Fermi Surface ofMg2Pb

Abstract

Experimental observations are reported of Landau quantum oscillations (LQO) in the electrical transport properties of the compound ${\mathrm{Mg}}_{2}$Pb in the range $H\ensuremath{\le}50$ kG and $T=1.2\ensuremath{-}4.2$ \ifmmode^\circ\else\textdegree\fi{}K. The results are associated with two bands of holes previously inferred in explaining the lowfield ($H\ensuremath{\le}5$ kG) field dependence of the Hall coefficient, confirming the earlier interpretation. The magnetoconductivity tensor elements derived from the nonoscillatory contributions to the Hall and transverse magnetoresistivity have been fitted with three bands of carriers labeled as light holes, heavy holes, and electrons. This establishes band overlap in ${\mathrm{Mg}}_{2}$Pb. The light-hole band (F = 0.27 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ G) is nearly spherical (\ifmmode\pm\else\textpm\fi{}2%) with ${m}^{*}\ensuremath{\simeq}0.04{m}_{e}$, $g\ensuremath{\simeq}11$, and contains 7.9 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ carriers/${\mathrm{cm}}^{3}$. The heavy-hole band [$F=(2.8\ensuremath{-}3.7)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ G] is a warped sphere, whose shape has been determined from experimental extremal cross sections using the Fermi-radius inversion method developed by Mueller. The heavy-hole cyclotron effective mass has been measured as 0.35 and 0.45 electron masses for orbits perpendicular to [100] and [111], respectively. This band contains 4.2 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ carriers/${\mathrm{cm}}^{3}$. These two valence bands are compared with similar valence bands in Ge via the model of Dresselhaus et al., The evidence for a Ge-like, rather than grey-Sn-like, valence-band ordering is consistent with the band calculation of Van Dyke and Herman. No LQO associated with the electron band were observed, although the analysis of classical magnetoconductivity data requires the presence of 4.1 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ electrons/${\mathrm{cm}}^{3}$ in order to explain the high-field value of $H{\ensuremath{\sigma}}_{12}$.