The Schrieffer–Wolff transformation for the underscreened Anderson lattice

We present a derivation of the Schrieffer–Wolff transformation for the Anderson Lattice Hamiltonian with a two-fold degenerate f-level in each site. The degeneracy of the f-electrons has been taken into account in order to describe uranium and other actinide magnetic compounds with a spin larger than 12, for example a total S=1 spin for the f-electrons. The transformed Hamiltonian has several terms as in the s=12 classical case, but we have obtained here both an exchange (Kondo) interaction between the S=1 f-spins and the spins of the conduction electrons, and also an effective f-band term. This f-band term describes better the underscreened Kondo lattice model which has been recently developed to explain the Kondo-ferromagnetism coexistence observed in uranium compounds such as UTe [N.B. Perkins, M.D. Nunez-Regueiro, J. R. Iglesias, B. Coqblin, Phys. Rev. B 76 (2007) 125101].