Effect of anisotropy on the magnon energy gap in a two-layer ferromagnetic superlattice

The magnon energy bands or spectra in a two-layer ferromagnetic superlattice are studied. It is found that a modulated energy gap exists in the magnon energy band along Kx direction perpendicular to the superlattice plane, which is different from the optical magnon gap at Kx=0. The anisotropy, the spin quantum numbers and the interlayer exchange couplings all affect the magnon energy gap. If the anisotropy exists, there will be no acoustic energy branch in the system. There is a competition effect of the anisotropy and the spin quantum number on the magnon energy gap. The competition achieves a balance at the zero energy gap, at which the symmetry of the system is higher. The two energy spectra of the two-layer ferromagnetic superlattice are lowered with increasing temperature.