When Must Double Exchange Be Used?

Recently it has been suggested that thermal electronic properties of magnetic mixed valence systems have to be studied by using an effective Hamiltonian different from the Heisenberg one, so successful for localized electron systems. The object of this paper is to specify conditions of validity of both Hamiltonians. In the first part, the theory of electron exchange in systems with electrons localized by electron-electron repulsion is quickly reviewed. The second part summarizes the results demonstrated for mixed valence systems of class III: for these systems, Heff = He + Hr + Het , where Ht , is the transfer Hamiltonian, He is the exchange (Heisenberg) one and Het is what we call the exchange-transfer one. In the last part we explain that as vibrations can relocalize the moving electrons (class II mixed valence systems), Heff can take again the form of the Heisenberg one at the minima of the potential surfaces but with a vibronic ferromagnetic contribution to the exchange parameter. At the saddle points, Heff = He + Hr . This last observation allows us to rationalize the values of the activation energy for thermal electron transfer in these systems.