Experimental Determination of thegFactor in Metallic Zn

Abstract

The de Haas-van Alphen (dHvA) oscillations associated with the 3rd-zone electron pockets ("needles") in Zn are split into resolved spin subpeaks when detected with the ac-modulation technique at $T\le 4°$K. At $P\sim 1$ bar, ${\Delta }_{s}F$ is 0.36, where ${\Delta }_{s}F$ is defined as the $\left|\Delta \right(\frac{1}{H}\left)\right|$ between neighboring subpeaks times the needle dHvA frequency $F$. The three needle $\mathrm{}\left|g\right|\mathrm{}$ values consistent with ${\Delta }_{s}F=0.36\mathrm{} \mathrm{are} 96, 170, \mathrm{and} 362$, in reasonable agreement with the values 90, 180, and 360 determined by Stark. The parameter ${\Delta }_{s}F$ decreases with increasing pressure (decreasing $\frac{c}{a}$ ratio) at a rate given by $\frac{d\ln {\Delta }_{s}F}{\mathrm{dP}}\cong -0.16\mathrm{}$ ${\mathrm{kbar}}^{-1\mathrm{}}$. At higher temperatures, the resolved spin splitting disappears and the apparent phase of the oscillations increases with increasing temperature (increasing $\frac{c}{a}$). The increase of the phase results from the dominant contribution of one spin state to the needle oscillations at higher temperatures coupled with the increase of ${\Delta }_{s}F$ with increasing $\frac{c}{a}$. The tendency of one spin-state contribution to dominate with increasing temperature is due to a difference between the effective masses associated with the 2 spin halves of a needle Landau level. The effective-mass difference is estimated by introducing arguments which depend heavily upon the conclusion, drawn from the experimental pressure dependence of the needle area and $m^{*}$, that the needles are very free-electron-like. When the Lifshitz and Kosevich expression for the oscillatory susceptibility is modified to include the difference in effective mass, the three $\mathrm{}\left|g\right|\mathrm{}$ values lead to different predictions for the temperature dependence of the phase of the needle oscillations. The value $\mathrm{}\left|g\right|=170\mathrm{}$ is selected, since it alone leads to an increase of the phase with temperature.