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A new technique, third harmonic de Haas-van Alphen (dHvA) wave shape analysis, is described for measurement of the spin-dependent interactions between conduction electrons and local moments in dilute alloys. We derive expressions for the harmonic content of the dHvA effect in a general case, including simultaneous contributions due to (1) magnetic interaction (MI or Shoenberg effect), (2) the spin-dependent scattering (SDS) of conduction electrons, and (3) exchange energy shifts in their Landau levels due to local moments, in addition to the usual Lifshitz-Kosevich harmonic content. The effects of MI and SDS mix nonlinearly in determining the observable amplitude and phase of each resultant dHvA harmonic. One important consequence of this mixing is that the observation of a spin splitting zero of the dHvA amplitude is not indicative of equal scattering rates for spin-up and spin-down electrons, in the presence of ML These techniques are then illustrated by applying them to studies of the dilute alloy systems Au(Fe ) and Au (Co), both of which are found to exhibit local magnetic moments, though apparently of quite different origin. For Au(Fe) the exchange energy shift (exchange field) and the spin-dependent scattering rates were determined as functions of (H,T). A 3:1 anisotropy of spin-up and spin-down electron scattering rates was observed for the (111) neck orbit. For Au( Co ) we report the first dHvA observations of interaction effects between impurities, via measurements of the spin-dependent scattering of conduction electrons by magnetic pairs of Co impurities. We conclude that the dHvA effect appears to be a sensitive probe for determining impurity spin behavior in a magnetic field, and for measuring cyclotron orbitally averaged values of the exchange constant Jo,bit in very dilute local moment systems. Similarly, the ability to resolve spin-dependent information allows the onset of solute interactions leading to magnetism to be observed at very low solute concentrations.Finally, the possibility of applying these same third harmonic wave shape analysis procedures for the measurement of conduction electron orbital gfactors in metals is briefly discussed, and one example of such a measurement for a Au(Ag) dilute alloy, is given

The k dependence of the conduction-electron-rare-earth-moment exchange interaction is directly measured for the first time and found to be opposite in sense for Gd and Yb impurities in Au. Atomic exchange dominates for Au(Gd), while a phase-shift analysis indicates that covalent mixing of conduction p waves accounts for the observed k dependence in Au(Yb).PACS numbers: 71.70.GmThe nature of the conduction-electron-localmoment exchange interaction in metals is a fundamental problem which has stimulated widespread interest. It is known empirically 1 that the exchange integral J which is observed in metals is the sum of two contributions with distinctly different origins: J=J SLt +J C m° ^at is the atomic ("direct" or "on-site") contribution, 2 " 4 which would occur also in a nonmetallic host containing magnetic impurities. If the conduction states ^ and the local states

0]. «/ cm is the covalent-mixing contribution 3 " 7 which is attributed to spin polarization of the conduction electrons in the neighborhood of a magnetic impurity. It arises from hybridization of the local magnetic states with the conduction-electron states, creating net conduction-electron spin opposite to that of the impurity. This is equivalent to an antiferromagnetic exchange coupling and leads to spin compensation of the local moment and a variety of Kondo anomalies in various properties.Theoretical models for both the atomic and covalent-mixing contributions are usually simplified by assumption of a single exchange constant for coupling between all conduction-electron states and the impurity. In this paper we present direct experimental evidence for significant T£ de-pendence of the exchange coupling in both the atomic and covalent mixing limits. We find that the strength of the interaction varies in opposite directions for the two cases, and in the covalentmixing case correlates with the p character of the conduction states. We also report the first measurements of the £ dependence of the up-and down-spin scattering rates for conduction electrons from rare-earth impurities and show how these data can be interpreted by the 5d virtualbound-state model.As prototypes of atomic and covalent mixing exchange we have chosen dilute alloys of Au(Gd) and Au(Yb), respectively. Gd has a very stable moment in all metallic hosts and always displays atomiclike ferromagnetic couplingo 8 " 10 Conversely, Yb is strongly affected by hybridization as evidenced by its variable valence (trivalent in Au but divalent in Ag) 11 and net antiferromagnetic exchange coupling, leading to Kondo anomalies at T K~0o 01 Ko 12 Such clear examples of atomic and covalent-mixing exchange are impossible to find among transition-metal solutes in noble-metal hosts o Our results were obtained from an analysis of the amplitude 5 harmonic content, and spin-splitting zeros of de Haas-van Al...

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