Theory of Spin-Wave Interactions in Ferro- and Antiferromagnetism

The spin-wave theory in an ideal Heisenberg model of a ferromagnet is studied using Holstein and Primakoff's method including the spin-wave interactions. Several earlier published results of the correction to the spontaneous magnetization produced by spin-wave interactions were in disagreement with each other, and they were not in agreement with Dyson's result which is regarded as rigorous at low temperatures. Our result is in agreement with Dyson's to the order which we have considered.

Our method can be applied to antiferromagnetism easily. We have obtained the correction arising from interactions between spin waves. The correction term is quite small. This means that the simple theory neglecting the spin-wave interactions is sufficient for practical purposes.