Pressure Dependence of the Low-Frequency de Haas—van Alphen Oscillations in Zn

Abstract

We report the results of measurements of the pressure dependence (to \ensuremath{\sim}4 kbar) of the de Haas-van Alphen (dHvA) oscillations associated with three sections of the Zn Fermi surface. For H along the hexad axis, the cross-sectional area of the 3rd-band electron pockets ("needles") increases with an initial rate given by $\frac{d\mathrm{ln}{S}_{1}}{\mathrm{dP}}=(32\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ k${\mathrm{b}\mathrm{a}\mathrm{r})}^{\ensuremath{-}1}$. The cyclotron effective mass of the needles is also an increasing function of pressure, with a slope given by $\frac{d\mathrm{ln}{{m}_{1}}^{*}}{\mathrm{dP}}=(14\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ k${\mathrm{bar}}^{\ensuremath{-}1}$. The minimum cross-sectional area of the waists of the combined 1st- and 2nd-band hole surface ("monster") increases at a rate given by $\frac{d\mathrm{ln}{S}_{2}}{\mathrm{dP}}=(3.94\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ k${\mathrm{bar}}^{\ensuremath{-}1}$ and the cross-sectional area of the diagonal arms of the monster decreases at a rate given by $\frac{d\mathrm{ln}{S}_{3}}{\mathrm{dP}}=\ensuremath{-}(1.27\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ k${\mathrm{bar}}^{\ensuremath{-}1}$. These experimental data are compared with the results of previous studies of the Fermi surface of Zn as a function of pressure and with the results of recent measurements of the effects of alloying upon the Zn Fermi surface. In addition, these results are compared with predictions of the nearly-free-electron model (NFEM), and in the case of the waist orbits a comparison is also made with the pressure behavior predicted by a screened point-ion-model pseudopotential. We conclude that previous reported results for the pressure dependence of the dHvA periods and ${m}^{*}$ for the needles in Zn are incorrect. The NFEM predictions are at least in qualitative agreement with experiment in the three cases studied. For the needles, the relation between the pressure and alloy results is in excellent agreement with the NFEM, and the observed $\frac{d\mathrm{ln}{m}^{*}}{\mathrm{dP}}$ agrees with the predicted NFEM behavior to within experimental uncertainty. In the case of the waist orbits, the agreement between the alloy results and the model predictions seems to be significantly poorer than for the pressure results.