The onset of vortex penetration into micron-sized ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ disks and squares is studied using local magnetization measurements. The vortex penetration field $H_p$ is observed to exceed the lower critical field $H_{c1\mathrm{}}$ at all temperatures below the superconducting transition temperature $T_c.$ The magnitude of $H_p$ is determined by sample size and geometry. Below 15 K, $H_p$ is approximately proportional to the sample width D, consistent with the Bean bulk pinning model. Above 15 K, $H_p$ is a function of the sample thickness-to-width ratio $t/D,$ and agrees with the Bean-Livingston surface-barrier effect.

• Received 16 November 2001

DOI:https://doi.org/10.1103/PhysRevB.65.184506