Unusual temperature dependence of the London penetration depth in all-organic \beta``-(ET)_2SF_5CH_2CF_2SO_3 single crystals

The temperature dependence of the in-plane, \lambda_{\parallel}, and interplane, \lambda_{\perp}, London penetration depth was measured in the metal-free all-organic superconductor \beta-ET (see title) ($T_c\approx$ 5.2 K). \lambda_{\parallel} ~T^3 up to 0.5 Tc, a power law previously observed only in materials thought to be p-wave superconductors. \lambda_{\perp} is larger than the sample dimensions down to the lowest temperatures (0.35 K), implying an anisotropy of \lambda_{\perp}/\lambda_{\parallel} ~ 400-800.