CPA susceptibility of the double exchange model

Abstract

We use a many-body coherent potential approximation (CPA) to study the paramagnetic state of the double exchange model with finite local spins S. Our CPA treats dynamical effects due to the quantum nature of the local spins in a local approximation, becomes exact in the atomic limit, and reduces to Kubo's one-electron CPA in the empty band limit and to dynamical mean field theory (DMFT) in the classical S→∞ limit. We solve the CPA equations of motion for all S in the strong Hund coupling limit, determining all quantities self-consistently. We show that the CPA does not give a ferromagnetic transition for any S; this is due to the local spin probability distribution function P( S z ) being inaccurately obtained. We bypass this difficulty by extrapolating P( S z ) from the exact (within DMFT) S=∞ result, and obtain a magnetic transition for all S with the expected Curie laws at band filling n=0, 1 .