Tm, Pr, and Tb impurities in a metallic host

Starting with a generalized Anderson Hamiltonian and a Schrieffer-Wolff transformation for R.E. systems a Hamiltonian Hsub(r) is derived which is appropriate for Tm, Pr and to a lesser extent for Tb impurities in a metallic host. It is shown that this Hamiltonian contains the Kondo Hamiltonian and that of Cocqblin and Schrieffer (which is valid for Ce and Yb impurities) as special cases. To investigate the properties of the Hamiltonian, crystal field effects are neglected and the equation-of-motion-method is applied. The corresponding system of 6 or 8 coupled integral equations is solved. The solution allows a discussion of the ferromagnetic and antiferromagnetic couplings which normally both occur. The condition for only ferromagnetic coupling of Hsub(r) is given. This condition is fulfilled in Tb4+ impurities. The resistivity is calculated for Pr2+, Pr3+, Tm2+, Tm3+ and Tb3+ impurities. (orig.)