The frequencies and linewidths of spin waves in one-dimensional (1D) and two-dimensional (2D) periodic superlattices of magnetic materials are found, using the Landau-Lifshitz-Gilbert equations. The form of the exchange¯eld from a surface-torque-free boundary between magnetic materials is derived, and magnetic-material combinations are identi¯ed which produce gaps in the magnonic spectrum across the entire superlattice Brillouin zone for hexagonal and square-symmetry superlattices. The magnon gaps and spin-wave dispersion properties of a uniform magnetic material under the in°uence of a periodic electric¯eld are presented. Such results suggest the utility of magnetic insulators for electric-¯eld control of spin-wave propagation properties.

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