A general electrodynamic theory is developed for dispersion characteristics of spin-electromagnetic waves (SEWs) propagating in multiferroic multilayers. The derivation is based on the full set of Maxwell's equations taking into account retardation effects. The multilayers are considered to be composed of an infinite number of ferrite and ferroelectric layers having arbitrary thicknesses, as well as arbitrary magnetic and electric parameters. As an example, spectra of SEWs are calculated and analyzed for a heterostructure containing two thin ferrite films separated by a thin ferroelectric film. An electric field tunability of the SEW dispersion characteristics at gigahertz frequencies is shown, providing an efficient control of SEW wave-numbers important for applications.

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