AuVandAlMn: Kondo Systems or Localized Spin-Fluctuation Systems?

Abstract

The predictions of the localized spin-fluctuation model and those of a theory of the lowtemperature behavior of the multiorbital Anderson model we have recently developed are compared with respect to both the bulk properties (resistivity, specific heat, and magnetic susceptibility) and the microscopic properties (impurity nuclear-resonance shift and relaxation rate) for the dilute magnetic alloys AuV and AlMn.Almost all models which have been proposed to describe the dilute magnetic alloy system may be regarded as special cases of the Anderson model. 1 For example, the s-d exchange model 2 may, by virtue of the Schrieffer-Wolff transformation, 3 be regarded as corresponding to the case \e d \,Uy>A, where e d is the resonance energy, U is the intraatomic Coulomb repulsion, and A is the resonance half-width; we shall refer to this limit of the Anderson model as the Kondo model. On the other extreme, the localized spin-fluctuation (LSF) model 4 corresponds to the limit |cJ«A; we shall regard the studies of the Wolff model by Suhl and co-workers, 5 despite their more ambitious attempt to treat the Coulomb interaction between all electrons on an equal footing, to be of this latter class insofar as the resonance level has been taken to be at the Fermi level in all the published work.Since the relative magnitudes of the parameters U, e d9 and A play such a fundamental role in all the models, the determination of these parameters from experiment is of great interest. As these quantities are not directly measured, however (unless optical or photoemission studies are undertaken), one must infer the value of these parameters from the theoretical results for the various models. Here one is confronted with the rather remarkable result obtained by Rivier and Zuckermann 4 -the LSF and the Kondo models would appear to be indistinguishable with regard to the predicted behavior of the system. Although we feel this result deserves a more detailed discussion than may be found in the literature, it is not our intention in this Letter to dispute this claim. Rather, we accept at face value all the results obtained by Rivier and Zuckermann (and others) from the LSF model and yet suggest that the predictions of the two models are distinguishable, provided we confine our attention to T<cT K and take into account the orbital degeneracy present in the real alloys studied.Before embarking on the detailed comparison between the predictions of the two models, it is worth noting the different mechanisms proposed in dealing with the absence of orbital paramagnetism. In the case of the LSF model, which is taken to be nonmagnetic in the Hartree-Fock sense, the absence of orbital paramagnetism is accounted for by the argument first given by Anderson 1 : The spin-enhancement factor a d is considered to be much greater than the orbital-enhancement factor a 0 because of the different dependence of o d and a 0 on J, the exchange integral.In the case of the Kondo model, however, the system is magnetic in the Hartree-Fock sense and the orbital paramagnet...