This thesis is intended studying the magnon of a spin system on semi-infinite 2D honeycomb lattices with the zigzag edge. In order phase, we use the Holstein-Primakoff(HP) representation approximation to rewrite the Heisenberg Hamiltonian in terms of boson operators. By generalized Bloch theorem, the Hamiltonian of the bipartite lattice can be calculated analytically. For the antiferromagnetic case, we find that there exists a edge magnon whose energy is lower than such that of the bulk magnon usually derived in a periodic system. The existence of edge magnon provides a possibility to produce ferromagnet spin polarization along the zigzag edge. Interestingly, the edge magnon has only one kind of spin flip mode, Sztot = -1, as the ferromagnetic spin eave. Besides, the linear dependent dispersion when the momentum approaches zero energy let it look like the antiferromagnetic spin wave. Combining both properties, we are aware that the edge magnon of this semi-infinite anti-ferromagnet can not be obtained by any one dimensional effective Heisenberg Hamiltonian because. In addition, we study the edge spin wave of the ferrimagnet and ferromagnet on the same lattices structure also. For ferrimagnet, the presence of the zigzag edge gives rise to edge magnon, but unlike antiferromagnet, the properties of this magnon tallies with those of one dimensional ferromagnet model. As to ferromagnet on honeycomb lattices, no edge magnon exists. Finally, we demonstrate the ferromagnet on triangular lattices, which can be considered as the small spin of the ferrimagnet on honeycomb lattices is integrated out. We may think this ferromagnet give the same consequence as the ferrimagnet. However, relative to the low-lying edge magnon occurring in latter one, the edge magnon in former is highly-lying mode over the bulk magnon.

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