Relation between double exchange and Heisenberg model spectra: Application to the half-doped manganites
Résumé
Properties in manganites are often interpreted in terms of double exchange mechanism. A dimer of manganese sites bearing a hole is seen as a mixed valence entity ruled by a double exchange Hamiltonian. They can, however, be considered as ferrimagnetic local units if the holes are localized on the bridging oxygen atoms as implicitly suggested by recent mean-field ab initio calculations. In the latter case, the physics is ruled by a Heisenberg Hamiltonian involving magnetic oxygen bridges. This Brief Report shows that the spectra resulting from the resolution of both models are analytically identical. This single resulting model spectrum accurately reproduces the spectrum of Zener polarons in Pr0.6Ca0.4MnO3 manganite studied by means of explicitly correlated ab initio calculations. Since the physics supported by each model are different, the analysis of the exact Hamiltonian ground-state wave function should enable one to determine the most appropriate model. Actually, neither the spectrum nor the wave-function analysis brings any decisive arguments to settle the question.