ABSTRACT
In this chapter, the author employs a self-consistent Green’s function theory to calculate the spin wave spectrum and the layer magnetizations at finite in two and three dimensions as well as in a thin film with surface effects. He shows and discusses analytical details and the validity of the method. The competition between thee interactions gives rise to a non-collinear spin configuration in the ground state. The SC lattice can support the DM interaction in the absence of the inversion symmetry. The absence of inversion symmetry can be also achieved by the positions of nonmagnetic ions between magnetic ions. For SW higher-energy modes, there has been an experimental breakthrough with the spin polarized electron energy loss spectroscopy. By a self-consistent Green’s function theory, obtain the expression of the spin wave dispersion relation in 2D and 3D as well as in a thin film.
