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On the spin wave approximation in the theory of magnetically ordered crystals Pink, David Anthony

Abstract

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.

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