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

Abstract

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 K x direction perpendicular to the superlattice plane. The magnetic anisotropy affects significantly the magnon energy gaps. The zero energy gap Δ ω 23 correlates with the conditions between anisotropy constants, D 1+ D 3= D 2+ D 4 and D 1= D 3 (or D 2= D 4), while the disappearance of the magnon energy gaps Δ ω 12 and Δ ω 34 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 Δ ω 12, Δ ω 23 and Δ ω 34 become larger. There is a competition effect of the anisotropy and the spin quantum number on the magnon energy gaps Δ ω 12 and Δ ω 23. When the symmetry of the system is higher, the competition can achieve a balance to cause the zero energy gap.