Damping of the de Haas-van Alphen oscillations in the superconducting state of MgB2

The de Haas\char21{}van Alphen (dHvA) signal arising from orbits on the $\ensuremath{\pi}$ Fermi surface sheet of the two-gap superconductor $\mathrm{Mg}{\mathrm{B}}_{2}$ 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 $\ensuremath{\pi}$ band gap is still present up to ${H}_{c2}$. The data are compared to current theories of dHvA oscillations in the superconducting state which allow us to extract estimates for the evolution of the $\ensuremath{\pi}$ band gap with magnetic field. Contrary to results for other materials, we find that the most recent theories dramatically underestimate the damping in $\mathrm{Mg}{\mathrm{B}}_{2}$.