Effect of Pressure and Magnetic Field on the Connectivity of the Fermi Surface of Zinc

Abstract

We report quantitative measurements of the pressure dependence (to ∼6 kbar) of the lengths of the one-dimensional angular regions of applied field producing open orbits in the basal plane in Zn (${\delta }_1$ and ${\delta }_3$ whiskers). We find that both whiskers increase in length with pressure with the following slopes: $\frac{d{\delta }_1}{\mathrm{dP}}=0.100\mathrm{}\pm 0.015$ deg/kbar, $\frac{d{\delta }_2}{\mathrm{dP}}=0.07\mathrm{}\pm 0.01$ deg/kbar. Our results indicate that the connectivity in the basal plane is enhanced by hydrostatic pressure, as is expected from nearly-free-electron considerations. A system for obtaining $4\pi$-steradian magnetic field scan of a stationary sample at 4°K is described. Qualitative measurements of the effect of high magnetic field (∼60 kOe) on the length of these whiskers showed that the length of ${\delta }_3$ was not affected but that a small increase in the length of ${\delta }_1$ could be detected with increasing field. The effect of pressure (to ∼5 kbar) on the period of the oscillations in the magnetoresistance associated with the minimum cross section of the needles is found to agree with the very-low-pressure He-gas work but not with work in the ice bomb or in frozen kerosene-oil mixtures. Consideration of all these results leads to a new zero-pressure assignment for the relation between Fermi-surface dimensions and the angular lengths of the whiskers. Using this assignment the following pressure derivatives of the radius $r$ of the monster, the height $h_N$, of magnetic breakdown on the needles, and the height $h_W$ of the waists of the monster are calculated: $\frac{d\ln r}{\mathrm{dP}}=-0.0009/\mathrm{kbar}$, $d\ln h_{N}dP=-0.007/\mathrm{kbar}$ and $\frac{d\ln h_W}{\mathrm{dP}}=0.015/\mathrm{kbar}$. The results of our pressure measurements on Zn are consistently different from those obtained in solid pressure-transmitting media other than He. A comparison is made of the various results in the literature on the pressure dependence of the period of the oscillatory component of transport phenomena in Zn for $H\parallel \mathrm{}\left[0001\right]\mathrm{}$, which we feel demonstrates the superiority of the solid-He technique for low-temperature pressure generation in the range 0-9 kbar.