Abstract
Ballistic Hall magnetometry is used to investigate the magnetization of a mesoscopic superconducting Pb square as a function of magnetic field $(H)$ and temperature $(T)$. Vortex penetration and expulsion fields are determined from magnetization curves at different temperatures below ${T}_{c}$ and are combined in an experimental $T\text{\ensuremath{-}}H$ phase diagram. Enhanced stability of the symmetry-matching vorticities $L=1$ and $L=4$ is observed. The experimental results are compared with theoretical calculations using the nonlinear Ginzburg-Landau theory for a thin square.
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