Magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy band in a four-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green's function technique. It is found that three modulated energy gaps exist in the magnon energy band along K_x direction perpendicular to the superlattice plane. The spin quantum numbers and the interlayer exchange couplings all affect the three energy gaps. The magnon energy gaps of the four-layer ferromagnetic superlattice are different from those of the three-layer one. For the four-layer ferromagnetic superlattice, the disappearance of the magnon energy gaps \Delta \omega _12 , \Delta \omega _23 and \Delta \omega _34 all correlates with the symmetry of this system. The zero energy gap \Delta \omega _23 correlates with the symmetry of interlayer exchange couplings, while the vanishing of the magnon energy gaps \Delta \omega _12 and \Delta \omega _34 corresponds to a translational symmetry of x-direction in the lattice. When the parameters of the system deviate from these symmetries, the three energy gaps will increase.