Absolute de Haas-van Alphen Frequency Measurements in Potassium

A precision value of the de Haas-van Alphen (dHvA) frequency for single crystals of potassium has been obtained. Free-standing samples of known orientation were used to avoid the errors from differential thermal contraction inherent in measurements on encapsulated samples. The oscillations of magnetization were measured using a small Bi magnetoresistive probe with a modulation technique. Accurate field measurements were made by monitoring the ${\mathrm{Cl}}^{35}$ NMR in a NaCl crystal positioned close to the sample in a highly uniform region of the magnetic field. After suitable corrections for the small anisotropy, we obtain the value $F_0=(1.8246\mathrm{}\pm 0.0006)\times {10}^8$ G for the dHvA frequency of an equivalent spherical Fermi surface. This value is significantly lower than the free-electron prediction of $F_0=1.832\mathrm{}\times {10}^8$ G, but not by the full 0.8% predicted by Overhauser on the basis of a charge-density-wave (CDW) ground state. However, the lattice constant (5.225±0.002 Å) used in making the theoretical predictions may be in error. A careful redetermination of its low-temperature value would allow a more meaningful test of the CDW theory. Until such a direct measurement is made, the present experiment may be considered as a determination of the lattice constant of potassium with two possible results: 5.236 Å from free-electron theory, or 5.215 Å if the CDW ground state is valid.