We present direct observation of vortices confined to a superconducting $4\times 4\mu {\mathrm{m}}^2$ square Pb film at $4.2\mathrm{K}$ with a high resolution scanning Hall probe microscope. Integrals of the magnetic field penetrating the square as a function of the applied field show that an applied-field dependence of vorticity $L$ agrees with calculations based on the Ginzburg-Landau (GL) equation for a square sample geometry. From asymmetric field distribution of the confined magnetic flux, the locations of vortices on the square are inferred for vorticities $L=1–5$. The obtained vortex patterns are analogous with the calculations in the framework of the full GL equation for temperatures considerably lower than the superconducting transition temperature $T_c$.

• Received 22 May 2007

DOI:https://doi.org/10.1103/PhysRevB.77.012502