Scanning Hall probe microscopy of vortex patterns in a superconducting microsquare

Abstract

We present direct observation of vortices confined to a superconducting $4\ifmmode\times\else\texttimes\fi{}4\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$ square Pb film at $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ 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 ${T}_{c}$.