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

The Hall coefficient and magnetoresistance in purified (99.995%) natural graphite single crystals have been measured from 25 to 25 000 gauss at 298°, 77°, and 4.2°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) ×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ with $\frac{n_e}{n_h}=1.0-1.15\mathrm{}$ over the above temperature range] and mobilities [(1.5-130)×${10}^4$ ${\mathrm{cm}}^2$/v sec with $\frac{{\mu }_e}{{\mu }_h}=1.10-0.79\mathrm{}$] 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 (∼${10}^5$ at 4.2°K and 23 kilogauss), along with the appearance of de Haas-van Alphen type oscillations in these properties, demonstrates the small effective masses ($0.03m_0, 0.06m_0$) and long relaxation times (2.5×${10}^{-11\mathrm{}}$ sec at 4.2°K). The mobility follows a $T^{-1.2\mathrm{}}$ law in the lattice-scattering region ≳50°K. Low-temperature results, showing carrier density differences and mobilities to be most sensitive to impurities, substantiate the relatively high purity of these crystals.