RPA-CPA theory for magnetism in disordered Heisenberg binary systems with long-range exchange integrals

Abstract

We present a theory based on Green's-function formalism to study magnetism in disordered Heisenberg systems with long-range exchange integrals. Disordered Green's functions are decoupled within the Tyablicov scheme and solved with a coherent potential approximation (CPA) method. The CPA method is the extension of Blackmann-Esterling-Beck approach to systems with an environmental disorder term which uses cumulant summation of the single-site noncrossing diagrams. The crucial point is that we are able to treat simultaneously and self-consistently the random-phase approximation (RPA) and CPA loops. It is shown that the summation of the s-scattering contribution can always be performed analytically, while the $p,d,f\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}$ contributions are difficult to handle in the case of long-range coupling. To overcome this difficulty we propose and provide a test of a simplified treatment of these terms. In the case of the three-dimensional disordered nearest-neighbor Heisenberg system, a good agreement between the simplified treatment and the full calculation is achieved. Our theory allows us in particular to calculate the Curie temperature, the spectral functions, and the temperature dependence of the magnetization of each constituent as a function of concentration of impurity. Additionally it is shown that a virtual crystal treatment fails even at low impurity concentration.