Magnon Energy Gap In Multi-Layer Superlattice

By the method of linear spin wave approximation and Green's function technology,this paper is to investigate the the magnon energy gap in magnetic multi-layer superlattice systems.For a four - layer ferromagnetic superlattice, it is revealed that there are four energy spectra branches and three energy gaps along the K_x direction.When the spin quantum numbers,the anisotropy constants and the interlayer exchange couplings of interlayers are equal to each other, two energy gaps vanish.Moreover, the absence of another magnon energy gap occurs at the condition that the sum of spin quantum numbers and anisotropy constants in interlayers are the same,at the same time, anisotropy constants in interlayer and every interlayer exchange couplings are equal. If the parameters of the system are apart from these condition above,the three energy gaps increase.In a four - layer ferrimagnetic superlattice system,four energy spectra branches and three energy gaps are observed along the K_x direction. When the sum of spin quantum numbers in the first,the second and the third layers is equal to the fourth layer spin quantum number,the first energy gap disappears. As the parameters of the system are aside from the condition,this energy gap increase.Furthermore,interlayer exchange couplings have no effect on this energy gap.When the first layer spin quantum number and the third layer spin quantum number are the same,what's more,four times of the second spin quantum number and 4/3 times of the fourth spin number are equal to the sum of the first and the second layer spin quantum number,at the same time, interlayer exchange couplings are equal to each other separately,the second magnon energy gap vanishes. If the sum of spin quantum numbers in the first,the second and the third layers is equal to the fourth layer spin quantum number, and the interlayer exchange couplings of interlayers are the same,the the third energy gap disappears. For a five - layer ferromagnetic superlattice,it is found that there are five energy spectra branches and four energy gaps in this system.As five spin quantum numbers are the same and five interlayer exchange couplings are equal,two magnon energy gaps vanish. Meanwhile,If five spin quantum numbers are the same, and five interlayer exchange couplings are equal or interlayer exchange couplings in interlayer are equal to 2 times of other interlayer exchange couplings,the third energy gap doesn't exist.When the value of three spin quantum numbers are the same and bigger than other spin quantum numbers,moreover, five interlayer exchange couplings are equal or interlayer exchange couplings in interlayer are equal to 1.5 times of other interlayer exchange couplings,the fourth energy gap is absent.Intralayer exchange couplings have no effect on the energy gaps.