Anisotropic superconductivity and dimensional crossover in TMET-STF 2 BF 4

Transcription

1 PHYSICAL REVIEW B, VOLUME 64, Anisotropic superconductivity and dimensional crossover in TMET-STF 2 BF 4 S. Uji, C. Terakura, and T. Terashima National Institute for Materials Science, Tsukuba, Ibaraki , Japan Y. Okano Institute for Molecular Science, Okazaki, Aichi , Japan R. Kato RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama , Japan Received 31 July 2001; published 13 November 2001 Resistance measurements have been performed to investigate the superconducting state for an organic superconductor (TMET-STF) 2 BF 4 with T c 4.1 K. The upper critical magnetic fields parallel and perpendicular to the conduction plane are determined and dimensional crossover from three dimensions 3D to 2D in the superconducting state is found at 3.5 K. The anisotropy of the critical field has a maximum at the crossover. The temperature dependence of the superconducting transition width is qualitatively understood in terms of the thermal activated flux motion and the crossover. DOI: /PhysRevB PACS number s : Ec, Kn I. INTRODUCTION Organic conductors have attracted considerable interest because of the characteristic properties relating to their low dimensionality of the electronic states. 1 Among various organic superconductors (TMET-STF) 2 BF 4, where TMET- STF is trimethylene ethylenedithio diselenadithiafulvalene Fig. 1 a, is known to have a unique crystal structure. 2 (TMET-STF) 2 BF 4 is a superconductor with T c of 4.1 K and the structure has a triclinic symmetry with a space group P1 Fig. 1 b. 3 The unit cell contains two crystallographically independent donor molecules, which form two conduction layers A and B along the a axis, respectively. The insulating BF 4 layer, parallel to the ac place, intervenes the A and B layers. Consequently, the b* axis becomes the least conducting axis. An interesting feature Fig. 1 c is that the band calculation 2 predicts two different Fermi surfaces FS s, two-dimensional 2D FS by the layer A, and onedimensional 1D FS by the layer B. This unique structure is expected to provide novel electronic properties. In order to investigate the electronic state of (TMET-STF) 2 BF 4, we have measured the resistance at high magnetic fields over a wide temperature range. We report the anisotropic superconducting properties and discuss dimensional crossover of the superconducting state. III. RESULTS Figure 2 shows the temperature dependence of the resistance at several magnetic fields along the b* axis. The inset presents the resistance in the whole temperature region at zero field. As the temperature decreases, the resistance has an upturn around 110 K shown by an arrow, and then decreases again. The superconducting transition is clearly seen at 4.1 K after a peak around 5 K. The sample was cooled from room temperature to 4.2 K for about 2 h for this ex- II. EXPERIMENT The resistance was measured by a conventional fourprobe ac technique with electric current along the least conducting b* axis. The experiments were done by using a 4 He cryostat with a superconducting magnet. Four gold wires 10 m were attached on both sides of the platelike single crystals using silver or gold paint. The temperature was controlled by a carbon glass thermometer. All the experiments were carried out at Tsukuba Magnet Laboratory, NIMS. FIG. 1. a TMET-STF molecule. b Crystal structure of (TMET-STF) 2 BF 4 from Ref. 2. There are two independently stacking TMET-STF molecules, layers A and B. c 2D FS formed by the layer A and 1D FS formed by the layer B /2001/64 21 / /$ The American Physical Society

