I. On the renormalizability of the locally enhanced spin fluctuation problem in dilute alloys

Abstract

We present a rotation invariant formulation of the problem of locally enhanced spin fluctuations in dilute alloys containing nearly magnetic impurities. We classify the divergences arising in the perturbational analysis of the renormalized electron self-energy, fluctuation self-energy, electron fluctuation vertex, and fluctuation vertices, with the help of a dimensional analysis. We show that for the parameters for which the Hartree-Fock criterion suggests the formation of a localized magnetic moment the theory is nonrenormalizable. However, we can approach the problem from the other side: the situation where the impurity is far from magnetic. Then it appears that the most important contribution to the renormalized local enhancement arises from the interaction among the spin fluctuations themselves. This problem can be recast into a functional integral. In this case we show that the interaction among the spin fluctuations prevents the formation of a local moment so that the impurity is actually much farther from becoming magnetic than expected within the Hartree-Fock calculation. Therefore in this limit the Hartree-Fock approximation describes qualitatively, although not quantitatively, the correct behavior of the impurity; the impurity never becomes magnetic. This seems to suggest that in general the impurity never becomes magnetic independent of the size of the parameters in the theory, sincea posteriori the nonmagnetic situation is the only self-consistent solution possible within the present theory. This anticipates that the stable fixed point for this problem of locally enhanced spin fluctuations is the situation with a vanishing local spin exchange interaction between electrons at the impurity site, which will be discussed fully in the next paper.