Magnetic susceptibility of the double-exchange model

Previously a many-body coherent potential approximation (CPA) was used to s tudy the double-exchange (DE) model with quantum local spins S, both for S = 1/2 and for general S in the paramagnetic state. This approximation, exac t in the atomic limit, was considered to be a many-body extension of Kubo's one-electron dynamical CPA for the DE model. We now extend our CPA treatme nt to the case of general 5 and spin polarization. We show that Kubo's one- electron CPA is always recovered in the empty-band limit and that our CPA i s equivalent to dynamical mean-field theory in the classical spin limit. We then solve our CPA equations self-consistently to obtain the static magnet ic susceptibility chi in the strong-coupling limit. As in the case of the C PA for the Hubbard model, we find unphysical behaviour in chi at half-filli ng and no magnetic transition for any finite S. We identify the reason for this failure of our approximation and propose a modification which gives th e correct Curie-law behaviour of chi at half-filling and a transition to fe rromagnetism for all S.