnetic layers. In addition, spin-pinning boundary conditions are assumed at the surfaces of each iron layer. The calculations are of sufficient generality so that the insulating dielectric layer may be replaced by a conductive metal layer. We find that standing spin-wave resonance may be excited in the layered structure, even for zero spin pinning at the iron-layer surfaces. From calculations of internal microwave fields within each layer, we deduce that the spin-wave resonance is due to an asymmetrical magnetic field excitation of each iron layer, although the layered structure as a whole is symmetrically excited. For iron-layer thicknesses of {≥}1500 A{} there is no discernible difference between the ferromagnetic resonance fields of the main line and the first-spin-wave--resonance mode---an accidental degeneracy. If nonzero spin pinning is assumed at each iron-layer surface, the accidental degeneracy is removed.