Hysteresis in mesoscopic superconducting disks: The Bean-Livingston barrier

Depending on the size of mesoscopic superconducting disks, the magnetization can show hysteretic behavior which we explain by using the Ginzburg-Landau (GL) theory and properly taking into account the demagnetization effects due to geometrical form factors. In large disks the hysteresis is due to the Bean-Livingston surface barrier while in small disks it is the volume barrier which is responsible for it. Although the sample magnetization is diamagnetic (negative) we show that the measured magnetization can be positive at certain fields as observed experimentally and which is a consequence of both the demagnetization effect and the experimental setup.