H c2 II (T) β"-(et) 2 SF 5 CH 2 CF 2 SO H p. =9.6 T (T c =5K) T c /u B H (T) T (mk) 200 H Plane. 56 mk

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1 Low temperature upper critical eld studies in organic superconductor -(BEDT-TTF) 2 SF 5 CH 2 CF 2 SO 3 F. Zuo, P. Zhang, X. Su, J. S. Brooks, J. A. Schlueter y, J. Mohtasham, R. W. Winter, and G. L. Gard z Department of Physics, University of Miami, Coral Gables, Florida National High Magnetic Field Laboratory, Tallahassee, Florida 3236 y Chemistry and Materials Science Divisions, Argonne National Laboratory, Argonne, Illinois 6439 z Department of Chemistry, Portland State University, Portland, Oregon 9727 Low temperature upper critical eld studies have been carried out in a new organic superconductor -(BEDT-TTF) 2 SF 5 CH 2 CF 2 SO 3 : For eld parallel to the superconducting layers, the upper critical eld determined from transport measurements exceeds the BCS Pauli limit at low temperatures. The angular dependence of the resistive transition shows that the upper critical eld can be best described by a quasi-two-dimensional model with a cusp near the eld parallel to the plane direction. PACS numbers: 74.7.Kn, Fy, 71.7.Ej, 74.8.Dm The layered organic molecular crystals (BEDT-TTF) 2 X (BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene) where X is an anion are particularly interesting because they are strongly correlated electron systems with a number of similarities to the high-t c cuprate superconductors including unconventional metallic properties and competition between antiferromagnetism and superconductivity. 1, 2 Furthermore, they are available in high purity single crystals and their low superconducting transition temperature makes experimentally accessible physical characterization of quantities such as the upper critical eld and Shubnikov-de Haas oscillations in steady magnetic elds. 3{5 In this paper we report the interlayer magnetoresistance measurements on a recently discovered organic superconductor -(BEDT-

2 F. Zuo et al. TTF) 2 SF 5 CH 2 CF 2 SO 3 at low temperatures and eld up to 18 Tesla. For eld parallel to the planes, the upper critical eld determined from the resistive transition exceeds unambiguously the BCS Pauli limiting eld. Critical eld as a function of angle shows a sharp cusp for eld near to parallel direction, consistent with two-dimensional layered structure. Single crystals of -(BEDT-TTF) 2 SF 5 CH 2 CF 2 SO 3 were synthesized by the electrocrystallization technique described elsewhere. 6 The interlayer resistance was measured with use of the four probe technique. Contact of the gold wires to the sample was made with a Dupont conducting paste or graphite paste. Typical contact resistances between the gold wire and the sample were about 1. A current of1 A was used to ensure linear I-V characteristics. The voltage was detected with a lock-in amplier at low frequencies of about 2 Hz. To avoid pressure eects due to solidication of grease, the sample was mechanically held by thin gold wires. 7 The data presented in this work were taken in a dilution refrigerator with eld up to 18 Tatthe National High Magnetic Field Laboratory at Tallahassee. Sample can be rotated in the eld and the orientation was determined by using a Hall probe at low elds. 2 H Plane β"-(et) 2 SF 5 CH 2 CF 2 SO mk mk 616 mk 468 mk 361 mk 174 mk 137 mk 14 mk 73 mk H c2 II (T) H p BCS =1.84k B T c /u B =9.6 T (T c =5K) Fig. 1 Magnetoresistance as a function of eld at dierent temperatures T (mk) Fig. 2 The temperature dependence of H c2jj. The dashed line is the BCS Pauli limit. Shown in Fig. 1isanoverlay ofinterlayer magnetoresistance as a function of eld at dierent temperatures from.72k to 73mK. The eld is applied parallel to the planes within the experimental errors of :2 o. With decreasing temperature, the resistive transition shifts toward higher eld. The resistive transition in parallel eld is typical of the low dimensional organic superconductors with a broad transition width in eld and a large positive magnetoresistance in the normal state. The inset shows a semi-log plot at 56 mk. Clearly, the resistance rises exponentially at small eld and

3 Low temperature upper critical eld studies... quasi-linearly at high eld. To analyze the data, the superconducting transition or the upper critical eld H c2 is dened at 1 level. Critical eld dened at higher levels show similar temperature dependence. Fig. 2 shows the temperature dependence of H c2 thus dened. With decreasing temperature, H c2 increases and saturates at about 11.3T for temperature below 1 mk. The base line is the BCS Pauli limit H p = 1.84 T c =9.6 T with T c = 5 K. 7 Clearly, H p dened this way is well under the measured upper critical elds T=26 mk T=26 mk H c2 (T) Normal of plane θ Field o 6 o 7 o 8 o 82 o o Fig. 3 Magnetoresistance as a function of eld at dierent angles. 88o 9 o θ (degrees) Data 3D fit 2D fit Fig. 4 The angular dependence of H c2. The lines are ts to the data. To look at the anisotropy of the upper critical eld, a systematic measurements have been taken as a function of angle ; dened between the eld direction and the normal of the plane. Plotted in Fig. 3 is an overlay of resistive transitions as a function of eld at dierent angles at a xed temperature of 26 mk. The eight curves are representative of the angular dependence from eld parallel to the plane ( = 9 o ) to nearly normal to the plane ( = 15 o ). With decreasing, the eld dependence of the resistive transition is drastically changed. For 6 o ; a well dened Subnikov de-hass (SdH) oscillation in the resistance can be observed. Details of the oscillation and its anomalous temperature and eld dependence have been published elsewhere. 8, 9 H c2 dened in at 1 level as a function of angle is shown in Fig. 4 at T = 26 mk. Clearly, H c2 decreases rapidly away from the parallel to the plane direction and is nearly saturated for 4 o. The two lines are t to the 3 dimensional anisotropic model and the 2 dimensional thin lm model. For 3D anisotropic model, the upper critical eld can be described h i 2 h i 2 by 1 Hc2 () cos() Hc2 () sin() =1;where is the upper critical eld

