The magnon energy bands in a superlattice composed of two alternating ferromagnetic materials with antiferromagnetic interlayer exchange coupling is studied, by means of Green's function method and the Tyablikov decoupling approximation. It is found that a modulated energy gap exists in the magnon energy band along direction perpendicular to the superlattice plane. The effect of the spin quantum numbers, the anisotropies, the interlayer exchange couplings and the external magnetic field on the energy gap has been investigated.
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