Electronic interaction in trimeric mixed valence clusters

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Abstract
The theory of double exchange is generalized to mixed valence (MV) trinuclear clusters. The results obtained by quantum-theoretical calculations of exchange and resonance splittings are compared to the results of the model theory which takes account of Heisenberg and double exchange. The comparison demonstrates unambiguously the coincidence of transfer parameters and the model double exchange parameters. The double exchange parameters of trinuclear MV clusters depend on total and intermediate spins as well as individual ion spin. The common effect of electron (or hole) migration and interion exchange interaction on the magnetic properties of dn -dn -d n+1 (n = 0, 1, 2, 3, 4, 5) and dn -dn -d n-1 (n = 1, 2, 3, 4) MV trimers is considered. Heisenberg and double exchange form exchange-resonance multiplets which are characterized by irreducible representations Γ of D 3h symmetry group of MV clusters. Double exchange splits Heisenberg multiplets but does not mix the states of different S. Level correlation diagrams for MV trimer clusters are plotted. The level trends and magnetic behaviour of MV trimers differ significantly from the classical Anderson-Hasegawa model obtained for dimeric MV clusters. In MV dimers strong double exchange (|p| ≫ |J|) leads to ferromagnetic ground state (S gs = S max) irrespective of the signs for p and J. In MV trimers several types of magnetic behaviour are possible depending on the signs and values for J and p parameters. In antiferromagnetic clusters (J < 0) with the migrating electron (p < 0) or hole (p > 0) strong double exchange reduces antiferromagnetic Heisenberg-type ordering and leads to ferromagnetic spins alignment (S gs = S max, when |p| ≫ |J|). In antiferromagnetic trimers, dn -dn -d n+1 (p > 0) and dn -dn -d n-1 (p < 0), the level with S gs = S min is the ground state irrespective of the value of p/J. In ferromagnetic exchange clusters (J > 0) with the migrating hole strong double exchange disorders the ferromagnetic spin ordering of the MV system.