Cluster Theory of a Dilute Antiferromagnet. Application to the Mn1–cZncF₂ System

A cluster theory of a dilute antiferromagnet which simultaneously takes into account the fluctuations in the longitudinal and transverse part of the exchange interaction is proposed. The present theory allows to describe the dependence of the line shapes of the spin excitation spectrum on the nonmagnetic atom concentration and the wave vector. A comparison with experimental results indicates that the predictions of the theory are valid in a wide range of concentrations when the long‐range order persists. It is pointed out that the coherent wave approximation accounts for the gross behaviour of the spin excitation spectrum. It is demonstrated that the results of the cluster theory are close to those of the coherent potential approximation, but more transparent and more suitable for comparison with experiment.