Quantum oscillations in the parent pnictide BaFe$_2$As$_2$ : itinerant electrons in the reconstructed state

We report quantum oscillation measurements that enable the direct observation of the Fermi surface of the low temperature ground state of \ba122. From these measurements we characterize the low energy excitations, revealing that the Fermi surface is reconstructed in the antiferromagnetic state, but leaving itinerant electrons in its wake. The present measurements are consistent with a conventional band folding picture of the antiferromagnetic ground state, placing important limits on the topology and size of the Fermi surface.