Impurity model for mixed-valent ions

Intermediate valent tri- and tetravalent manganese ions play an important role in (Formula presented)-based systems. We consider a Mn impurity with five orbitals in cubic symmetry which hybridize with conduction electrons. The exchange interaction in the (Formula presented) shell maximizes the impurity spin. We study the valence of the Mn impurity as a function of the splitting of the (Formula presented) to (Formula presented) orbitals in zero magnetic field and for the totally spin-polarized state. The lifting of the degeneracy of the (Formula presented) levels due to a small quadrupolar field, related to the Mn-O bond length or a Jahn-Teller effect, is also investigated. Possible implications on the magnetoresistance are discussed.