2 UJI, TERAKURA, TERASHIMA, OKANO, AND KATO PHYSICAL REVIEW B FIG. 2. Temperature dependence of the resistance at several magnetic fields. Inset: Resistance in the whole temperature region at zero field. Arrow shows an upturn around 110 K. periment. Similar temperature dependence in the in-plane resistance has already been reported by Kato et al. 2 The upturn around 110 K is cooling rate dependent and hysteretic. This anomaly may be due to lattice distortion or glasslike transition. 4 However, x-ray experiments have not revealed any structural phase transition so far. 5 The peak around 5 K is not hysteretic and T c is insensitive to the cooling rate. For H 1 T, the superconducting transition is completely suppressed. The resistance increase observed at low temperatures is enhanced at higher fields. Figures 3 a and 3 b show the resistive transition curves for the magnetic fields perpendicular to the conduction plane (H b*) and along the a axis (H a), respectively. When the field is rotated in the ac plane, significant difference is not found in the resistive transition, suggesting that the superconducting property is almost 2D in nature. When energy dissipation due to flux motion is pronounced, which causes the broadening of the resistive transition, the determination of the upper critical field (H c2 ) becomes ambiguous. In addition, superconducting fluctuation effects on the conductivity near T c, which is generally evident for low-dimensional superconductors with high T c, make the transition broad. For convenience, we define H c2 when R/R n 0.5, where R n is the normal state resistance given by extrapolating R(H) from the higher field region. Even if H c2 is defined for R/R n 0.1 or 0.9, our conclusions do not change qualitatively. Figure 4 a shows the upper critical fields H c2 for H a and H b*. As temperature decreases, H c2 for H a has a positive curvature and then shows a trend toward saturation below 3.5 K. For H b*, no sign of the saturation is found down to 1.8 K. The overall feature of the temperature dependence is similar to other 2D organic superconductors, -(ET) 2 Cu(NCS) 2 Ref. 6 and -(ET) 2 NH 4 Hg(SCN) 4. 7 For anisotropic 3D superconductors, 8 the Ginzburg- Landau GL coherence lengths parallel and perpendicular to the conduction plane and are determined from the parallel and perpendicular upper critical fields 0 2 T T, 1 FIG. 3. Resistive transition for the magnetic fields a perpendicular to the conduction plane (H b*) and b along the a axis. 0 2 T 2, where 0 is the flux quantum. The field angle dependence of the critical field is cos 2 H 2 c2 sin 1, where is the angle of the field from the direction perpendicular to the conduction plane. The anisotropy of the critical field is defined by m /m 1/2 /, 4 where m and m are the effective masses perpendicular and parallel to the conduction plane, respectively. On the other hand, for 2D superconducting layers Josephson-coupled superconductors, the parallel upper critical field is modified as 9 2 T d/ 12, 5 where d is the superconducting layer spacing. The angular dependence of the critical field is given by

3 ANISOTROPIC SUPERCONDUCTIVITY AND... PHYSICAL REVIEW B FIG. 5. Angular dependence of the upper critical field at 2 K. Solid and dashed lines are fits for the 2D model and anisotropic 3D model, respectively. FIG. 4. a Upper critical fields H c2. b Coherence lengths for parallel and perpendicular to the conduction plane, and the anisotropy. The solid line is a guide to the eye. cos H 2 c2 sin 1. 6 There is a qualitative difference in the slope of H c2 ( ) near 90 between the above two models. When the layers are strongly coupled, i.e., is much longer than the layer spacing, the material should act as an anisotropic 3D superconductor anisotropic 3D model, and the critical fields are described by Eqs. 1 and 2. In this case, H c2 ( ) has a rounded curve for 90. When the 2D superconducting layers are separated well, but weakly coupled by Josephson tunneling effect 2D model, the critical fields should be expressed by Eqs. 2 and 5. The value of H c2 ( ) shows a cusp for 90. Figure 4 b shows the coherence length for both field directions determined by the anisotropic 3D model, and the anisotropy of the critical field. The in-plane coherence length gradually decreases in the whole temperature range with decreasing temperature, but the interplane coherence length steeply decreases and then shows a kink at 3.5 K, where reaches about 20 Å. This value 20 Å is comparable to the layer spacing, i.e., a half of the b* lattice constant ( 15 Å). 3 The anisotropy of the critical field has a maximum around 3.5 K. Even when H c2 is defined for R/R n 0.1 or 0.9, we see similar maximum behavior around 3.5 K. Figure 5 shows the angular dependence of H c2 at2k. The dotted and solid lines are the calculated curves for the anisotropic 3D model Eq. 3 and the 2D model Eq. 6, respectively. The experimental results are in better agreement with the 2D model than the anisotropic 3D model, i.e., this salt at 2 K can be modeled as a 2D superconductor. Josephson-coupled superconducting layers have been theoretically investigated, and the crossover from the 3D to 2D superconductors is expected to take place for d, 8,10 12 where the inflection of as shown in Fig. 4 a is observed. Therefore, we can conclude that the dimensional crossover of the superconducting state from 3D high-t region to 2D low-t region takes place at 3.5 K. In Figs. 3 a and 3 b, we define the transition width H as H(R/R n 0.1) H(R/R n 0.9). In Fig. 6, the transition width H is presented as a function of temperature. For H b*, H monotonically increases with decreasing temperature, but H for H a has a maximum at the dimensional crossover. This behavior will be discussed later. IV. DISCUSSION A. Temperature dependence of upper critical field A positive curvature in vs T plots has been reported for various low-dimensional superconductors, organic FIG. 6. Transition width H as a function of temperature

