de Haas-van Alphen Effect in Dilute Alloys of Bismuth in Lead

An in situ NMR technique has been used to make accurate (∼2 parts in ${10}^4$) measurements of several de Haas—van Alphen frequencies in pure lead for two of the primary symmetry directions, [100] and [110]. By the same method the variation of the [100] $\beta$ frequency with the addition of up to 0.2% bismuth has been investigated. The alloy results identify the $\beta$ oscillations as being due to an electronlike piece of Fermi surface. At small impurity concentrations, the dependence of the frequency on concentration is in good agreement with the rigid-band model. However, at the higher concentrations there is a tendency for the frequency changes to be smaller than predicted by the rigid-band model and we interpret this trend to be due to an increase in the density of states, indicating that electrons are beginning to fill the fourth zone. It is not clear from our results whether the fourth zone begins above or below the pure-lead Fermi energy, but taken at face value, our measurements would suggest that it begins about 4 meV above the Fermi energy.