Anomalous Skin Depth and Radio-Frequency Size Effect in Gallium

The reactive skin depth in gallium has been measured at a frequency of 1 MHz. Average Gaussian curvatures in $k$ space have been calculated, and have been correlated with the augmented-plane-wave (APW) calculation by Wood and with the dc resistivity experiments by Cochran and Yaqub. The results indicate that the APW model overestimates the average curvature of the major sheets of the Fermi surface which lie (roughly) perpendicular to the $a$ axis. The anisotropy of the average curvatures is in semiquantitative agreement with the measured values of ${\rho }_B{l}_B$, where ${\rho }_B$ and $l_B$ are the bulk resisitivity and mean free path. The topology of the small sheets of the Fermi surface is studied using the radio-frequency size effect (RFSE) in a field parallel to the surface. Several closed RFSE contours are found and the areas are compared with published de Haas-van Alphen (dHvA) data. In addition, new RFSE data are presented which are relevant to the interpretation of Goldstein and Foner's dHvA measurements for two of the major sheets. In particular, the results do not support their suggestion that partial magnetic breakdown occurs between bands 7 and 8 of Wood's model.