Determination of the spin-splitting factor gc for Landau levels from the first three harmonics in the de Haas–van Alphen effect

A simple and convenient method is proposed for extracting the spin-splitting factors gc associated with extremal orbits around the Fermi surface from knowledge of the amplitudes Ar of the first three harmonics in the de Haas–van Alphen effect. In the approach suggested here, the quantity of prime interest is the dimensionless ratio α = A22/A1A3, which is independent of both the detailed shape of the Fermi surface and the Dingle temperature. Information about the relative phases of the harmonics allows corrections to be made for the Shoenberg magnetic interaction.In a first application of this three-harmonic method, the dHνA waveform has been studied in disk-shaped samples of Pb using a sensitive magnetoresistive-probe technique, and gc has been determined for the orbits ν and ν′ on the third-zone electron surface. We have also attempted to calculate the splitting factors within the framework of the 4 OPW band-structure model of Anderson, O'Sullivan, and Schirber. However, the simplification of using 4 OPW's throughout the Brillouin zone is found to lead to serious errors and inconsistencies as far as these differential magnetic quantities are concerned.