Decoupling of superconducting planes of La$_{1.905}$Ba$_{0.095}$CuO$_4$ in a transverse magnetic field

We have measured the resistivity parallel and perpendicular to the CuO$_2$ planes in single crystals of La$_{1.905}$Ba$_{0.095}$CuO$_4$ for magnetic fields up to 35~T applied along the $c$-axis. Below the zero-field superconducting transition temperature of 32 K, we observe that, above a threshold field, the $c$-axis resistivity grows with field, eventually reaching a maximum and then decreasing. At the resistivity maximum, interlayer pair tunneling becomes insignificant. Under the same field and temperature conditions, the in-plane resistivity remains quite low, reflecting robust superconductivity. We identify a regime in which the superconducting planes are effectively decoupled. At 20~K, a field much greater than 35~T would be required to destroy the in-plane pairing, despite the fact that the field also induces both charge and spin stripe order (J.S. Wen {\it et al.}, arXiv:1009.0031).