Zero-Point Spin Reduction of an Antiferromagnet

Abstract

Zero-point spin reduction in the low-dimensional antiferromagnet is discussed by the spin wave theory taking into accOtmt kinematical interaction due to finite magnitude of spin. This method is applied to KCuF, and the result is in good agreement with the ob­ served one. Furthermore the values of zero-point spin reduction of several other chain· structure antiferromagnets are predicted. §.1. Introduction A large zero-point spin reduction in the antiferromagnet of the low dimen~ sionality has recently been observed. In the layer-structure antiferromagnet K 2MnF 4, the observed values of zero-point spin reduction agree with those of a simple two-dimensional spin-wave theory.D It has been found that the zero-point spin reduction in the one-dimensional antiferromagnet' KCuF 8 is nearly 45%. 2) However, the kinematical interaction d,ue .to the restriction on the number of spin deviations possible at any given site cannot always be neglected i.n the antiferro- · magnet of the low dimensionality even at absolute zero. Especially the zero-point spin reduction of the ideal spin-wave theory diverges in the one0dimensional Heisen­ berg antiferromagnet. As the zero-point spin reduction should not. be over the spin magnitude S, the divergence means that the spin-wave theory which does not take· account of the kinematical interaction cannot be trusted. The effect of the kinematical interaction for zero-point spin reduction was first estimated by Herbert 8J for the Heisenberg antiferromagnet with each spin 8=1/2,, but he did not give any attention to the low-dimensional antiferromagnet. In the present paper his method is extended to the case of general S, and the effe'ct of the ki~ematical interaction is taken into account in the calculation of the zero-point spin reduction, and several antiferromagnetic chain-structure compounds are dis­ cussed.