On the spin wave approximation in the theory of magnetically ordered crystals

The question of the self-consistency of spin wave theory as applied to different spin arrangements in magnetically ordered crystals has been reinvestigated. A set of equations, involving the probabilities of finding a given number of spin deviations at a given site first proposed by Van Kranendonk and Van Vleck (1958) in connection with a simple cubic antiferromagnet at a temperature of 0°K, is generalised and solved exactly for an arbitrary temperature. Two sets of equations are solved both for the case of a simple cubic antiferromagnet and for more general spin arrangements, collectively referred to as spiral spin arrangements. In solving for the probabilities a method is developed for easy calculation of the thermal average of certain functions of number operators. Finally, numerical results are given for some probabilities connected with: (i) the simple cubic antiferromagnet and (ii) a model of the rare earth metal, dysprosium. The latter is of some interest in view of the investigations of spiral spin arrangements in recent years.Science, Faculty ofPhysics and Astronomy, Department ofGraduat