4 F. Zuo et al. for eld perpendicular to the plane and the is for parallel to the plane, is the angle between the eld and the normal of the plane. For a 2D 1, 11 thin lm Tinkham and Klemm has obtained the following expression: H h i c2() cos() 2 Hc2 () sin() = 1: The main dierence is that at =9 o, H c2 () for the 3D model is smooth or bell-shaped with dh c2() =. On the d other hand, H c2 () has a cusp at =9 o for the 2D case. If the upper critical eld is determined solely by coupling of the eld to the spins then it will be independent ofthe eld direction. Bulaevskii 12 considered the case where the paramagnetic limit is larger than the upper critical eld for elds perpendicular to the layers but smaller than the upper critical eld determined by orbital eects for elds parallel to the layers. The angular dependence is then given by H c2 () cos() 2 h i 2 Hc2 () = 1, versus curve which has 1;where = H p. This also results in an H c2 a cusp at =9 o. Indeed the angular dependence is dicult to distinguish from 2D model. While both ts seem reasonable at rst sight, clear deviations are seen at near =9 o. A cusp-like feature is observed experimentally, as in the 2D t, while the 3D t is rounded with a negative curvature at the top. A better agreement with the data for the 2D model at large angles is also evident with the 3D t lying systematically under the data. At 26 mk, the 2D or the Bulaevskii model 12 gives = 1.4 T and =11.9 T. The upper critical eld determined from transport measurements has been under a lot of debate in the cuprate superconductors. 13 For eld perpendicular to the planes, H c2 (T ) dened at certain fractional normal state resistance typically gives rise to a positive curvature at low temperatures. Various mechanisms have been proposed for the unconventional temperature dependence. However, it has been suggested that the H c2 thus dened corresponds to irreversibility orvortex melting line. For eld parallel to the planes, vortex moving along the plane encounters negligible pinning as there is no normal core associated with Josephson vortices. Magnetization is practically always reversible in this orientation. The resistive onset eld is clearly well separated from irreversibility eld and reects the true upper critical eld. 14 The origin for the apparently much larger H c2 than the simple BCS H P is not clear. One possibility is that the Pauli limiting eld is enhanced due to strong electron correlations, as suggested in another BEDT-TTF based organic superconductor. 15 Another possibility is that the inhomogeneous state is realized at low temperature and high eld, such that the upper critical eld in plane p for a Josephson coupled system can exceed the Pauli 16, 17 limit by a factor of 2. Careful examination is necessary to distinguish

5 Low temperature upper critical eld studies... the models. In summary, we have observed an upper critical eld determined from resistive transition considerably larger than the BCS Pauli limiting eld. The upper critical eld is saturated at low temperatures. Angular dependence of the resistive transition is consistent with the highly anisotropic nature of the title compound with a cusp-like angular dependence for eld near the plane. One of us (FZ) acknowledge useful discussion with Drs. R. H. McKenzie and J. Wosnitza. The work is supported in part by NSF grant No. DMR and the Petroleum Research Fund ACS-PRF AC5. Work at the National High Magnetic Field Laboratory was supported by NSF Cooperative Agreement No. DMR and the state of Florida. Work performed at Argonne National laboratory was supported by the U.S. Department of Energy, Oce of Basic Energy Sciences, Division of Materials Sciences, under Contract No. W ENG-38. REFERENCES 1. R. H. McKenzie, Science 278, 82 (1997). 2. H. Kino and H. Fukuyama, J. Phys. Soc. Jpn. 65, 2158 (1996). 3. T. Ishiguro, K. Yamaji, and G. Saito, Organic Superconductors, Second edition (Springer-Verlag, Berlin, 1998). 4. J. Wosnitza, Fermi Surfaces of Low Dimensional Organic Metals and Superconductors (Springer Verlag, Berlin, 1996). 5. I. J. Lee et al., Phys. Rev. Lett. 78, 3555 (1997). 6. Urs Geiser et al., J. Am. Chem. Soc. 118, 9996 (1996). 7. X. Su et al., Phys. Rev. B 59, 4376 (1999). 8. J. Wosnitza et al., Synth. Metals, 13, 2 (1999). 9. F. Zuo et al., Phys. Rev. B (in press). 1. M. Tinkham, Phys. Rev. 129, 2413 (1963); Introduction to Superconductivity, (McGraw-Hill, New York, 1985), p R. A. Klemm, A. Luther, and M. R. Beasley, Phys. Rev. B 12, 877 (1975). 12. L. N. Bulaevskii, Int. J. Mod. Phys. B 4, 1849 (199). 13. G. Blumberg, M. Kang, and M.V. Klein, Phys. Rev. Lett. 78, 2461 (1997). 14. S. Wanka et al., Phys. Rev. B 57, 384 (1998). 15. F. Zuo et al., cond-mat/ L. N. Bulaevskii, Sov. Phys. JETP 38, 634 (1974). 17. P. Fulde and R.A. Ferrell, Phys. Rev. 135, A55 (1964); A.I. Larkin and Yu.N. Ovchinnikov, Sov. Phys. JETP 2, 762 (1965).