Electronic structure and resistivity of the double exchange model

The double exchange (DE) model with quantum local spins S is studied; an eq uation of motion approach is used and decoupling approximations analogous t o Hubbard's are made. Our approximate one-electron Green function G is exac t in the atomic limit of zero bandwidth for all 5 and band filling n. Since as n --> 0 it reduces to the result of a dynamical coherent potential appr oximation (CPA) due to Kubo, we regard our approximation as a many-body gen eralization of Kubo's CPA. G is calculated self-consistently for general S in the paramagnetic state and for S = 1/2 in a state of arbitrary magnetiza tion. The electronic structure is investigated and four bands per spin are obtained centred on the atomic limit peaks of the spectral function. A resi stivity formula appropriate to the model is derived from the Kubo formula a nd the paramagnetic state resistivity rho is calculated; insulating states are correctly obtained at n = 0 and n = 1 for strong Hund coupling. Our pre diction for rho is much too small to be consistent with experiments on mang anites so we agree with Millis et al that the bare DE model is inadequate. We show that the agreement with experiment obtained by Furukawa is due to h is use of an unphysical density of stares.