  The Zener polarons recently found in half-doped manganites are usually seen
as mixed valence entities ruled by a double exchange Hamiltonian involving only
correlated electrons of the metals. They can however be considered as
ferrimagnetic local units if the holes are localized on the bridging oxygen
atoms as implicitely suggested by recent mean-field it ab initio calculations.
In the latter case, the physics is ruled by a Heisenberg Hamiltonian involving
magnetic oxygen bridges. This paper 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 explicitely correlated ab initio
calculations. Since the physics supported by each model are different, the
analysis of the exact Hamiltonian ground state wave function should a priori
enables one to determine the most appropriate model. It will be shown that
neither the spectrum nor the wavefunction analysis bring any decisive arguments
to settle the question. Such undecidability would probably be encountered in
experimental information.
