Scanning Hall probe microscopy of vortex patterns in a superconducting microsquare

We present direct observation of vortices confined to a superconducting 4 4 m2 square Pb film at 4.2 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 Tc.