Frequency Mixing of Magnetic Oscillations: Beyond Falicov-Stachowiak Theory

The interpretation of de Haas--van Alphen oscillations in the presence of magnetic breakdown is usually based on the semiclassical theory of Falicov and Stachowiak (FS). There are now glaring discrepancies between its predictions and experiments, especially in quasi-two-dimensional organic conductors. We present an extension of the theory, using the appropriate constraints of conserved electron density, which explains the occurrence of frequencies not predicted by FS, and makes explicit the amplitudes as a function of Fermi surface parameters. The results involve a tunneling amplitude between different sheets as in FS, but other parameters as well, such as the areas of different orbits.