Magnetization of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ micrometer thin ring and its depinning line

We demonstrate a geometrical effect on the depinning line (DL) of the flux line lattice of the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ high-T$_c$ superconductor (HTSC) micrometer ring. The DL shifts to notably lower temperatures in comparison to bulk crystals and thin flakes of the same sample. The shift is attributed to a decrease in the overall pinning potential due to a double size effect, namely: a) the ring thickness $\sim 1~\mu$m being smaller than the pinning correlation length, and b) the increase in the effective London penetration depth of the vortices (Pearl vortices). The large shift of the DL to lower temperatures may influence the suitability of this HTSC for applications in microstrip antennas and THz emitters.