Determination of the Fermi Surface of MgB$_2$ by the de Haas-van Alphen effect

We report measurements of the de Haas-van Alphen effect for single crystals of MgB$_2$, in magnetic fields up to 32 Tesla. In contrast to our earlier work, dHvA orbits from all four sheets of the Fermi surface were detected. Our results are in good overall agreement with calculations of the electronic structure and the electron-phonon mass enhancements of the various orbits, but there are some small quantitative discrepancies. In particular, systematic differences in the relative volumes of the Fermi surface sheets and the magnitudes of the electron-phonon coupling constants could be large enough to affect detailed calculations of T$_{c}$ and other superconducting properties.