Generalized CPA approach to the disordered Heisenberg ferromagnet

Abstract

A ferromagnetic binary alloy is considered where each component has spin S_A, S_B and concentration X_A, X_B=1-X_A, respectively. The interaction is given by the Heisenberg hamiltonian with exchange constants J^{alpha beta} between nearest-neighbour spins S_alpha , S_beta ( alpha , beta =A or B). It is shown that neglecting fluctuations in the static field seen by a spin S_A (S_B), generalized CPA equations can be written for the configurational average matrix G_ij, with components G_ij^{alpha beta} . The formalism is symmetric in both components and valid for arbitrary values of the exchange constants and spins. In the general case it is expected to be good only for intermediate values of the concentrations, because it fails to reproduce the known exact results in the dilute limit X_alpha <alpha J^{alpha alpha} /S_alpha J^{alpha alpha} )=1, where alpha =A or B if alpha =B or A.