Simple Physical Theory of Spin Wave Interactions

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Abstract
A simple and powerful new method for the treatment of spin wave interactions is introduced and used to obtain the corrections to the energy and magnetization of ferromagnets, antiferromagnets and ferrimagnets. The results previously obtained by Dyson and by Oguchi using complicated analysis are reproduced and extended by means of elementary considerations which throw light on the physical interpretation of the corrections. In the case of a ferromagnet the validity of the random phase approximation is discussed, and the properties of the continuous medium model are calculated: in particular, the spin wave exchange-collision cross section is obtained in a simple way.