Generalized CPA approach to the disordered Heisenberg ferromagnet

Abstract

A ferromagnetic binary alloy is considered where each component has spin SA, SB and concentration XA, XB=1-XA, respectively. The interaction is given by the Heisenberg hamiltonian with exchange constants Jalpha beta between nearest-neighbour spins Salpha , Sbeta ( alpha , beta =A or B). It is shown that neglecting fluctuations in the static field seen by a spin SA (SB), generalized CPA equations can be written for the configurational average matrix Gij, with components Gijalpha 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 Xalpha <<1( alpha =A or B) due to the approximate treatment of the local field that suppresses the p and d modes and modifies the energy of the s modes. However, it is shown that the theory reproduces the exact results when the values of the impurity and host spins are restricted by the condition (Salpha Jalpha alpha /Salpha Jalpha alpha )=1, where alpha =A or B if alpha =B or A.