Fermi Surface in Gallium Determined from the Radio-Frequency Size Effect

The external cross sections of the Fermi surface (FS) in a gallium single crystal were measured by using the radio-frequency size effect (RFSE), with rf frequencies of 2-8 MHz. The single crystal was grown in a shape of a plate with thickness $\approx 0.2$ mm, and its crystal axis was verified within one degree of arc. The derivative of the real part of the surface impedance of the plate with respect to the magnetic field was measured, and the RFSE signals of various line shapes were observed for magnetic fields below 500 G. An interpretation of these line shapes is given. The results of the experiment are compared with the FS predicted from calculations using an augmented-plane-wave (APW) expansion for the wave functions carried out by Wood and with the results of several other experimental methods. The comparisons show that the APW predictions for $E_F=0.400\mathrm{}$ Ry are quite accurate for some bands. The APW band 7 is verified in three orthogonal planes with an accuracy better than 30%. The APW band 5 is verified in two orthogonal planes, and the deviation is less than 25%. The APW band 8 is verified in a plane with an accuracy of better than 10%. The existence of the APW band 6 is strongly indicated in two orthogonal planes, and its topology is suggested by the experiment.