Variational mean-field approach to the double-exchange model -: art. no. 054411

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial f'acts: the use of a mean-field ansatz: that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-held techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.