We present an electrical transport study of the two-dimensional (2D) organic conductor tau [P-(S,S)-DMEDT-TTF](2)(AuBr2) (AuBr2)(y) (where y similar to0.75) at low temperatures and high magnetic fields. The interplane resistivity p(zz) increases with decreasing temperature, with the exception of a slight anomaly at 12 K. Under a magnetic field B, both p(zz) and the in-plane resistivity plane p(xx) show a pronounced negative and hysteretic magnetoresistance. In spite of a negative residual resistivity ratio in zero field, Shubnikov-de Haas (SdH) oscillations are observed in some (high quality) samples above 15 T. Furthermore, contrary to the single closed orbit Fermi surface (FS) predicted from band structure calculations (where a single star-shaped FS sheet with an area of similar to 12,5% of A(FBZ) is expected), two fundamental frequencies F-l and F-h are detected in the SdH signal. These orbits correspond to 2.4 and 6.8% of the area of the first Brillouin zone (AFBZ). with effective masses mu (i) = 4.4 +/-0.5 and mu = 7.5 +/-0.1, respectively. The angular dependence, in tilted magnetic fields, of F-l and F-h, reveals a 2D character of the FS, but no evidence for warping along the k(z) direction (e.g., the absence of a beating effect in the SdH signal) is observed. Angular dependent magnetoresistance (AMRO) further suggests a FS which is strictly 2D where the interplane hopping t(c) is virtually absent or incoherent. The Hall constant R-xy is field independent, and the Hall mobility mu (H) increases by a factor of similar to3 under moderate magnetic fields. Hence the field does not alter the carrier concentration, even in the presence of a large negative magnetoresistance, but only increases the lifetime tau (s). Our observations suggest a unique physical situation where a stable 2D Fermi liquid state in the molecular layers, are incoherently coupled along the least conducting direction. The magnetic field not only reduces the inelastic scattering between the 2D metallic layers, as seen in the large negative magnetoresi stance and SdH effect, but it also reveals the incoherent nature of the interplane transport in the AMRO spectrum. Finally. the observed Fermi surface is at odds with band structure calculations. The observation of small pockets may suggest FS reconstruction. However, the very flat bands in the electronic structure, combined with the variable charge transfer, may be the origin of these effects. The apparent ferromagnetic character of the hysteresis in the magnetoresistance, remains an unsolved problem.
