Theory of a Tm impurity in metals in a jj-coupling model

A Tm magnetic impurity with U= infinity is considered in the jj-coupling scheme in the limit of zero j.j coupling. The model has SU(N) symmetry. The spin-fluctuation energy scale is found in the f 12 and f 13 Kondo limits via Haldane scaling arguments. The model possesses a 1/N expansion; selecting the leading-N diagrams in perturbation theory, the Yafet-Varma integral equation is derived. This is solved analytically in the f 1 and f 2 Kondo limits and the results for N to infinity are found to be in accord with scaling theory. The energy separation between the singlet ground state and the N-fold-degenerate excited state is found as a function of f occupation in the large-N limit. The results are found to differ significantly with data on LaTmSe and YTmSe. A model with large j.j coupling is also considered and does not significantly improve the agreement.