Electronic properties from analysis of the harmonic content of the de Haas-van Alphen effect: Application to dilute magnetic alloys

Abstract

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 MI. 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 J orbit, 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.