| This paper is based on the model of Heisenberg, which studies the transition temperature of three layers'super lattice and magnon energy gap of two layers'ferromagnetism super lattice with Green Function.As for three layers'ferromagnetism super lattice system, the variation of the transition temperature is adding along with bigger spin quantum number. At the same, the effect of spin quantum number of every layer on transition temperature is same except there is little difference among magnetic moment in low temperature. When the parameter of anisotropy is zero, however the spin quantum number changes, the effects of interlamination transition coupling coefficient J12 and J31 on transition temperature is almost the same: the transition temperature is becoming bigger and bigger along with the strengthening of interlamination transition coupling, while its variation is becoming smaller and smaller. The transition temperature and its variation is adding with the adding of the parameter of anisotropy D1 or D2 or D3 whether the spin quantum number is equal or not. When the spin quantum number is equal, the effect of the parameter of anisotropy on transition temperature is almost the same; what's more, the effect of the related parameter of anisotropy is more effective when the interlamination transition coupling is strong. The effect of parameter of anisotropy on transition temperature is heavier with a bigger S(the variation is quick). At the low temperature, magnetic moment of ferrimagnetic super lattice is generally bigger than that of ferromagnetic.As for two layers'ferromagnetism super lattice system, the influence of spin quantum number S1 and S2 on energy gap width ?ωis same; when the difference of the spin quantum is very tiny to some extent, the energy gap disappears while external magnetic field and parameter of anisotropy is zero. The width of energy gap firstly decreases and then augments linearly when spin quantum is not equal and parameter of anisotropy is equal. The width of energy gap ?ωaugments linearly with the augmentation of external magnetic field when spin quantum number is equal and D1> D2. It will decreases to disappear firstly and then augments linearly when D1 <D2. The width of energy gap ?ωwould augment linearly with the augmentation of the external magnetic field when S2>S1. The width of energy gap ?ωwill decreases to disappear firstly and then augments linearly with the augmentation of external magnetic field when S1> S2. |
