  We have experimentally investigated the magnetisation of a mesoscopic
aluminum loop at temperatures well below the superconducting transition
temperature $T_{c}$. The flux quantisation of the superconducting loop was
investigated with a $\mu$-Hall magnetometer in magnetic field intensities
between $\pm 100 {Gauss}$. The magnetic field intensity periodicity observed in
the magnetization measurements is expected to take integer values of the
superconducting flux quanta $\Phi_{0}=h/2e$. A closer inspection of the
periodicity, however, reveal a sub flux quantum shift. This fine structure we
interpret as a consequence of a so called giant vortex state nucleating towards
either the inner or the outer side of the loop. These findings are in agreement
with recent theoretical reports.
