The Spin-Wave Theory as a Variational Method and Its Application to Antiferromagnetism

The spin-wave theory in a modified form is applied to antiferromagnetism. The interaction between different modes of spin-waves, which is due to the higher order terms omitted in the customary spin-wave treatment, is taken into account in a self-consistent manner. It is shown that the interaction terms cause a change of the frequency spectrum of spin-waves which is equivalent to the existence of an anisotropic field. The upper limits of the ground levels are calculated. The variational method can also be applied to the discussions of the stable configurations of magnetization vectors in anisotropic and external fields, and it is consistent with the molecular field theory.