Electric field controllable magnetic coupling of localized spins mediated by itinerant electrons: A toy model

In this paper, we propose a toy model to describe the magnetic coupling between the localized spins mediated by the itinerant electron in partially delocalized mixed-valence (MV) systems. This minimal model takes into account the key interactions that are common for all such systems, namely, electron transfer in the valence-delocalized moiety and magnetic exchange between the localized spins and the delocalized electrons. The proposed descriptive model is exactly solvable which allows us to qualitatively and quantitatively discuss the main features of the whole class of partially delocalized MV systems. In the case of relatively strong exchange coupling, the combined action of these two interactions is shown to give rise to a specific kind of double exchange coupling termed here as "external core" double exchange. In the opposite case of relatively strong electron transfer, the general Hamiltonian is shown to be reduced to the effective Hamiltonian of indirect exchange of the localized spins. We argue a possibility to efficiently control the magnetic coupling of the localized spins using an external electric field acting on the delocalized part of the system. Finally, we discuss the perspectives of the present model for molecular spintronics and spin qubits.