Triple approach to determination of the c-axis penetration depth in BSCCO crystals

The c-axis penetration depth $\lambda_c$ in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) single crystals as a function of temperature has been determined using three high-frequency techniques, namely: (i) measurements of the ac-susceptibility at a frequency of 100 kHz for different sample alignments with respect to the ac magnetic field; (ii) measurements of the surface impedance in both superconducting and normal states of BSCCO crystals at 9.4 GHz; (iii) measurements of the surface barrier field $H_J(T)\propto 1/\lambda_c(T)$ at which Josephson vortices penetrate into the sample. Careful analysis of these measurements, including both numerical solution of the electrodynamic problem of the magnetic field distribution in an anisotropic plate at an arbitrary temperature and influence of defects in the sample, has allowed us to estimate $\lambda_c(0)\approx 50 \mu$m in BSCCO crystals overdoped with oxygen ($T_c\approx 84$ K) and $\lambda_c(0)\approx 150 \mu$m at the optimal doping level ($T_c\approx 90$ K). The results obtained by different techniques are in reasonable agreement.