Theory of Critical Magnetic Scattering of Neutrons by Ferromagnet and Antiferromagnet

Abstract

The statistical theory of the localized model of ferromagnetism has been developed using the effective Hamiltonian method. The present method is an extensive application of that by Strieb, Callen and Horwitz. The result is reduced to that of the Bethe approximation in the Ising model in one limit, and to that of the constant coupling approximation in the Heisenberg model in the other limit. The method has been generalized to calculate the spin pair correlation functions, which are very important for the cross section in the critical magnetic scattering of neutrons. The spin pair correlation functions have been obtained in Ornstein-Zernike type in the vicinity of the critical temperature. The results obtained by Elliott and Marshall, Mori and Kawasaki, and Tahir-Kheli and Callen are compared with the present results and are criticized. The present results are in good agreement with the experimental results. The method has been extended to the antiferromagnetic case.