Effects of competition between the anisotropy and the spin quantum number on the magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy bands are studied for a four-layer ferromagnetic superlattice, with regard to the effects of the competition between the anisotropy and the spin quantum number. A special attention is also paid on the effects of the symmetry of the system. It is found that three modulated energy gaps exist in the magnon energy band along Kx direction perpendicular to the superlattice plane. The magnetic anisotropy affects significantly the magnon energy gaps. The zero energy gap Δω23 correlates with the conditions between anisotropy constants, D1+D3=D2+D4 and D1=D3 (or D2=D4), while the disappearance of the magnon energy gaps Δω12 and Δω34 corresponds to a translational symmetry of x-direction in a unit cell. When the parameters of the system deviate from these conditions, the energy gaps Δω12, Δω23 and Δω34 become larger. There is a competition effect of the anisotropy and the spin quantum number on the magnon energy gaps Δω12 and Δω23. When the symmetry of the system is higher, the competition can achieve a balance to cause the zero energy gap.