4 UJI, TERAKURA, TERASHIMA, OKANO, AND KATO PHYSICAL REVIEW B FIG. 7. Anisotropy of the critical field as a function of normalized temperature by T c for various 2D superconductors. The arrows indicate the dimensional crossover for (TMET-STF) 2 BF 4, 2H-TaS 2 intercalated with PY and Nb/Cu superlattice. materials, 6,7 intercalated layer compounds, 13 metal superlattices, 14 and high-t c superconducting cuprates The positive curvature in has been theoretically studied by many authors 11,22 27 and the origin is still controversial. However, it may be worthwhile to discuss the anisotropy of the critical field on the basis of the dimensional crossover. In Fig. 7, we plot as a function of temperature for various 2D superconductors. The arrows indicate the dimensional crossover for (TMET-STF) 2 BF 4, 2H-TaS 2 intercalated with pyridine PY and Nb/Cu superlattice. A typical layered material, 2H-TaS 2 intercalated with PY, has a broad maximum around T/T c 0.65, and the dimensional crossover occurs at T/T c For a conventional metal superlattice Nb/Cu, changes around T/T c 0.50, but has no maximum behavior. 14 The crossover temperature is determined to be 3.5 K (T/T c 0.60). The dimensional crossover has not been reported for the other materials. For typical organic superconductors -(ET) 2 Cu(NCS) 2 Ref. 6 and -(ET) 2 NH 4 Hg(SCN) 4, 7 monotonically decreases with decreasing temperature. In this temperature region, the superconductivity is 2D in nature, so that the dimensional crossover is probably present at a higher temperature near T c. For high-t c compounds open symbols, the data are relatively scattered and limited in high temperature regions because of too high H c Since a large number of papers have been published for the high-t c compounds, only representative data are presented. For highly anisotropic layered superconductors, the detailed temperature dependence of the upper critical fields have been theoretically investigated by Klemm et al. KLB theory. 11 They extended the Lawrence-Doniach model based on Josephson coupling between the layers and discussed the effects of the layer coupling, the pair breaking due to the Pauli paramagnetism, and the spin-orbit scattering on. The temperature dependence of strongly depends on these three parameters. For 2H-TaS 2 intercalated with PY, increases up to 20 T, which is about three times as large as the Pauli limit 28 H p 4k B T c / B. The detailed behavior of and is well reproduced by KLB theory 13 with reasonable fitting parameters. For Cu/Nb superlattices, normal metallic not insulating layer intervenes between the superconducting layers. 14 In this case, proximity effect rather than Josephson coupling effect should be considered. Although the behavior in KLB theory has a very complicated form, depending on the above three parameters, a few important features are derived from this theory. When the interlayer coupling is weak, has a pronounced increase below the crossover temperature, where becomes comparable to the layer spacing. Especially, for weak coupling and spin-orbit scattering, the increase of is the most pronounced and is expected to exceed H p as long as the pair breaking effect is small. This is the case for 2H-TaS 2 intercalated with PY. For most organic conductors, the orbital angular momentum is quenched the g factor is close to 2.00, so the spinorbit scattering effect is expected to be small. For relatively strong interlayer coupling and weak spin-orbit scattering, the rapid increase of is suppressed below the crossover. However, maximum behavior in is enhanced at the crossover temperature because the inflection in the temperature dependence of becomes evident. This is probably the case for (TMET-STF) 2 BF 4. B. Resistive transition width The effects of the superconducting fluctuation on the conductivity have been extensively studied especially for the high-t c superconductors. 29 Generally, the fluctuation effect becomes more enhanced for shorter coherence length, and is evident only near the transition temperature. Judging from the coherence length for (TMET-STF) 2 BF 4, we can conclude that the fluctuation effect is negligibly small in the temperature range except very close to T c. For (TMET-STF) 2 BF 4, is longer than the layer spacing above the crossover temperature, so that the superconducting state is 3D in nature. The flux motion causes energy dissipation, i.e., broadens the transition width, as long as the flux motion has the part perpendicular to the current. It may be reasonable to assume that the transition widths for in the whole temperature range H b* and above the crossover for H a are mainly caused by the energy dissipation due to the flux motion. Tinkham developed a model based on the flux dynamics, and gave an expression of the width and shape of the resistive transition. 24 In this model, the resistance is R/R n I 0 A 1 T/T c 3/2 /2H 2,

