Extension Theory for Magnon of a Ferromagnetic Superlattice

We prove that the extension theory for lattice Green's functions can be used to study Heisenberg ferromagnetic systems. As an example, the magnon spectrum of a ferromagnetic superlat tice is calculated by the extension theory for lattice Green's functions cooperated with the transfer matrix technique. The spectrum of magnetic excitation near the surface of a ferromagnetic superlattice is also presented.