Magnonic spectra of ferromagnetic composites versus magnetization contrast

It 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 materials but were very weakly sensitive to the contrast in spontaneous magnetizations of the two materials. Accordingly, in this paper we introduce a new mathematical definition of the exchange field acting in inhomogeneous medium. With this new definition the present theory gives magnonic spectra reasonably sensitive to magnetization contrast, as they should be from the physical view point; moreover, the magnetization contrast now becomes a gap-creating factor as well.