Magnetic Field Dependence of the Hall Effect and Magnetoresistance in Graphite Single Crystals

Abstract

The Hall coefficient and magnetoresistance in purified (99.995%) natural graphite single crystals have been measured from 25 to 25 000 gauss at 298\ifmmode^\circ\else\textdegree\fi{}, 77\ifmmode^\circ\else\textdegree\fi{}, and 4.2\ifmmode^\circ\else\textdegree\fi{}K with the field oriented parallel to the hexagonal axis. Special care was taken in the micromanipulation and strain-free mounting of these small soft crystals. Fast minority carriers due to Fermi-surface warping were discovered by their effect on the low-field Hall coefficient behavior. The compensating effect between the majority electron and hole densities [(5-2) \ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ with $\frac{{n}_{e}}{{n}_{h}}=1.0\ensuremath{-}1.15$ over the above temperature range] and mobilities [(1.5-130)\ifmmode\times\else\texttimes\fi{}${10}^{4}$ ${\mathrm{cm}}^{2}$/v sec with $\frac{{\ensuremath{\mu}}_{e}}{{\ensuremath{\mu}}_{h}}=1.10\ensuremath{-}0.79$] makes the Hall coefficient very sensitive to the temperature, impurities, and field where it even changes sign. A quadratic low-field room-temperature magnetoresistance dependence progresses at higher fields to an impurity-insensitive ${H}^{1.78}$ behavior. The large magnetoresistance ratio of graphite (\ensuremath{\sim}${10}^{5}$ at 4.2\ifmmode^\circ\else\textdegree\fi{}K and 23 kilogauss), along with the appearance of de Haas-van Alphen type oscillations in these properties, demonstrates the small effective masses ($0.03{m}_{0}, 0.06{m}_{0}$) and long relaxation times (2.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}11}$ sec at 4.2\ifmmode^\circ\else\textdegree\fi{}K). The mobility follows a ${T}^{\ensuremath{-}1.2}$ law in the lattice-scattering region \ensuremath{\gtrsim}50\ifmmode^\circ\else\textdegree\fi{}K. Low-temperature results, showing carrier density differences and mobilities to be most sensitive to impurities, substantiate the relatively high purity of these crystals.