Competition between double exchange and purely magnetic Heisenberg models in mixed valence systems: application to half-doped manganites.

A truncated Hubbard model is developed for the description of the electronic structure of odd-electron TM-L-TM units (TM=transition metal and L=ligand). The model variationally treats both the double exchange and purely magnetic Heisenberg configurations. This Hubbard model can either be mapped on a purely magnetic Heisenber model in which the bridging oxygen is also magnetic or on a double exchange model owing to the hybridization of the magnetic and ligand or bitals. The purely magnetic Heisenberg model is analytically solved in the general case of two metals (having n magnetic orbitals) bridged by a magnetic oxygen. The comparison of the analytical expressions of the Heisenberg energies to those of the double exchange model reveals that the two model spectra are identical except for one state which does not belong to the model space of the double exchange Hamiltonian. Consequently, the fitting of the model spectra to accurate ab initio spectra does not discriminate between the physically different models. These concepts are illustrated for the Mn-O-Mn unit (or Zener polaron) found in the half-doped manganite Pr(0.6)Ca(0.4)MnO3. It is shown that in the present case the projections of the ab initio ground state wave function onto both model spaces are almost identical provided that one uses properly localized orbitals, proving that the magnetic description of the Zener polaron and the double exchange viewpoint of the electronic structure are equally valid.