Ionic Hamiltonians for transition metal atoms: effective exchange coupling and Kondo temperature

An ionic Hamiltonian for describing the interaction between a metal and a d-shell transition metal atom having an orbital singlet state is introduced and its properties analyzed using the Schrieffer–Wolf transformation (exchange coupling) and the poor man's scaling method (Kondo temperature). We find that the effective exchange coupling between the metal and the atom has an antiferromagnetic or a ferromagnetic interaction depending on the kind of atomic fluctuations, either or , associated with the metal-atom coupling. We present a general scheme for all those processes and calculate, for the antiferromagnetic interaction, the corresponding Kondo-temperature.