5 ANISOTROPIC SUPERCONDUCTIVITY AND... PHYSICAL REVIEW B FIG. 8. Normalized resistance curves calculated by Eq. 7 a with the parameter A 1.8 for H b* and b with A 60 for H a. where I 0 is the modified Bessel function, and A is constant proportional to the ratio of the zero field critical current to T c. The model predicts a positive curvature of and the temperature dependence of the transition width H (T c T) 2/3. The width H in Fig. 6 actually has the (T c T) 2/3 dependence in the whole temperature range for H b* and above the crossover for H a. In Figs. 8 a and 8 b, we plot the normalized resistance curves calculated by Eq. 7 with the single fitting parameter A 1.8 for H b* and A 60 for H a, respectively. These curves should be compared with the results in Figs. 3 a and 3 b. In spite of only single fitting parameter, the overall features seem reproduced well in the whole temperature range for H b* and above the crossover for H a. For H a, the calculated resistive transitions below the crossover are much broader than the experimental results. The reason is discussed later. The values of A give the zero field critical currents of 230 A/cm 2 for H b* and 7700 A/cm 2 for H a. For H b*, this model is not directly applicable because only small part of the flux, whose motion is perpendicular to the current, contributes to the broadening. Therefore, the obtained value of A is not reliable for H b*. The value 7700 A/cm 2 for H a, which is two orders of magnitude smaller than that of YBC, 24 may not be unresonable value. Below the crossover temperature, becomes comparable to the layer spacing. In this temperature range, (TMET-STF) 2 BF 4 is the 2D superconductor, which has the insulating layers intervening the superconducting layers. Therefore, when the field is applied parallel to the conduction plane ac plane, the normal cores of the fluxes can fit in the insulating layers and may be pinned there intrinsic flux pinning. If this pinning energy is large enough, the flux motion should be strongly suppressed and thus the transition becomes sharp as temperature decreases. This is a possible explanation of the decrease of H for H a below the crossover. In the above discussion, we have assumed that this material can be modeled as superconducting layers separated by BF 4 insulating layer, i.e. superconducting state are realized in both layers A and B. However, it may be possible that only one of two layers shows superconductivity and the other remains normal metallic state because the electronic structure is different between them as suggested by the band calculation. 2 In this case, this material should be modeled as the S-I-N-I-S-I layer structure where S, I, and N denote superconductor, insulator, and normal metal, respectively. Proximity effect in addition to Josephson coupling effect must be treated. No theoretical investigation about such system has been performed, but the dimensional crossover should takes place if the coherence length changes over the superconducting layer spacing and thus the above discussion remains valid. V. SUMMARY We have measured the resistance for the organic superconductor (TMET-STF) 2 BF 4 with T c 4.1 K and found that the dimensional crossover of the superconducting state takes place around 3.5 K. The anisotropy of the upper critical fields has a maximum at the crossover, which is qualitatively explained by KLB theory. The temperature dependence of the superconducting transition width and the maximum behavior of the transition width for H a are consistently explained in terms of Tinkham model and the crossover. ACKNOWLEDGMENTS We would like to thank H. Sawa, H. Tajima, T. Nakamura, and J. Yamaura for helpful discussions. 1 For reviews, see T. Ishiguro and K. Yamaji, Organic Superconductors Springer-Verlag, Berlin, 1990 ; J. M. Williams, J. R. Ferraro, R. J. Thorn, K. D. Carlson, U. Geiser, H. H. Wang, A. M. Kini, and M. H. Whangbo, Organic Superconductors: Synthesis, Structure, Properties, and Theory Prentice-Hall, Englewood Cliffs, NJ, R. Kato, K. Yamamoto, Y. Okano, H. Tajima, and H. Sawa, Chem. Commun. Cambridge 1997, Y. Okano, H. Sawar, S. Aonuma, and R. Kato, Chem. Lett. 1993, 1851; Synth. Met. 70, S. Kyoden, N. Hanasaki, H. Tajima, Y. Okano, and R. Kato, Synth. Met. 103, H. Sawa et al. unpublished. 6 G. Saito, H. Yamochi, T. Nakamura, T. Komatsu, T. Ishiguro, Y. Nogami, Y. Ito, H. Mori, K. Oshima, M. Nakashima, S. Uchida, H. Takagi, S. Kagoshima, and T. Osada, Synth. Met. 42,

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