Tt had been shown recently that the calculated magnonic spectra of two-dimensional periodic ferromagnetic composites can present frequency ranges forbidden for the propagation of magnon excitations throughout the composite. However, those forbidden energy gaps were found to be highly sensitive to the exchange contrast between the component ferromagnetic ma- terials but were very weakly sensitive to the contrast in spontaneous mag- netizations of the two materials. Accordingly, in this paper we introduce a new mathematical definition of the exchange field acting in inhomogeneous medium.
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