Eur. Phys. J. B 21, 31–37 (2001) T HE EUROPEAN P HYSICAL JOURNAL B c  EDP Sciences Societ` a Italiana di Fisica Springer-Verlag 2001 Unconventional field and angle dependences of the Shubnikov-de Haas oscillations spectra in the quasi two-dimensional organic superconductor (BEDO-TTF) 2 ReO 4 H 2 O C. Proust 1, a , A. Audouard 1, b , V. Laukhin 2,3 , L. Brossard 1 , M. Honold 4 , M.-S. Nam 4 , E. Haanappel 1 , J. Singleton 4 , and N. Kushch 2 1 Laboratoire de Physique de la Mati` ere Condens´ ee c , Laboratoire National des Champs Magn´ etiques Puls´ es, INSA, 135 avenue de Rangueil, 31077 Toulouse, France 2 Institute of Problems of Chemical Physics, RAS, Chernogolovka, MD 142432, Russian Federation 3 Institut de Ciencia de Materiales de Barcelona, Campus de la UAB, 08193 Bellaterra, Spain 4 University of Oxford, Department of Physics, Clarendon Laboratory, OX1 3PU, UK Received 22 August 2000 and Received in final form 20 December 2000 Abstract. We report on the inter-layer oscillatory conductance of the two-dimensional organic supercon- ductor (BEDO-TTF)2ReO4H2O measured in static and pulsed magnetic fields of up to 15 and 52 T, respectively. In agreement with previous in-plane studies, two Shubnikov-de Haas oscillation series linked to the two electron and the hole orbits are observed. The influence of the magnitude and orientation of the magnetic field with respect to the conducting plane is studied in the framework of the conventional two- and three-dimensional Lifshits-Kosevich (LK) model. Deviations of the data from this model are observed in low fields strongly tilted with respect to the normal to the conducting plane. In this latter case, the observed behaviour is consistent with an unexplained lowering of the cyclotron effective mass. At high magnetic field, the oscillatory data could have been compatible with the occurrence of a magnetic break- down orbit built from the hole and electron orbits. However, the increase of the cyclotron effective mass, linked to the electron orbits, as the magnetic field increases above ∼12 T is consistent with a field-induced phase transition. In the lower field range, where the conventional LK model holds, the analysis of the angle dependence of the oscillations amplitude suggests significant renormalisation of the effective Land´ e factor. PACS. 71.18.+y Fermi surface: calculations and measurements; effective mass, g factor – 74.70.Kn. Or- ganic superconductors – 72.15.Gd. Galvanomagnetic and other magnetotransport effects 1 Introduction (BEDO-TTF) 2 ReO 4 H 2 O is a quasi two-dimensional or- ganic superconductor, which is known to undergo several phase transitions. Indeed, as the temperature is lowered from room temperature, a first order phase transition, cor- responding to a reorientation of the ReO − 4 anions, takes place at around 210 K [1–4]. It is also worth to note that water molecules can be removed from crystals under vac- uum at room temperature, leading to changes in the crys- tal structure, with a characteristic time of the order of one day [5]. This phenomenon, which is reversible and frozen at lower temperature, induces significant decrease of the resistivity and suppresses the phase transition at 210 K [6]. As the temperature further decreases another a Present address: Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada b e-mail: audouard@insa-tlse.fr c UMR-CNRS 5830 phase transition towards a semimetallic state occurs at a temperature of roughly 30 K [2–4,7–9] (in the follow- ing, this phase transition will be referred to as the low temperature phase transition). Finally, the onset of the superconducting transition takes place at around 2 K. According to band structure calculations based on crystallographic data obtained at a temperature of 170 K [1], i.e. below the first order phase transition, Fermi surface (FS) of (BEDO-TTF) 2 ReO 4 H 2 O is com- posed of two electron tubes and one hole tube with a cross-sectional area of 2.5 and 5% of the first Brillouin zone (FBZ) area, respectively (see Fig. 1). Magnetoresistance data collected at low magnetic field have revealed two se- ries of Shubnikov-de Haas oscillations, referred to here- after as S 1 and S 2 . Their respective frequencies, F 1 and F 2 , correspond to orbit areas of 0.75 and 1.5% of the FBZ area [4,10–12]. Since F 1 is half of F 2 , these frequencies have been ascribed to the electron and hole orbits, re- spectively, although there is a discrepancy by a factor of more than 3 between experimental data and band struc- ture calculations. According to reflectivity data of [9], the