The de Haas--van Alphen effect in the superconducting state of MgB$_2$.

The de Haas-van Alphen (dHvA) signal arising from orbits on the $\pi$ Fermi surface sheet of the two-gap superconductor MgB$_2$ has been observed in the vortex state below $H_{c2}$. An extra attenuation of the dHvA signal, beyond those effects described in the conventional Lifshitz-Kosevich expression, is seen due to the opening of the superconducting gap. Our data show that the $\pi$ band gap is still present up to $H_{c2}$. Using current theories of dHvA oscillations in the superconducting state we extract estimates for the evolution of the $\pi$ band gap with magnetic field. Contrary to results for other materials, we find that the most recent theories dramatically underestimate the damping in MgB$_2$.