Magnetic mixed-valence d²-d¹-d¹ trimers with partial electron delocalization: vibronic coupling and magnetic properties

The energy levels and magnetic properties of a triangular mixed-valence cluster d¹-d¹-d² with electron delocalization in a pair of sites are examined from a model that takes into account electron transfer, magnetic exchange, and vibronic coupling. We show that the electron transfer process involves besides the usual double-exchange parameter, and additional parameter referred to as exchange transfer. This last parameter accounts for the interaction between the moving electron of the mixed valence pair and the electron localized in the third side. We notice that the role of double exchange is to stabilize a ferromagnetic alignment of the spins on the mixed-valence pair. A comparison of this result with the cases of fully delocalized mixed-valence dimers and trimers is presented. The interplay of double-exchange and pairwise exchange interactions on the preferred spin orientations of the distorted triangle is discussed in connection with the problem of spin frustration. For the exchange-transfer parameter we notice that, depending on its sign relative to that of the double-exchange parameter, this can stabilize either higher or lower spin states. Finally, the magnetic properties of the trimer in presence of vibronic coupling are discussed using the semiclassical adiabatic approach. Some relevant situations, which illustrate the trapping effect of this coupling with the subsequent effective reduction of double exchange, are presented.