Electronic structure and resistivity of the double exchange model

The double exchange (DE) model with quantum local spins S is studied; an equation of motion approach is used and decoupling approximations analogous to Hubbard's are made. Our approximate one-electron Green function G is exact in the atomic limit of zero bandwidth for all S and band filling n. Since as it reduces to the result of a dynamical coherent potential approximation (CPA) due to Kubo, we regard our approximation as a many-body generalization 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 magnetization. The electronic structure is investigated and four bands per spin are obtained centred on the atomic limit peaks of the spectral function. A resistivity formula appropriate to the model is derived from the Kubo formula and the paramagnetic state resistivity is calculated; insulating states are correctly obtained at n = 0 and n = 1 for strong Hund coupling. Our prediction for is much too small to be consistent with experiments on manganites 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 his use of an unphysical density of states.