Competition between several model Hamiltonians in half-doped manganites

Ab initio calculations combined with the effective Hamiltonian theory of Bloch provide a rational way to determine model Hamiltonians. The embedded cluster approach is the most reliable method of extraction of effective interactions for the study of highly correlated material. In the specific case of half-doped man-ganites, several model Hamiltonians can be considered to reproduce the local physics generated by the interactions between the magnetic sites according to the position of the doping holes. While a double exchange mechanism takes place between the Mn sites if the holes are localized on the metals, a purely magnetic Heisenberg Hamiltonian should be considered for a localization of the holes on the bridging oxygens. For intermediate situations in which both elements share the doping holes, a truncated Hubbard model which treats variationaly double exchange and Heisenberg configurations seems to be the most appropriate. This model can be mapped on both simpler double exchange and Heisenberg Hamiltonians. The analytical spectrum of the Heisenberg model in the case of two metals bridged by a magnetic oxygen is identical (except for one state) to the double exchange one, for a peculiar relation between the electronic interactions of the two models. Finally, the most appropriate hamiltonians is a refined double exchange model which combines the Anderson-Hazegawa and the Girerd-Papaefthymiou antiferromagnetic contributions.