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Effective-medium theory of long-wavelength spin waves in magnetic superlattices.

We explore the theory of long-wavelength spin waves in superlattices which incorporate magnetically ordered films that interact either through dipolar fields generated by spin motions or exchange couplings at interfaces or those mediated by an intervening nonmagnetic film. We show that for long wavelengths one may replace the superlattice by an effective medium described by a permeability tensor composed of those of the constituent films. Our treatment applied to a semi-infinite lattice of ferromagnetic films reproduces results obtained earlier in a full theory by Camley, Rahman, and Mills. We also develop an effective medium theory of Y-Gd superlattices in the anti-phase-domain configuration, with transverse field applied. We obtain a rich spectrum of surface spin waves in this case. We also obtain Green's functions for the average medium description of the Y-Gd system and use these to discuss surface-mode contributions to the spectral densities explored by Brillouin scattering.