Mixed-valence double exchange

Considering the isotropic exchange and the geometry of an isosceles triangle, the magnetic susceptibility of mixed-valence (double exchange) systems can be evaluated according to the formula... 

The literature on double exchange is not very extensive. The main papers dealing with the problem discussed here are the original work by Anderson and Hasegawa (10), and papers by Karpenko (33), Borshch et al. (30), Belinskii et al. (34) and Girend (31). Particularly noteworthy is the analysis by Noodleman and Baerends (35) in their theoretical study of the electronic structure of ferredoxins with Fe2S2 cores. Quite recently, Belinskii (32) has published an extensive theoretical study for mixed-valence trimers with D3h symmetry. 

In summary, by combining the information obtained from the new mixed-metal clusters with the progress made in describing the spin coupling of delocalized mixed valence dimm with double exchange, we can anticipate new insight into the electronic structure of many clusters of interest in bio-inorganic chemistry. 

To model several other electronic situations (e.g., in mixed-valence compounds), the Heisenberg Hamiltonian can be augmented by specific exchange operators that accommodate, for example, double exchange, antisymmetric exchange, anisotropic exchange, or biquadratic exchange. 

In the case of the mixed-valence manganites with the perovskite stracture, Zener s double-exchange (DE) mechanism has been used to explain the CMR effect (Zener, 1951c). In this model, a strong Hund s coupling is presumed to exist between the itinerant... 

Krockel M, Grodzicki M, Papaefthymiou V, Trautwein AX, Kostikas A (1996) Tuning of electron delocalization in polynuclear mixed-valence clusters by super-exchange and double exchange. J Biol Inoig Chem 1 173-176... 

Fig. 8 Effect of the double exchange on the energy pattern of mixed valence dimer...

Fig. 10.16. Temperature dependence of the magnetic susceptibility (a) and the effective magnetic moment (b) for the mixed-valence d6 —d5 dimer with S(> = 2 J/hc = -100 cm-1, g = 2 solid— t/hc — 0 (no double exchange) long dashed—t/hc = 1000 cm-1 medium dashed— t/hc = 2000 cm-1 short dashed—t/hc = 3000 cm-1.

Fig. 11.15. Temperature variation of the effective magnetic moment for the mixed-valence dl-dl-

Spin (hole) localisation and/or delocalisation leads to the concept of double exchange in mixed-valence systems. This has a close relationship to the Jahn-Teller effect in polynuclear systems, occurring when the (hypothetical) ground state is orbitally degenerate and disappearing when the nuclear distortion removes the orbital degeneracy. 

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